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Sustainable control of Ascaris lumbricoides (worms) in a rural, disease endemic and developing community

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Title:
Sustainable control of Ascaris lumbricoides (worms) in a rural, disease endemic and developing community a systems approach
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Book
Language:
English
Creator:
Gray, Monica Annmarie
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
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Subjects

Subjects / Keywords:
Parasite
Diarrhea
Chemotherapy
Excreta reuse
Soybean
Dissertations, Academic -- Civil Engineering -- Doctoral -- USF   ( lcsh )
Genre:
non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: Parasitic infections, inadequate sanitation, and poor nutrition represent major etiologies that operate in synergy to cause some of the world's most disabling diseases. Citizens of developing nations, especially children living in rural areas, are the most affected. Current research and subsequent interventions have attempted to solve these issues using vertical interventions aimed at minimizing specific health outcomes. This approach does not consider the interaction among causes and the interrelationship between human beings and their environment. Challenges solved in this manner often fail to produce sustainable results or worse, create new problems. This project proposed the systems approach framework to address these challenges.The systems thinking dynamical modeling software, STELLA®, was used to model the conditions that promoted and/or hindered Ascaris lumbricoides and other gastrointestinal parasitic diseases in the rural developing community of Paquila, Guatemala. The interventions chosen were: administration of anti - helminthic drugs, supplying protein nutrition, and an excreta management system that allowed for effluent recycling to crop production. A new design for a Solar Latrine was proposed and the solar heating and microbial deactivation processes were modeled using the commerically available, Finite Element Method software COMSOL®. From the simulations, disease eradication was most likely to occur when at least 50% of the host population were treated every 3 months for 2 years or more with an anti - helminthic drug of 94% efficacy or better, latrine coverage and usage were at least 70%, and nutrition was provided at about 1.1 g protein per kg (human mass) per day.Given the climatic conditions in Paquila and the proposed latrine design, sustained treatement temperatures of up to 65°C were possible in the fecal materail and with a minimum of 1 month (4 months maximum) retention time, it was concluded that the resulting humanure would meet US EPA Class A Biosolids microbial requirements.
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2008.
Bibliography:
Includes bibliographical references.
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Mode of access: World Wide Web.
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System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Monica Annmarie Gray.
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Title from PDF of title page.
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Document formatted into pages; contains 234 pages.
General Note:
Includes vita.

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University of South Florida
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aleph - 002021442
oclc - 428441501
usfldc doi - E14-SFE0002576
usfldc handle - e14.2576
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SFS0026893:00001


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Sustainable Control of Ascaris Lumbricoides (Worms) in a Rural, Disease E ndemic and Developing Community: A Systems Approach b y Monica Annmarie Gray A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of C ivil and Environmental Engineering College of Engineering University of South Florida Major Professor: Noreen Poor Ph.D. Scott Campbell, Ph.D. Elaine Howes, Ph.D. Maya Trotz, Ph.D. Michael VanAuker, Ph.D Date of Approval: June 30, 2008 Keywords: parasite, diarrhea, chemotherapy, excreta reuse, soybean, nutrition, predator prey, Solar Latrines, Paquila, Gu atemala, Finite E lement Method, STELLA, COMSOL Copyright 200 8 Monica An nmarie Gray

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DEDICATION Corthia Anne Clarke: my sister and my best friend, when you left to be with God, I was very sad and even now I miss you very much At the same time I am happy because to live is Christ and to die is great gain. You were my greatest chair leader in form and I cannot imagine how awesome you are now that you are transformed and a part of my cloud of witnesses. We had many dreams, and this was one of them, so I am dedicating this work to you. I promise to honor your memory by continuing on with the others. Your unconditional love for me, taught me that it was okay to be myself, thank you! I love you honey bunny. Tell God mi sey how die. Monica Annmarie Gray: Monica, exactly eighteen years ago, in pure innocence, you expressed the desire to go to the highest level possible in education. It was only when you got to UWI, that you realized that there was further to go and so on you went. You have worked hard and sacrificed much, but have never really stopped to say, thank you to yourself So, this work is also dedicated to you, Monica Annmarie Gray. What a wonderful journey! This manuscript is a testament of your ability to dream, plan and accomplish goals thru prayer, help from family, friends, and foes, and diligent work. Since that time all those years ago, you have come up with a lot more dreams, bigger dreams and I know that there will be many more. Monica, I hope that as you embark on these new dreams, you will one day look back on this document and draw strength and the necessary courage to go forward towards those endeavors. This accomplishment while great will pass, so continue to give birth to you. Continue to grow. Continue to dream. Continue to be you. I am so proud of you, Dr. Monica Annmarie Gray.

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ACKNOWLEDGEMENTS There is no self made woman. What I have accomplished is a result of a confluence of help, encouragement, critique and love from every person that I have been so blessed to meet and associate with. While the following list is neither exhaustive nor in any real order of importance, it is my feeble attempt to express my heart felt gratitude to all who inspired me. I thank you, my God, my father for being: fai thful, loving and kind. This manuscript is evidence, proof positive that you fulfill your promises. Thank you. I acknowledge Dr. Noreen Poor, for taking me under your wings and being patient through the various changes. I thank my committee members for your advice and encouragement. To my friends and support group: Sunita Wright, Michael McIntosh, Kelly Rice Taylor, Charleen Austin, Allison Clarke, Melville McIntosh, Grace Shaw Greaves, Max Moreno, Ken Thomas, Ryan Michael, Winston Anderson, Douglas Oti, Roland Okwen and family, Tanya Jackson, Darlene Cunningham, and Erlande Omisca thank you. To my family: Sevelyn Gray (mom), Glennis Gray (dad), Oneil Gray (brother), Nadine Reid and Donna Washington (sisters), Michael Reid (brother in law ), Tam eika Reid (niece) and Michael Reid (nephew) thank you.

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NOTE TO READER The original of this document contains color that is necessary for understanding the data. The original dissertation is on file with the USF library in Tampa, Florida.

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i T ABLE OF CONTENT S LIST OF TABLES .......................................................................................................... vii LIST OF FIGURES ....................................................................................................... xi ii ABSTRACT ................................................................................................................. xv ii 1 INTRODUCTION ...................................................................................................... 1 1.1 Problem statement ...................................................................................... 1 1.2 Current approach ........................................................................................ 1 1.3 Research approach ..................................................................................... 2 1.4 Goals and overview ..................................................................................... 3 2 BACKGROUND AND SCOPE ................................................................................... 5 2.1 Introduction ................................................................................................. 5 2.2 Epidemiological models ............................................................................... 6 2.2.1 Triangle model .............................................................................. 6 2.2.2 Wheel model ................................................................................. 7 2.3 Infectious diseases ...................................................................................... 8 2.3.1 Diarrheal diseases and parasitic infections ................................. 10 2.3.2 Indicator organisms ..................................................................... 12 2.4 Ascaris lumbricoides ( Ascaris ) .................................................................. 15 2.4.1 Adult worm .................................................................................. 16 2.4.2 Ascaris eggs ............................................................................. 19 2.4.2.1 Ascaroside (lipid) layer .................................................... 20 2.4.2.2 Chitinous layer ................................................................ 21 2.4.2.3 Vitelline layer ................................................................... 21 2.4.2.4 Uterine layer .................................................................... 21 2.4.2.5 Ascaris egg structure and its persistence ....................... 22 2.5 Human Ascaris population dynamics ...................................................... 2 2

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ii 2.5.1 Age ............................................................................................. 23 2.5.2 Gender ........................................................................................ 24 2.5.3 Ethnicity ...................................................................................... 2 4 2.6 Physical environment ................................................................................ 2 5 2.6.1 Geographical location ................................................................. 2 5 2.6.2 Housing ...................................................................................... 2 6 2.6.3 Water supply ............................................................................... 2 6 2.6.4 Excreta disposal ......................................................................... 2 7 2.7 Socia l environment .................................................................................... 2 8 2.7.1 Population .................................................................................. 2 8 2.7.2 Hygiene ...................................................................................... 29 2.7.3 Preexisting infections and polyparasitism .................................... 29 2.7.4 Diet and nutrition ......................................................................... 29 2.7.5 Socio economic status ............................................................. 31 2.8 Proposing sustainable solutions ................................................................ 32 2.9 Summary and conclusions ........................................................................ 3 5 3 METHODOLOGY .................................................................................................... 3 7 3.1 Background ............................................................................................... 3 7 3.2 Objectives and subtasks ........................................................................... 4 1 3.2.1 Objective 1 .................................................................................. 4 1 3.2.2 Objective 2 .................................................................................. 4 1 3.2.3 Objective 3 .................................................................................. 4 2 3.3 Study design ............................................................................................. 4 2 3.3.1 Systems approach ...................................................................... 4 2 3.3.2 STELLA .................................................................................... 43 3.3.3 COMSOL .................................................................................. 4 5 3.4 Site selection ............................................................................................. 4 6 3.4.1 Study village ............................................................................... 4 6 3.4.2 Study population ......................................................................... 49 4 EPIDEMIOLOGICAL MODEL .................................................................................. 5 1 4.1 Introduction ............................................................................................... 5 1

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iii 4.2 Population dynamics ................................................................................. 54 4.2.1 General population dynamics ...................................................... 54 4.2.2 Predator prey dynamics ........................................................... 5 5 4.2.3 Host parasite dynamics ............................................................ 5 7 4.2.4 Deterministic host parasite dynamics ....................................... 58 4.2.4.1 Deterministic host population equations .......................... 59 4.2.4.2 Deterministic parasite population equations .................... 59 4.2.4.3 System of deterministic equations for host parasite dynamics ........................................................... 6 0 4.2.5 Stochastic host parasite population dynamics .......................... 6 0 4.2.5.1 Stochastic host population equation ................................ 6 2 4.2.5.2 Stochastic worm population equation .............................. 6 3 4.2.5.3 Stochastic egg population equation ................................. 6 6 4.2.5.4 System of stochastic equations for host parasite dynamics ........................................................... 6 7 4.2.5.5 Statistical distribution and spatial pattern of w orms among hosts ........................................................ 68 4.2.6 Simplifying host, worm and egg population dynamics ................. 7 0 4.2.6.1 Units inconsistency in Anderson and May ( 1978) ............ 7 1 4.2.6.2 Hybridized equations for host population ......................... 7 2 4.2.6.3 Hybridized equations worm population ............................ 7 3 4.2.6.4 System of hybridized equations for host parasite dynamic s ........................................................... 7 6 4.2.7 Population dynamics in terms of mean worm burden, ................................................................................... 7 6 4.2.7.1 Basic reproductive rate .................................................... 78 4.2.8 Control by chemotherapy ............................................................ 8 1 4.3 Dynamical modeling in STELLA .............................................................. 8 4 4.3.1 Step 1: Reproducing host parasite trajectories from literature .............................................................................. 8 4 4.3.1.1 Step 1 results and discussion: reproducing trajectories from literature ............................................... 86

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iv 4.3.2 Determining conditions for parasite dynamics in Paquila ........................................................................................ 87 4.3.2.1 Step 2 results and discussion: host p arasite dynamics ........................................................... 9 1 4.3.2.2 Step 2 results and discussion: varying egg survival, 2 ...................................................................... 9 1 4.3.2.3 Step 2 results and discussion: varying worm natural death rate, .................................................... 9 3 4.3.2.4 Step 2 results and discussion: varying p arasite induced host death rate, ............................. 95 4.3.2.5 Step 2 results and discussion: clumping parameter, .................................................................... 97 4.3.3 Modeling population mean with chemotherapy ........................... 99 4.3.3.1 Step 3 results and discussion: mean worm burden as a function of Ro ............................................ 101 4.3.3.2 Step 3 results and discussion: using d ifferent drugs ............................................................... 102 4.3.3.3 Step 3 results and discussion: varying proportion treated ......................................................... 1 05 4.3.3.4 Step 3 results and discussion: varying t reatment length and frequency ..................................... 1 06 4.3.3.5 Cost effectiveness of best and worst case scenarios .............................................................. 1 08 4.4 Summary and conclusions ...................................................................... 1 09 5 NUTRITION MODEL ............................................................................................. 112 5.1 Background ............................................................................................ 112 5.1.1 Protein nutrition and parasitic infections .................................... 113 5.1.2 Soybean ................................................................................... 113 5.1.3 Goals and objectives ................................................................. 115 5.2 Excreta model development .................................................................... 1 15 5.2.1 Excreta and nutrient production ................................................ 1 15 5.2.2 STELLA excreta simulation ..................................................... 1 16

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v 5.3 Soybean model development .................................................................. 117 5.3.1 Nutrient requirements of hosts .................................................. 117 5.3.2 Land requirement ...................................................................... 118 5.3.3 Nitrogen demand requirement from humanure ......................... 119 5.3.4 STELLA soybean simulation ................................................... 120 5.4 STELLA integrated population dynamics ............................................... 124 5.4.1 Chemotherapy and nutrition ...................................................... 124 5.5 Summary and conclusions ...................................................................... 126 6 SOLAR HIGH RATE LATRINE ........................................................................... 128 6.1 Background ............................................................................................. 128 6.1.1 Excreta treatment in developing countries ................................ 128 6.1.2 Solar Latrines ............................................................................ 129 6.1.3 Goals and objectives ................................................................. 130 6.2 Solar Latrine design and modeling ....................................................... 131 6.2.1 Current design description ........................................................ 131 6.2.2 New Solar Latrine design .......................................................... 132 6.2.2.1 Solar Processing Trough (SPT) capacity r equirement calculations ................................................ 137 6.2.3 Determination of the total instantaneous radiation o n vault glazing ......................................................................... 138 6.2.3.1 Solar insolation and climatic data for study village ............................................................................ 141 6.2.4 Heating and microbial inactivation model development and performance ................................................. 142 6.2.4.1 Microbial quality requirements ....................................... 142 6.2.4.2 Process criteria requirements ........................................ 1 43 6.2.5 Numerical methods ................................................................... 1 44 6.2.5.1 Heat transfer ................................................................. 1 46 6.2.5.2 Microbial inactivation ..................................................... 147 6.2.5.3 Model simulation ........................................................... 1 47 6.2.5.4 Results and discussion .................................................. 1 48 6.2.6 Summary .................................................................................. 152

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vi 6.3 STELLA modeling of solar latrine and integrated intervention ........................................................................................... 153 6.3.1 Solar Latrine intervention .......................................................... 153 6.3.1.1 Evaluating the stationary egg population assumption .................................................................... 153 6.3.1.2 Results and discussion of stationary egg population assumption .................................................. 155 6.3.1.3 Solar Latrine intervention ............................................... 155 6.3.1.4 Results and discussion of latrine intervention.................................................................... 157 6.3.2 Simultaneous Solar Latrine and chemotherapy i nterventions ............................................................................. 159 6.3.2.1 Results and discussion for simultaneous latrine and chemotherapy interventions ......................... 160 6.3.3 Integrated Solar Latrine, chemotherapy and n utrition i nterventions ................................................................ 164 6.3.3.1 Results and discussion for simultaneous Solar Latrine, chemotherapy and nutrition interventions .................................................................. 165 6.4 Summary and conclusions ................................................................... 170 7 CONCLUSIONS AND FUTURE STUDIES ........................................................... 171 7.1 Summary .............................................................................................. 1 71 7.2 Limitations and assumptions ................................................................ 172 7.3 Findings and conclusions ..................................................................... 173 7.4 Future studies ...................................................................................... 174 LIST OF REFERENCES.............................................................................................. 176 APPENDICES ............................................................................................................. 195 Appendix A ....................................................................................................... 196 Appendix B ....................................................................................................... 197 Appendix C ....................................................................................................... 216 ABOUT THE AUTHOR ...................................................................................... End Page

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vii LIST OF TABLES Table 2.1: Classification of fecal oral infectious diseases and a ssociated pathogens ............................................................................. 10 Table 3.1: Automatically generated model equations in STELLA ........................... 4 4 Table 3.2: Breakdown of the disease diagnosis at area clinics (Full table in Appendix A) ........................................................................................ 49 Table 4.1: Nomenclature and definitions used in Human Ascaris model ..................................................................................................... 53 Table 4.2: Nomenclature and definitions used in Section 4.2.1 ............................... 54 Table 4.3: Nomenclature and definitions used in Section 4.2.2 ............................... 55 Table 4.4: Nomenclature and definitions used in Sections 4.2.4.1 and 4.2.4.2 (Boccara, 2004) .......................................................................... 59 Table 4.5: Nomenclature and definitions used in Section 4.2.5 (Maynard Smith, 1974) ........................................................................... 60 Table 4.6: Nomenclature and definitions used in Section 4.2.5.1 ............................ 62 Table 4.7: Nomenclature and definitions used in Section 4.2.5.2 ............................ 63 Table 4.8: Nomenclature and definitions used i n Section 4.2.5.3 ............................ 6 6 Table 4.9: Nomenclature and definitions used in Section 4.2.5. 5 ............................ 68 Table 4.10: Nomenclature and definitions used in Anderson and May (1978) and May and Anderson ( 1978) .................................................... 71 T able 4.11: Relative lifespans of human, worm and egg populations in the lifecycle of Ascaris (CIA 2008) ..................................................... 7 4

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viii Table 4.12: Nomenclature and definitions used in Section 4.2.8 ............................... 81 Table 4.13: Proportion of host's worm burden kill by drug in a single treatment (Keiser and Utzinger, 2008) .................................................... 8 2 Table 4.14: Popul ation parameters for host model (Anderson and May, 1978) ...................................................................................................... 84 Table 4.15: Population parameters for parasite equation ( Anderson and May, 1978) ...................................................................................... 85 Table 4.16: STELLA output population values for host parasite equation from Anderson and May ( 1978) ................................................ 87 Table 4.17: Host population parameters for Paquila .................................................. 89 Table 4.18: Parasite population parameter for Paquila .............................................. 9 0 Table 4.19: Mean worm burden of Paquila in response to varying egg survival rates .......................................................................................... 9 2 Table 4.20: Mean worm burden of Paquila in response to varying worm life expectancies ..................................................................................... 94 Table 4.21: Mean worm burden of Paquila in response to varying parasite pathogencity ............................................................................. 96 Table 4.22: Host population of Paquila in response to varying parasite pathogencity ........................................................................................... 96 Table 4.23: Mean worm burden and disease prevalence in Paquila for v arying clumping parameter, ............................................................... 98 Table 4.24: Model parameters for the chemotherapy simulation ............................. 100 Table 4.25: Chemotherapy application for treatment periods of 2 and 5 years with different drugs ..................................................................... 1 04

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ix Tabl e 4.26: Mean worm burden dynamics for varying proportion of population treated ................................................................................. 106 Table 4.27: Mean worm burden dynamics for varying treatment period and frequency ...................................................................................... 108 Table 5.1: Protein and soybean requirements ....................................................... 118 Table 5.2: Soybean nutrient upta ke at 1089 kg soybeans per acre (4*103 km2) yield .................................................................................. 119 Table 5.3: Percentage soybean nitrogen demand fulfilled by humanure ................ 120 Table 5.4: Host population at different levels of protein interventions .................... 1 23 Table 5.5: Mean worm burden for different levels of protein interventions ......................................................................................... 1 2 3 Table 5.6: Host population at different levels of protein interventions with chemotherapy ............................................................................... 125 Table 5.7: Mean worm burden for different levels of protein i nterventions with chemotherapy .......................................................... 125 Table 6.1: Symbols used in developing solar tables .............................................. 138 Table 6.2: Criteria for meeting Class A requirements (U S EPA, 1992) .................. 143 Table 6.3: Nomenclature used in numerical modeling ........................................... 146 Table 6.4: COMSOL input variables .................................................................... 148 Table 6.5: Symbols used in modeling Solar Latrine intervention ........................... 153 Table 6.6: Comparison of the host population and mean worm burden dynamics in response to assumption .................................................... 155 Table 6.7: Response of mean worm burden to different rates of p opulation use in latrine intervention .................................................... 158 Table 6.8: Response o f host population to different rates of p opulation u se in latrine intervention .................................................... 159

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x Table 6.9: Response of mean worm burden to different rates of p opulation use in latrine intervention with 27% of host receiving chemotherapy ....................................................................... 161 Table 6.10: Respons e of host population to different rates of p opulation use in latrine intervention with 27% of host receiving chemotherapy ....................................................................... 162 Table 6.11: Response of mean worm burden to different rates of population use in latrine intervention with 50% of host receiving chemotherapy ....................................................................... 163 Table 6.12: Response of host population to different rates of p opulation use in latrine intervention with 50% of host receiving chemotherapy ....................................................................... 164 Table 6.13: Response of mean worm burden to different rates of population use in latrine intervention with 27% of host receiving chemotherapy and all having optimal protein supplement ........................................................................................... 166 Table 6.14: Response of host population to different rates of p opulation use in latrine intervention with 27% of host receiving chem otherapy and all having optimal protein supplement ........................................................................................... 167 T able 6.15: Response of mean worm burden to different rates of population use in latrine intervention with 50% of host receiving chemotherapy and all having optimal protein supplement ........................................................................................... 168

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xi T able 6.16: Response of host population to different rates of p opulation use in latrine intervention with 50% of host receiving chemotherapy and all having optimal protein supplement ........................................................................................... 169 Table A 1: Complete breakdown of disease diagnosis at area clinics (Boca Costa Medical Mission, 2004) .................................................... 196 Table B 1: Host parasite STELLA generated equations from Anderson and May (1978) .................................................................... 197 Table B 2: Host parasite STELLA generated equations for Paquila .................. 198 Table B 3: STELLA generated equations for population mean with chemotherapy ...................................................................................... 199 Table B 4: STELLA generated equations for excreta production .......................... 200 Table B 5: STELLA generated equations for the effect of nutrition on hosts survival ....................................................................................... 202 Table B 6: STELLA gene rated equations for the effect of nutrition and chemo on hosts survival ............................................................... 205 Table B 7: STELLA generated equations for all three populations separated ............................................................................................. 208 Table B 8: STELLA generated equations for hosts population response to latrine intervention ............................................................. 209 Table B 9: STELLA generated equations for hosts population response to latrine and chemo interventions ........................................ 211 Table B 10: STELLA generated equations for hosts population response to latrine, chemo and nutrition interventions .......................... 2 13

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xii Table C 1: Solar incidence radiation on the south facing Solar Latrine panel in Paquila, Guatemala for the months May to August .............................................................................................. 216

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xiii L IST OF FIGURES Figure 2.1: Epidemiologic triangle ( adapted from Webber and Rutala ( 2001)) .......................................................................................... 7 Figure 2.2: Modi fied wheel model (adapted from Webber and Rutala ( 2001)) ..................................................................................................... 8 Figure 2.3: Larval migration of Ascaris in human beings (Ukoli, 1984) ..................... 17 Figure 2.4: Ascaris blocking small intestine (Ukoli, 1984) ......................................... 19 Figure 2.5: Ascaris egg showing the basic layers of the shell (Ukoli, 1984) ...................................................................................................... 20 Figure 2.6: Threshold saturation theory (Shuval et al ., 1981) ................................ 3 4 Figure 3.1: Life cycle of Ascaris (Ukoli, 1984) ........................................................... 39 Figure 3.2: Systems thinking representation of host dynamics in STELLA ................................................................................................ 4 4 Figure 3.3: Finite element mesh in COMSOL for a rectangular geometry ................................................................................................ 4 5 Figure 3.4: Map of Guatemala showing village of Paquila (see star below Coatepeque) (CIA 2008) ............................................... 4 7 Figure 3.5: Breakdown of the disease diagnosis at area clinics (Boca Costa Medical Mission, 2004) ................................................................. 49 Figure 4.1: Flow chart of human Ascaris population dynamics .............................. 58 Figure 4.2: STELLA representation of host's equation ............................................ 85 Figure 4.3: STELLA representation of w orm's equation .......................................... 86

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xiv Figure 4.4: STELLA reproduction of Figure 4 from Anderson and May ( 1978) with population mean added ................................................ 87 Figure 4.5: STELLA representation of host's equation for Paquila (equation [4.43 ]) ..................................................................................... 89 Figure 4.6: STELLA representation of parasites equation for Paquila (equation [4.43]) ..................................................................................... 90 Figure 4.7: Host parasite dynamics for Paquila ..................................................... 9 1 Figure 4.8: Mean worm burden of Paquila in response to varying egg survival rates .......................................................................................... 9 3 Figure 4.9: Mean worm burden of Paquila in response to varying worm life expectancies ..................................................................................... 94 Figure 4.10: Host population of Paquila in response to varying parasite pathogencity ............................................................................. 97 Figure 4.11: Mean worm burden in Paquila for varying clumping parameter, ........................................................................................... 99 F igure 4.12: STELLA representation of chemotherapy model for equation [4.68] ..................................................................................... 100 Figure 4.13: Variation of mean worm burden when Ro = 1 ....................................... 101 Figure 4.14: Mean worm burden dynamics for different values of Ro ........................ 102 Figure 4.15: Chemotherapy application f or treatment period s of 2 and 5 years with different drugs ..................................................................... 1 0 3 Figure 4.16: Mean worm burden dynamics for treatment period of 15 years using different drugs ................................................................... 1 04 Figure 4.17: Mean worm burden dynamics for varying proportion of population treated ................................................................................. 105

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xv Figure 4.18: Mean worm burden dynamics for varying treatment period and frequency ............................................................................ 107 Figure 4.19: Comparing effectiveness of two possible treatment strategies .............................................................................................. 109 Figure 5.1: STELLA representation of excreta production ..................................... 117 Figure 5.2: Result of excreta production and processing in solar and latrine vaults ......................................................................................... 117 Figure 5.3: STELLA representation of host population illustrating effect of nutrition on hosts survival ....................................................... 121 Figure 5.4: STELLA representation of parasite population illus trating effect of nutrition on parasites survival ................................................. 121 Figure 5.5: Soybean production cycle with effect of supplying nutrient ................... 122 Figure 5.6: STELLA representation of parasite population illustrating nutrition and chemotherapy .................................................................. 124 Figure 6.1: Curre nt Solar Latrine design ................................................................. 132 Figure 6.2: Isometric cut away view of new Solar Latrine design ......................... 1 3 3 Figure 6.3: Section view thru new Solar Latrine design .......................................... 135 Figure 6.4: Detail view of Solar Processing Trough (SPT) ...................................... 135 Figure 6.5: Side view showing details of water collection system ........................... 136 Figure 6.6: Plan view of new Solar Latrine showing perforated vent p ipe i n solar vault ................................................................................. 137 Figure 6.7: Conceptual model of solar insolation on a horizontal or inclined surface .................................................................................... 139 Figure 6.8: Exce r pt form solar insolation tables for Paquila showing data f or May 1 ...................................................................................... 142

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xvi Figure 6.9: Processing time required to deactivate microorganisms at specific temperatures (Feachem et al., 1983) ................................... 144 Figure 6.10: Solar Processing Trough as modeled in COMSOL showing finite e lement s mesh .............................................................. 145 Figure 6.11: Surface plot showing temperature fronts at time t = 2900 hours .................................................................................................... 149 Figure 6.12: Temperature variation at location (0.3, 0.15) of SPT ............................ 149 Figure 6.13: Concentration of microbes at (0.3, 0.15 ) as function of time ................. 150 Figure 6.14: STELLA model of host population with all three p opulations separated .......................................................................... 153 Figure 6.15: STELLA model of parasite population with all three p opulations separated .......................................................................... 154 Figure 6.16: STELLA model of egg population with all three populations separated .......................................................................... 154 Figure 6.17: STELLA model of egg population with latrine intervention .................. 156 Figure 6.18: Infective egg, worm and host population and mean worm burden to latrine intervention ................................................................ 157

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xvii SUSTAINABLE CONTROL OF ASCARIS LUMBRICOIDES (W ORMS) IN A RURAL, DISEASE ENDEMIC AND DEVELOPING COMMUNITY: A SYSTEMS APPROACH Monica Annmarie Gray ABSTRACT Parasitic infections, inadequate sanitation, and poor nutrition represent major etiologies that operate in synergy to cause some of the worlds most disabling diseases. Citizens of developing nations, especially children living in rural areas, are the most affected. Current research and subsequent interventions have attempted to solve these issues using vertical interventions aimed at minimizing specific health outcomes. This approach does not consider the interaction among causes and the interrelationship between human beings and their environment. Challenges solved in this manner often fail to produce sustainable results or worse, create new problems. This project propose d the systems approach framework to address these challenges. The systems thinking d ynamical modeling software, STELLA, was used to model the conditions that promoted and/or hindered Ascaris lumbricoides and other gastrointestinal parasitic diseases in the rural developing community of Paquila,

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xviii Guatemala. The interventions chosen were: administration of anti helminthic drugs, supplying protein nutrition, and an excreta management system that allowed for effluent recycling to crop production. A new design for a Solar Latrine was proposed and the solar heating and microbial deactivation processes w ere modeled using the commerically available, Finite Element Method software COMSO L. From the simulations, disease eradication was most likely to occur when at least 50% of the host population were treated every 3 months for 2 years or more w ith an anti helminthic drug of 94% efficacy or better latrine coverage and usage were at least 70%, and nutrition was provided at about 1.1 g protein per kg (human mass) per day Given the climatic conditions in Paquila and the proposed latrine design, sustained treatement temperatures of up to 65oC were possible in the fecal materail and with a minimum of 1 month (4 months maximum) retention time it was concluded that the resulting humanure would meet US EPA Class A Biosolids microbial requirements.

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1 1 INTRODUCTION 1.1 Problem statement Parasitic organisms, inadequate sanitation, poor nutrition, and their synergistic interactions represent major etiologies of the worlds most disabling diseases. Over half the worlds population does not have access to improved sanitation (Jimenez et al. 2006). Intestinal parasitic infections, which are usually associated with lack of sanitation, affect an estimated 3.5 billion people worldwide ( Corrales et al ., 2006; Santiso, 1997). The poor nutritional status of those affected increases; their susceptibility to infection, duration and degree of morbidity, and likelihood of mortality ( Gendrel et al. 2003). The questions this research undertakes are: giv en that these same challenges have been successfully dealt with in developed nations, can they be sustainably solved in a rural, disease endemic, developing community, and if so, what will it take? 1.2 Current approach The traditional approach to problem so lving has been; isolation of each effect, determination of the dominant cause(s) and suggestion of vertical intervention programs, whose effectiveness are measured by quantifying specific health outcomes ( Buchholz et al ., 2007; Novick et al., 2008). Theref ore, areas endemic for the above conditions receive combinations of discipline specific programs such as medication (Watkins et al. 1996), excreta disposal (Corrales et al. 2006; Pruss and Mariotti, 2000), water (Caslake et al. 2004; Mcguigan et al. 1998; Walker et al. 2004), water and excreta disposal (Esrey et al ., 1991), personal and domestic hygiene (Curtis and Cairncross,

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2 2003a; Feachem, 1984), and school feeding programs (Hall, 2007; Stephenson et al ., 2000). The community is then evaluated for any improvement in the disease outcome of interest, such as reduction in the number of worms per person or variation in diarrheal incidence over the intervention period (Muller et al. 1989). Methods of intervention and analysis used are usually not standardized across disciplines and thus, collected data can be highly unstructured and tend to lack external validity (Fewtrell et al. 2005; Heller et al. 2003; Varghese et al. 2008). This approach has facilitated a number of innovations in individual areas such as water supply engineering, but has led to fragmentation of the public health delivery system. This outlook has persisted despite emerging evidence that problems solved in this manner often fail or worse, create new problems (Corrales et al. 2006; Espinosa et al ., 2008; Stepek et al., 2006; Sterman, 2006). 1.3 Research approach This research proposes a systems approach to solving these challenges. In this framework, the human parasite relationship is considered the axis around which social and ecologi cal conditions revolve to create and maintain parasite persistence (Buchholz et al. 2007; Holling, 2001). Parasite endemicity is viewed therefore as a self organizing collective behavior or emergent property of the host parasite environmental continuum. This by definition is a complex system (Boccara, 2004). The systems approach recognizes the inherent nonlinearity of the interactions among system agents which is accounted for when modeling the controlling mechanisms that lead to emergence (Buchholz et al. 2007; Holling, 2001). For this work, key interventions found in the literature such as improvements in sanitation and nutritional status, and mass chemotherapy are chosen and then dynamically modeled singly and concomitantly, to determine the sust ainability of either approach. This

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3 research hypothesized that, given the synergistic interaction among system variables, it will take an effective complement of interventions to sustainably resolve the issues in the system rather than the usual individual applications. This approach encourages interdisciplinary input, acknowledges that the whole is greater than the sum of its parts, provides solutions that will be more readily integrated into the communitys culture, and is therefore more likely to be sust ainable (Buchholz et al. 2007; Coreil et al., 2001). 1.4 Goals and overview The overarching aim is to model the critical components that characterize the conditions required for the sustainable control of parasitic infections in a rural, disease endemic, developing community typified by poor sanitation and nutrition. The project has two main goals: Development of STELLA models that include combinations of the human parasite relationship, mass chemotherapy, crop production, and human excreta management, and Design and then modeling in COMSOL, of a high rate Solar Latrine to determine the extent to which pathogens can be predictably deactivated in human excreta. This document has seven chapters. The current chapter summarizes the motivation for considering the problem under investigation and the specific strategies that will be undertaken to develop appropriate solutions. Chapter 2 discusses the conceptual framework adopted to limit the scope of study. Details of the methodologies to be pursued within t he proposed framework are advanced in Chapter 3. Chapter 4 presents the modeling of the host parasite populations and the impact of chemotherapeutic interventions on the mean worm burden. Soybean cultivation, human excreta recycling to crop cultivation and the impact of nutrition and chemotherapy are

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4 modeled in Chapter 5. Chapter 6 covers the design of a high rate Solar Latrine, modeling of the inactivation process and the impact of combined chemotherapy, nutrition and latrine interventions. Finally, Chapter 7 summarizes the findings, conclusions, limitations and assumptions, and future direction for this work. This project combines the disciplines and sub disciplines of Environmental and Agricultural Engineering, and Public Health.

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5 2 BACKGROUND AND SCO PE 2.1 Introduction Infectious diseases occur worldwide, however, developing countries are characterized by much higher incidence and prevalence rates (Coreil et al. 2001; Esrey et al. 1991). The etiologic agents are primarily transmitted via the fecal or al route (Tinuade et al. 2006). Compromised diets and inadequate sanitation, conditions that are more often than not indigenous to rural developing areas, operate individually and concomitantly to predispose community members to reoccurring infections ( Th ein Hlaing and Myat Lay, 1990; Venkatachalam and Patwardhan, 1953). Over time equilibrium develops between host population and infectious agents that results in disease endemicity (Bundy and Golden, 1987). About a hundred years ago these conditions epit omized the experiences of developed countries such as the United States (Burstrom et al. 2005; Spencer et al. 1967; Woldemicael, 2000). In retrospect, it was the confluence of social and ecological factors which aided and/or hindered sustainable transfer of solutions to these challenges (Curtis and Cairncross, 2003b). Similarly, for developing countries, these circumstances arise out of and are driven by concomitants of socio economic underdevelopment and an environment that facilitate the proliferation of pathogens (Santiso, 1997; Ukoli, 1984). These generating factors present unique barriers against and opportunities for sustainable resolutions (Richmond and Peterson, 2001). It is therefore important to understand the synergistic interactions among the microbes, human hosts, and their

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6 environments, in order to propose solutions that are economically viable, culturally sensitive and ecologically sustainable. 2.2 Epidemiological models Epidemiological models are conceptual models that are used to represent the environmental factors that regulate and promote host microbe interactions (Webber and Rutala, 2001). The Triangle and Wheel models for infectious diseases will be discussed here. Regardless of the form these models take, they are fundamentally b ased on the chain of infection assumption. That is, an infection is only possible if the following are in place (Oleckno, 2002): The pathogen has some reservoir outside the host where it can survive until it is able to come in contact with its definitive host, for example soil. The susceptible person is exposed to the pathogen. That is, the individual comes in contact with the microbe, such as using containers contaminated with fecal matter. There is some route and transport mechanism between the reservoir and the host through which the organism can enter the host, such as through the hosts food supply. 2.2.1 Triangle model This model proposes that disease occurs when there is an imbalance among host, agent and environmental factors (Oleckno, 2002). Host factors include personal traits and behaviors, genetic predispositions and immunologic differences which influence the probability for disease and degree of morbidity. Conditions external to host and pathogen that facilitate the disease process are considered an environmental factors and include physical, biological, social or combinations of these. Time delays

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7 associated with developmental phases, incubation time and period of infectivity play very important roles in the stability of host microbe relationship and subsequent disease endemicity within the human community. The epidemiologic triangle is illustrated below in Figure 2.1 Figure 2.1: Epidemiologic triangle (adapted from Webber and Rutala (2001)) 2.2.2 Wheel model The Wheel model has an agent host environment paradigm similar to that of the Triangle model but these factors are conceptualized differently. The hosts with their inherent characteristics form the core across which interactions with biological (including pathogens), physical and social environments take place (Webber and Rutala, 2001). This model is adopted for this research with a minor change. This Modified Wheel model has at its core the host and the microorganism with their inherent proximate

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8 characteristics which facilitate their dependence on and regulation of exchanges with the physical and social environment. This model is illustrated in Figure 2.2 : Figure 2 2 : Modified wheel model ( adapted from Webber and Rutala (2001)) 2.3 Infectious diseases The preceding discussion was advanced without formal definition and classification of infectious diseases, which will be addressed now. Moore (2002) defines a disease as any condition that creates harm to an individuals well being through a distinct pa thological process having characteristic signs and symptoms. In general, diseases may be classified according to the duration of the illness, the incidence and prevalence in a community, or by the causative agents (Nadakavukaren, 2000). An acute disease is of relatively short duration, the individual is likely to survive and the effects tend to be reversible, otherwise, the disease is said to be chronic (Moore, 2002). Endemic refers to the expected prevalence of a disease in a particular community

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9 (Oleckno, 2002). If there is an unexpected outbreak among a large number of individuals, the disease is considered epidemic (Nadakavukaren, 2000). Infectious or communicable diseases occur when microbes such as bacteria, viruses and parasites are transmitted direct ly or indirectly among human beings and/or animals (Cairncross and Feachem, 1983). It should be noted that these categories are not mutually exclusive. Therefore, an infectious disease can be acute or chronic and endemic or epidemic within an individual or community, respectively. There are many ways of categorizing communicable diseases. The conventional system is according to the pathogenic agents, for example, bacterial (Typhoid), viral (Dengue), protozoal (Malaria) and helminthic (Ascariasis) (Cairncros s and Feachem, 1983; Heymann, 2004). Strictly speaking, protozoa (unicellular) and helminthes (multi cellular animals) represents the two main categories of parasites (Stepek et al. 2006). However, this definition is normally relaxed to include bacteria, viruses and protozoa as microparasites and helminthes as macroparasites, thereby grouping all infectious pathogens under the parasitic umbrella (Anderson and May, 1992; Santiso, 1997). A more practical approach is to classify according to the mechanism of transmission, for example fecal oral, water and excreta related diseases (Cairncross and Feachem, 1983). This work focuses on infectious diseases that are transmitted via the fecal oral route and demarcate the pathogens according to microparasit es, those that cause diarrheal diseases, and macroparasites, those responsible for true parasitic infections (see Table 2 1 ).

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10 Table 2 1 : Classification of fecal oral infectious diseases and associated pathogens Categories Infection Pathogen Diarrheal Diseases Cholera Bacteria E. coli diarrhea Bacteria Shigellosis (bacillary dysentery) Bacteria Cryptosporidiosis Protozoa Giardiasis Protozoa Rotavirus diarrhea Virus Parasitic Infections Ascariasis Helminthes Trichuriasis Helminthes Hookworm Helminthes 2.3.1 Diarrheal diseases and parasitic infections Although all pathogens discussed above can cause diarrhea, these diseases are generally associated with microparasites (Dobson, 1988; Feachem, 1984; Gendrel et al. 2003). When microparasites are ingested they simultaneously develop and multiply to produce more infective stages. Infectious diarrheal diseases tend to be acute and the etiological organisms are sometimes able to confer immunity to the host after an epi sode (Dobson, 1988). Macroparasites, in contrast, tend to produce chronic, asymptomatic, debilitating diseases, and usually do not similarly reward the hosts for their trouble (Stepek et al. 2006). The organism develops into the adult life stage without r eplication (Anderson and May, 1992). The host and pathogen adapt to each in a true parasitic relationship (Markell et al ., 1986). For both types of organisms, however, infection usually occurs when transmission stages are passed into the environment with excreta and come in contact with a susceptible host.

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11 Globally, infective diarrhea is a leading cause of morbidity and mortality especially among children, ranking third of the top fatal childhood diseases (Curtis and Cairncross, 2003a; Nguyen et al. 2006). For example, in the United States there are about 4 million diarrheal related hospitalizations annually (Heymann, 2004). Worldwide, children suffer about 1.5 billion bouts annually, with a median of 2 3 episodes (Kosek et al., 2003; Meddings et al ., 2004). However, children living in developing countries that are most affected, accounting for about 90% of the 3 million deaths claimed by these diseases annually (Curtis and Cairncross, 2003a; Meddings et al. 2004; Tinuade et al. 2006). Parasitic infect ions are normally caused by metazoans (multi cellular animals) of which the most medically important are the helminthes or worms. This group includes cestodes (tapeworms), trematodes (flukes) and nematodes (roundworms) (Moore, 2002; Stepek et al. 2006). The gastrointestinal nematodes: hookworms, Trichuris trichiura and Ascaris lumbricoides are among the most prevalent and are of great public health importance ( O'Lorcain and Holland, 2000; Stephenson et al. 2000). There are more than one billion cases as sociated with each organism (Naish et al. 2004). An estimated 50% of the worlds population harbors at least one, with most infected with all three simultaneously, resulting in 60, 000 deaths annually (Glickman et al. 1999; Smith et al. 2001). These org anisms are associated with intestinal blockages, cognitive impairment and malnutrition, especially anemia (Curtale et al ., 1998; Stephenson et al ., 2000). As is the case for microparasites, children under 5 years old in developing communities are dispropor tionately affected (Saldiva et al., 1999). This demarcation between diarrheal and parasitic diseases is really an academic and clinical convenience. In reality, infectious diseases usually occur simultaneously and as a result, differential diagnosis for the causative agent of over half the diarrheal cases

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12 have not been possible (Curtis and Cairncross, 2003b). It is easy to see why this may occur. For example, during a diarrheal episode, the intestinal hurry may expel both micro and macroparasites and decidi ng which caused what becomes moot. To further complicate the issue, invading pathogenic protozoal/bacterial/viral agents may exacerbate helminth infections and vice versa (Boes and Helwigh, 2000). Since all forms of microbial intestinal inflammation tend t o have similar pathological symptoms, the definitive etiological agent is usually underdetermined (Stephenson et al. 2000). From a public health perspective it is therefore more important to consider the transmission modality in order to prescribe sustai nable interrupting intervention as opposed to trying to diagnose specific pathogens. This is the strategy adopted for this work. As discussed above, diarrheal and parasitic diseases are usually of fecal origin and the vector that mediates the transmission is excreta. Therefore, to determine if the hosts living area has been contaminated by feces, environmental samples are tested for indicator organisms that are known to be exclusively associated with excreta (Droste, 1997). 2.3.2 Indicator organisms Indicator or ganisms are widely used to determine the sanitary quality of environmental samples (Pachepsky et al. 2006). For this research, A. lumbricoides was chosen to represent infectious disease organisms because it has many qualities of an ideal indicator organis m, and is a better indicator organism for identifying fecal contamination than traditional total and fecal coliforms (Ishitani et al. 2005; Muller et al. 1989). The following is a discussion of the characteristics of an ideal indicator organism as put fo rward by Droste (1997) and Hazen (1988) and the ability of A. lumbricoides to fulfill these requirements:

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13 Indicator must be present when pathogens are present and absent when pathogens are not and must originate in the digestive tract of humans only . I n general, organisms that cause diarrheal diseases and parasitic infections are almost always transmitted by the fecal oral route (Curtis and Cairncross, 2003a; Feachem, 1984). A. lumbricoides can only survive to adulthood in human intestine, and is ther efore exclusively associated with the pathogenic source (Crompton, 1989). Further, in areas endemic for A. lumbricoides poly parasitism is usually common (Fleming et al. 2006; Quihui Cota et al. 2004; Saldiva et al. 1999). The infection transmission stages, the eggs, are passed out in feces along with all other potential pathogens making it a great clinical and environmental indicator (Muller et al ., 1989). In contrast, contemporary indicators, such as members of the coliform group, can occur in humans, animals, soils and vegetation, and thus can be present in the absence of any identifiable source of fecal pollution (Droste, 1997). In addition, these indicator bacteria may not be appropriate for the tropics, where w ater sources are of higher temperature and nutrient levels, conditions which promote extra intestinal re growth (Moe et al., 1991). Therefore, the presence of A. lumbricoides eggs is a definite confirmation of fecal contamination. The indicator should occur in high numbers and its density correlate with health hazards associated with the pollution source . Estimates of over 1014 A. lumbricoides eggs are released into the environment daily worldwide (Anderson and May, 1985). The worm burden determines t he morbidity and mortality potential of infection (Guyatt and Bundy, 1991). Fecal egg counts are indirectly correlated to the health hazard posed by A. lumbricoides The number of eggs produced by the mature female is relatively constant, so assuming a 1:1 female male ratio, the number of worms harbored by an individual can be ascertained (Hall and Holland, 2000). Once in the environment, the

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14 eggs do not reproduce and can therefore predict the prevalence and incidence rates in a community (Muller et al ., 1989). It should approach the resistance to disinfectants and environmental stress including toxic materials, of the most resistant pathogen potentially present at significant levels in the sources That is, the indicator should survive longer than path ogens in the extra intestinal environment. The eggs of A. lumbricoides are able to survive under extreme natural and treatment conditions (Arfaa, 1984). They are resistant to adverse conditions of low temperature, desiccation and strong chemicals, and ca n remain viable in soil for at least 7 years (Brownell and Nelson, 2006). However, high pH and temperatures, and direct sunlight are lethal ( Capizzi Banas and Schwartzbrod, 2001). It should be noted that because the method of detection does not include c ulturing the eggs, their inactivation does not interfere with being able to deduce fecal contamination. Should be easily, rapidly and reliably identified and enumerated, and analysis should be inexpensive Definitive diagnosis is by identifying the characteristic eggs in fecal and environmental samples. The demand for mass examination in Japan led to the development of a new stool examination procedure, the cellophane thick smear technique (Kobayashi et al., 2006). This method proved to be so simple, se nsitive and economical that it was standardized by the World Health Organization (WHO) (Ash et al. 1994). Soil samples require a different approach and a standardized method is still being developed (Gessel et al. 2004). The indicator should not itself be pathogenic A. lumbricoides is pathogenic to human beings. However a surrogate, Ascaris suum the species that infects pigs is available for use in experimental studies, since the two species are morphologically and biologically similar (Crompton et al. 1989; WHO, 1967). A. suum is easier to obtain in large numbers (Brownell and Nelson, 2006), with experiments in pigs serving as useful

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15 models to elucidate pathology of A. lumbricoides in humans (Boes and Helwigh, 2000), and shows host specificity (Anderson and May, 1985). A. suum serves as an excellent model because its life cycle in pigs is similar to A. lumbricoides in human beings, and the pig is metabolically and physiologically similar to humans as is obvious from its extensive use in biochemical research (Boes et al. 1998; Carrera et al. 1984). 2.4 Ascaris lumbricoides (Ascaris) Each infectious agent has inherent features that determine its pathogenic success. These include its size, nutrient requirement for reproduction and development, and tolerance of environmental conditions. These factors together determine how well the organism will colonize its reservoir and/or host, the number of members required to cause illness (pathogencity) and case fatality rate or virulence of the organism. For example, Ascaris is one of the most accomplished parasites and the worldwide prevalence is testament of its ability to resist insults from seasonal changes and public health interventions such as mass chemotherapy (Anderson and May, 1982). Research has shown that the longevity of the adult worm, female fecundity, the environmental resistance of the eggs and the resulting time delays in parasite production and transmission represent biological features that contribute to Ascaris endemicity (May and Anderson, 1978). While population processes such as nonlinearity between infection intensity and ho st death rates, aggregated worm distribution among community members and density dependent constraints on parasite population growth within individual hosts interact to regulate and maintain the Ascaris human relationship (Anderson and May, 1978; Cromp ton et al. 1989). The following sections will discuss these characteristics and describe how they contribute to the organisms global notoriety.

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16 2.4.1 Adult worm The adult worm causes Ascariasis, which is the most common and prevalent intestinal nematode infection worldwide (Peng et al. 2003; Sahba and Arfaa, 1967; Thein Hlaing et al. 1984). An estimated 1.5 billion persons are infected with Ascaris, resulting in approximately 10,000 deaths annually (Brownell and Nelson, 2006; Cooper et al. 2001; de Silva et al. 1997a ). Humans usually contract infection by ingesting eggs containing second or third stage larvae ( O'Lorcain and Holland, 2000; Peng et al. 2003). Triggered by specific physiologi cal factors like the presence of carbon dioxide and temperature of 38 oC, second stage larvae hatch in the walls of the duodenum (Clarke and Perry, 1988; Crompton, 2001). The larvae then embark on an amazing journey through multiple organs (see Figure 2.3 ). They first penetrate the gut wall and enter the blood circulatory system (Markell et al. 1986). They reach the liver about 6 hours after infection and undergo moulting (Heymann, 2004). Within 9 10 days the third stage larvae arrive at the lungs wher e they continue to grow (O'Lorcain and Holland, 2000). About 20 days after initial ingestion, the fourth stage larvae move up the trachea and are swallowed to reenter the small intestine (Heymann, 2004). It takes about another month for juveniles to become sexually developed adults.

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17 Figure 2 3 : Larval migration of Ascaris in human beings (Ukoli, 1984) The average lifespan of the adult worms is about a year but a maximum of 2 years is possible, which is very long for a parasite (Bethony et al. 2006). The adult worms are the largest of the intestinal nematodes of humans and most closely resemble the common garden earthworms, Lumbricus after which they are named (Markell et al. 1986). The mature females occasionally reach 49 cm in length while the males are seldom over 30 cm (Brown and Cort, 1927). The very high fecundity of the female worm is attributable to its large size (Hall and Holland, 2000). A gravid female worm have been purported to be able to lay up to 200,000 eggs per day (Arfaa, 1984)! Thus the long lifespan and high egg production rate maintain a continuously high supply of the infective stages in the environment and subsequently increase the risk of infections to susceptible host. Ascaris is dioecious and polygamous, that is, both sexes are required to produce embryonated (fertilized eggs that can develop to become infective) and males mate with multiple females respectively (Croll et al. 1982). As a result, an infected person may produce unfertilized and fertilized eggs or a mixture of both depending on mating activities of the worm population inside a given host (Peng et al. 2003). The mating

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18 probability is a function of the worm density and is very high for Ascaris because the number of worms in the host population is not normally dis tributed but tends to cluster, with the majority being harbored by a small number of persons (Boes et al. 1998; O'Lorcain and Holland, 2000). There are two major reasons for this phenomenon. These are: differences in human behavior such as eating and personal hygiene habits, and the heterogeneity in the spatial distribution of the infective eggs (Anderson, 1982). This distribution of worm numbers among hosts ensures that there is always a portion of the human population producing fertilized eggs (Schmi d and Robinson, 1972; Schulz and Kroeger, 1992). Also, for those hosts with light and moderate infections, the worms survival and fecundity are not reduced by density dependent host immunological responses as with the case of heavy infestations (Anderso n and May, 1982). Thus, maximum egg production and worm life expectancy rates are possible at lower worm burdens. During larval migration some hosts may develop pneumonitis and asthmatic attacks (Markell et al. 1986). In general, Ascariasis is clinically symptomless, but becomes less so as the intensity, number of worms per host increases (Komiya and Yanagisa, 1964; Margolis et al. 1982; Sahba and Arfaa, 1967). Light infections of worm density less than 20 worms per host usually present minor symptoms unl ess adult worms undergo uncharacteristic migration to pancreas, bile ducts, gallbladder or liver (Crompton, 1989; Hall and Holland, 2000). Children experience temporary growth retardation, which is completely reversible upon treatment and improved nutrition (d e Silva et al. 1997a). Heavy infections of worm burdens greater than 40 worms per host are likely to cause death (Hall and Holland, 2000; Thein Hlaing et al. 1987). Intestinal obstruction (see Figure 2.4 ) is the most common of the severe complicati ons associated

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19 with high worm burdens and usually results in death especially in children (de Silva et al. 1997b). Figure 2 4 : Ascaris blocking small intestine (Ukoli, 1984) The actual worm burden cannot be ascertained without anthelminthic treatment, therefore fecal egg concentration is the typical surrogate (Hall and Holland, 2000). Egg counts give an indirect measure of the intensity of infection and are expressed as eggs per gram of feces (epg). It is assumed that the greater the epg the higher the density (number of worms per unit volume of organ) of sexually mature female worms in the intestine (Margolis et al. 1982; O'Lorcain and Holland, 2000 ). Light infections are defined by less than 5000 epg, while greater 50,000 epg co nstitutes heavy worm burden (WHO, 1967). 2.4.2 Ascaris eggs Ascaris eggs are typical of those of the phylum Nematoda One of the features responsible for the success of Ascaris and other nematodes is the structure and chemical composition of the egg shell that makes it resistant to harsh environmental conditions (see Figure 2 5 ). The main function of the shell is to maintain a homeostatic environment for the developing embryo and protect it from adverse environmental conditions as it passes from the host (Wharton, 1983). The three i nner fundamental

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20 layers are formed from secretion by a fertilized oocyte (egg produced after female mates) (Wharton, 1980a). These include an inner lipid layer (ascaroside layer), a middle chitinous layer and an outer vitelline layer (Bartley et al. 1996; Wharton, 1980a). Ascaris possesses an additional outer layer, a sort of final finish that the female adds to the eggs as they leave her uterus (Foor, 1967). Figure 2 5 : Ascaris egg showing the basic layers of the shell (Ukoli, 1984) 2.4.2.1 Ascaroside (lipid) layer The chemical composition of the lipid layer in Ascaris is very unique: 75% of a special class of fats called ascarosides and 25% protein (Brownell and Nelson, 2006; Wharton, 1980a). It immediately surrounds the embryo and is most responsible for the eggs thermal resistance (ascarosides have high melting point of 82 oC) and relative impermeability to toxic substances (Bird and Mcclure, 1976; Ukoli, 1984). This layer is permeable to oxygen (developing egg is an obligate aerobe), organic solvents, and small amounts of water vapor, but is hydrophobic (Clarke and Perry, 1980; Passey and Fairbairn, 1955). The permeability of the ascaroside layer varies. For example, there is an increase in permeability during external incubation between 44 65 oC and hatching in the hosts alimentary tract (Barrett, 1976).

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21 2.4.2.2 Chitinous layer The chitinous layer is the thickest layer of the shell and is an engineering wonder. It consists of a series high tensile strength chitin microfibers dispersed in a protein coat that is able to withstand deforming forces (Wharton, 1983). The fibers are orientated at random, with the resulting arrangement resembling interconnecting ridges (like roof trusses) which provide structural strength to the eggs and protect it against mechanical damage. 2.4.2.3 Vitelline layer This layer consists of lipoprotein (f at protein) similar to the lip layer. This layer is usually thin but may become thickened as the egg becomes fully formed and is not usually visible under a light microscope (Ukoli, 1984). It is permeable to organic solvent and melts at approximately 70 oC (Fairbairn, 1957). 2.4.2.4 Uterine layer The uterine layer is composed of glycoprotein which is progressively stabilized by a quinine tanning process, analogous to cuticle hardening in insects, as the egg leaves the host (Clarke and Perry, 1988). For example, if the eggs are taken prematurely from the uterus before this final spit shine the egg shell is colorless and soluble in acids, alkalis and various enzymes and does not completely embryonate in direct sunlight (Fairbairn, 1957). However, when they ar e fully developed and are passed out in feces, the eggs are brown and insoluble in all reagents except sodium hypochlorite (Wharton, 1983). It has been hypothesized that the development of color that occurs during embryo formation (development of second st age larva) protects the egg from the harmful effects of ultraviolet, which coincidentally is the most resistant phase of the life cycle (Black et al. 1982; Fairbairn, 1957).

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22 2.4.2.5 Ascaris egg structure and its persistence The Ascaris shell is able to slow, but not completely prevent water vapor loss. The water loss rate is dependent on the surrounding relative humidity and temperature (Wharton, 1979). After exposure to above 60 65 oC for 3 days the ability of the egg shell to slow down the rate of water loss disappears and the egg collapses as a result of desiccation (Wharton, 1980b). Oxygen consumption and water loss is higher at higher temperatures, which corresponds to the higher developmental rate (Brown, 1928; Wharton, 1980a). Embryonated (infective) eggs can withstand desiccation better than unembryonated since they consume oxygen more slowly (Brown and Cort, 1927). The infective eggs are dormant and can survive in the soil for several years (Barrett, 1976; Komiya and Kobayashi, 1965). In addition, due to the average relative lifespans of the egg, worm and human populations; 2 6 weeks, 1 year and 69 years respectively, the infective stages are assumed to always be in steady state (May and Anderson, 1978). Therefore, high egg output, over a relatively l ong reproduction time, coupled with potentially high survival rates of infective stages provides a continuous stream of opportunity for disease transmission and maintenance in the hosts community. 2.5 Human Ascaris population dynamics Proximate factors are those hosts characteristics that influence the level of exposure to pathogenic organisms, susceptibility to infection, morbidity of the resulting disease and subsequent health outcome (Webber and Rutala, 2001). For instance, research shows that children under 15 years old and certain families tended to reacquire pre control worm intensities after chemotherapy stops (Crompton, 1989; Thein

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23 Hlaing et al. 1987). The following sections will discuss the interrelationship between age, gender and ethnicity, and an individuals predisposition to infection. 2.5.1 Age The hosts age is an important determining factor for disease prevalence and intensity because of its association with exposure rates and ability to resist infection. For example, the prevalence of Asc aris infection normally increase rapidly during early childhood to as much as 92% among school aged children up to 15 years old but tapers to about 65% for adults in endemic areas (Croll et al. 1982; O'Lorcain and Holland, 2000; Thein Hlaing et al. 1984 ). However, in hyper endemic areas 100% prevalence rates in adult age classes are not uncommon (Anderson, 1980b; Young et al. 2007). The trend for the variation in the number of worms per person is not so easy to describe since intensity is a function of the hosts physiology and density dependent constraints. That is, children because of their small gut size are not physically able to host as many worms as their adult counterparts ( de Silva et al. 1997b). Also, as the number of worms increase, compe tition of increasingly scarce resources hinders worm growth and establishment (Bottomley et al. 2007). Homes with small children are more likely to have yards contaminated with fecal matter (Schulz and Kroeger, 1992). The eggs of helminthes tend to follow an aggregated distribution, with high concentrations close to residences and around latrines where children tend to frequent and are therefore more exposed to the infective stages (Muller et al. 1989; Schulz and Kroeger, 1992; Thein Hlaing et al. 1984) In addition, while Ascaris infection does not impart lasting immunity to the host, it has been hypothesized that exposure to repeated infection during early life may induce some level of protection to adults (O'Lorcain and Holland, 2000). This may account in part for the relatively low infection intensities found in adult members of endemic communities. Finally, age

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24 related differences in incidence and prevalence may be due to changes in the pattern contact with infectious stages due to changes in roles and responsibilities as children grow older (Okyay et al. 2004). 2.5.2 Gender Females generally have higher disease prevalence rates than males (Crompton, 1988). These may represent differences in exposure rates that arise due to culturally defined rol es. For example a female who has to handle childrens feces on a regular basis may be more exposed to much higher concentrations of microparasites than her male counterpart that works outside the home. On the other hand, the male may be more exposed to soi l transmitted helminthes such as Ascaris if he works in fields fertilized with night soil (Curtale et al. 1998). However, these results can be confounded by age and cultural factors. For example, in an area where pica (habit of eating soil) is practic ed, boys ages 1 5 tended to have higher prevalence rates, while female rates are higher within the 11 18 age groups (Glickman et al. 1999). 2.5.3 Ethnicity Infectious disease incidence is normally higher among certain ethnic groups (Kightlinger et al. 1998)., It has been found, however that ethnicity in these cases is a proxy for socio economic status, which is a more valid explanation for the observed differences (Coreil et al. 2001). It is possible that cultural behaviors as well as genetic difference s may also create heterogeneity which causes a particular group of persons to be more susceptible to an infectious agent or enhance the pathogencity and virulence of the organism.

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25 2.6 Physical environment The physical environment plays an important role in the promotion and establishment of diseases (Stephenson et al. 2000). Ascaris as well as other infectious diseases pathogens, are usually endemic in areas that have inadequate excreta disposal, low quality water supply, poor housing, and moist and warm clim ates (Crompton et al. 1985; Santiso, 1997). For this work, these factors will be classified into two groups, namely, the natural and built environments. The natural environment is defined in the usual sense and comprises the geographical location of the community, and its resulting climate and ecology. The built environment consists of the type of housing and the sanitation infrastructure available to the community. 2.6.1 Geographical location The energy from the sun modifies, controls and determines the clima te of an area (Moore, 2002). Most developing countries are geographically located in the tropics between latitudes 35 oN and 35 oS and consequently receive the greatest amounts of solar insolation (Eggers Lura 1979 ). These regions are usually warm and humid, conditions that shorten the developmental cycles of plants and animals (Santiso, 1997). As a result, over 40% of the worlds plants and animals make the tropics their home (Nadakavukaren, 2000). Thus, while parasites can be found everywhere in the world, they are most abundant and persistent in these communities (Stromberg, 1997). For example, low prevalence rates are normally reported in countries with drier climates, since the infective stage requires a high relative humidity to survive (Crompton, 1988). Annual seasonal variations can influence the intensity of disease transmission ( Thein Hlaing et al. 1984). For example, contamination of yard soil was found to be higher during the rainy season than during the dry seasons (Schulz and Kroeger, 1992 ).

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26 In addition, changing weather conditions determine planting and harvesting seasons, consequently increasing the contact rate between community members and infective stages and resulting in very high parasite transmission (Gunawardena et al. 2004). Recy cling night soil to crops has been shown to be a major source of gastrointestinal infections, therefore, peak prevalence rates have been observed to coincide with crop cycles (Kobayashi et al. 2006). For parasites with lifespans greater than a year, as is the case for Ascaris these patterns do not significantly affect their net stability ( Thein Hlaing et al. 1984). Seasonal factors are therefore more relevant in determining when the reproduction and transmission rates are at their lowest in order t o maximize the outcomes of control measures. 2.6.2 Housing Generally, the poorer the quality of housing and community services, the more likely infectious diseases will persist resulting in higher prevalence rates (O'Lorcain and Holland, 2000; Webber and Rutala, 2001). The risk of mortality is 58% lower among children born in households with a good environment than among those born to lower quality housing conditions, even after controlling for socioeconomic variables (Woldemicael, 2000). Similar statistic s were observed for overcrowding (Schulz and Kroeger, 1992). Dirt floors can be excellent transmission loci especially for soil transmitted helminthes (Grimason et al. 2000). 2.6.3 Water supply The water supply diffusion rate (percentage of population service d by a potable water supply system) is usually very slow for developing communities (Ishitani et al. 2005). Contact with contaminated water results in up to 60 billion episodes of gastrointestinal illness annually most of whom are under age five (Caslake et al. 2004;

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27 Curtis and Cairncross, 2003a; Walker et al. 2004). Children from households that use water from rivers and lakes are 44% more likely to die from diarrheal diseases than their counterparts who have access to piped supplies, even after control ling for demographic and socio economic factors (Woldemicael, 2000). The literature is very conflicting on the benefits and health outcomes from water supply interventions (Fewtrell et al. 2005; Gasana et al. 2002; Huttly et al. 1997). For instance, Fewtrell et al. (2005) reported that increasing the amount of water, irrespective of purity has been shown to improve health. In areas where environmental fecal contamination is high, water supply improvements no matter how high the quality offer very litt le health impact (Esrey et al. 1991). Thus, while it seemed intuitive that providing water of high quality and quantity should correct these insults, this is generally not the case. 2.6.4 Excreta disposal Promiscuous defecation by children and unhygienic dispos al of their feces by adults play a more important role in determining childhood growth, morbidity and mortality, than does water quality, especially where the prevalence of diarrhea is high (Esrey et al. 1991; Jinadu et al. 2004; Schulz and Kroeger, 1992). For example, a child born to a household without toilet facility is at 64% more risk of dying from parasitic diseases than one with such amenities (Woldemicael, 2000). The type of disposal facility was found to be important, with flush toilets having a greater impact on mortality reduction than pit latrines (Esrey et al. 1991). For developing countries however, the required physical infrastructure and water resources needed for contemporary flush toilets are generally nonexistent or insufficient to meet the demands of the rapidly growing populations, rendering their application unsustainable (Langergraber and Muellegger, 2005). For example, Schulz and Kroeger ( 1992) found that if sewage

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28 system were inadequate, homes with flush toilets had yards that were equally contaminated with Ascaris eggs as those with latrine systems. The lack of proper disposal systems can therefore lead to groundwater contamination, resulting in further infections (Gannon et al. 1991). As a result only 67% of the population of developing countries have adequate facilities for excreta disposal (Palamuleni, 2002). There is however a drive to provide latrines in response to the Millennium Development Goals (Waterkeyn and Cairncross, 2005). Since the eggs of soil transmitted helminthes are not immediately infective, any kind of latrine that helps to avoid fecal contamination of the floor, yard, or fields will limit transmission, however, hygiene practices are very important (Muller et al. 1989). For example, if an earth floor l atrine is poorly maintained, it can become a focal point for disease transmission (Grimason et al. 2000). Dirty latrines may result in higher disease incidence than would occur if people were practicing widely scattered open defecatation (Cairncross and F eachem, 1983). 2.7 Social environment The human hosts, their behavioral and cultural practices represent the social environment. These are intermediate and distal factors that cause community members to be exposed to or protected from infection but do not infl uence disease occurrence directly (Coreil et al. 2001). These include host density, individual health behaviors (hygiene practices, preexisting conditions, diet and nutrition), and socio economic status. 2.7.1 Population The population of developing countries has been increasing steadily and is expected to account for more than 95% global projected growth over the next 1 2

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29 decade (Moore, 2002). While there is an exodus from rural to urban areas, it is the former that will account for the bulk of this growth (Kosek et al. 2003). The subsequent overcrowding can lead to conditions favorable for the efficient transmission of pathogens, resulting in higher intensity infections among households with more members ( O'Lorcain and Holland, 2000). 2.7.2 Hygiene From the above discussions, it can be concluded that it is not enough to construct affordable latrines and provide clean water, but hygiene education interventions is also essential for success. Traditionally hygiene interventions are typically of two types, those focusing on health and hygiene education, and those promoting hand washing with soap and water (Fewtrell et al. 2005; Jinadu et al. 2004). Human activities are not always in their best interest. For example cultural beliefs that consider fecal matter fro m children to be innocuous can cause community members to be nonchalant during handling, which can lead to higher infection risks especially in areas where diarrheal diseases are prevalent (Yeager et al. 1999). Therefore behavioral interventions are cruci al to the success of control programs (Webber and Rutala, 2001). 2.7.3 Preexisting infections and polyparasitism Conditions that encourage Ascaris endemicity also support many other gastrointestinal parasites. Thus, where diarrheal diseases are endemic, polypar asitism is usually also common (Keiser and Utzinger, 2008). 2.7.4 Diet and nutrition Specific dietary habits can increase the hosts risk for infection or be protective against disease. For example, in areas where geophagia (soil eating) is culturally

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30 practi ced, participants are at higher risk of ingesting soil dwelling pathogenic organisms and a normally found to have infection intensities above community average (Geissler et al. 1998; Glickman et al. 1999; Young et al. 2007). Eating uncooked fruits and vegetables that have been fertilized with human excreta may also lead to higher disease incidence (Feachem et al. 1983). One of the most important factors that determines the magnitude of morbidity and likelihood of mortality from infectious diseases in endemic areas is the nutritional status of the host (Boes and Helwigh, 2000). Under nutrition at any age can compromise the host defense systems (Stephenson et al. 2000). However, young children and pregnant women are particularly vulnerable because of t heir inherently high nutritional demand (Bundy and Golden, 1987). Further, the additional metabolic requirements from the pathogens put them in less favorable health conditions to resist other insults (Bundy and Golden, 1987). One third of young children in developing countries experience linear growth retardation or stunting in early childhood as a result of chronic undernutrition (Morgan, 2005; Saldiva et al. 1999). Ascariasis and diarrhea are known to play a major role in the etiology of childhood malnutrition (O'Lorcain and Holland, 2000). This is because nutritional, especially protein energy, deficiencies often cause suppression of immune response, which can lead to unrestrained establishment and increased survival of parasites (Gendrel et al. 2 003; Stephenson et al. 2000). For example children with average burden of 26 worms were reported to have lost about 4 g of protein daily intake due to parasitic interference with the digestive process (Stephenson et al. 2000; WHO, 1967). Periodic dewormi ng of Ascaris infected pre school children have been shown to improved growth in areas where protein energy malnutrition is common (Stephenson, 1980).

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31 Other nutrients of special importance include fat, carbohydrate, vitamin A and iron (Stephenson, 1980). Fecal fat excretion has been shown to decrease after deworming (Macinko et al. 2006). The typical diet in developing countries derives 75% of total calorie intake from carbohydrates and so any interference with absorption can have serious consequence s (Carrera et al. 1984). Reduced absorption of vitamin A have been associated with protein deficiencies (Stephenson, 1980; Woodruff and Wright, 1984). However, the malnutrition infection interaction is not confined to a linear, one way causal relations hip. That is, nutritional deficiencies tend to promote and intensify infections as well as infections may promote nutritional imbalances due to increased energy requirements to fight them (Boes and Helwigh, 2000). On the other hand, as the host becomes mor e malnourished, worm burden and fecundity may be reduced as nutrients become increasingly unavailable (Bundy and Golden, 1987). Parasitic infections can and often do cause decreased food intake (Saldiva et al. 1999). Thus, infectious diseases may affect nutritional status as well as pre existing nutritional status may increase the risk of and/or exacerbate illness (Stephenson et al. 2000). 2.7.5 Socio economic status Socio economic factors represent the availability of resources that promote life, health and wellbeing. These include but are not limited to, household and community economic status, type of residences and physical infrastructure, health care availability, mothers education, and political stability (Woldemicael, 2000). The social capacity of the community is also important and includes the ability of members to come together and solve common challenges (Coreil et al. 2001). Throughout history and in nearly every country, the poor has been identified as the population most at risk for adverse health outcomes (Morgan, 2005). There is usually

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32 a culture of entrepreneurship embedded in the social heritage of peoples of developing countries (Brentlinger et al. 2007; Ukoli, 1984). According to the Global Entrepreneurship Monitoring (GEM) report, which measures what fraction of a countrys adult population that has attempted or started a business, developing nations usually have the highest numbers. The rationale proposed has been that individuals are usually forced to seek their own employment because of high unemployment rates or the contradiction between industry requirements and cultural outlook (Johansson, 2008). Control programs, where they have been mounted, have underestimated the socio cultural and human behavioral factors which play a part in enhancing transmission of infection (Brentlinger et al. 2007). In addition they have underutilized an important resource that is virtually a staple in developing communities, that is, social capacity (Coreil et al. 2001). Social networks are usu ally extensive and are reminiscent of small towns in developed countries. 2.8 Proposing sustainable solutions An individuals health status is a dynamic equilibrium among host factors, characteristics of the infectious agent, and environmental influences occurring over time (Webber and Rutala, 2001). Parasitic diseases are prevalent in the tropics because of the c ombined effects of ecological and climatic factors, dietary and sanitation constraints, human behavioral and cultural practices, population density, and socio economic conditions. The warm and humid climates of these areas facilitate faster development and proliferation of large numbers infectious agents (Ukoli, 1984). The climatic conditions also encourage human behavior that increases contact between infectious stages and susceptible individuals. Ascaris was chosen to represent these pathogens because i t has several characteristics of an ideal indicator organism (Muller et al. 1989; Schulz and Kroeger, 1992).

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33 Ascaris, as well as other infectious disease pathogens are usually endemic in areas of developing countries that have high population densities and low socio economic status (Crompton et al. 1985; Santiso, 1997). However, population density impacts disease occurrence more on a community rather than a national level and is usually surrogated by low socio economic status. This is evidence by the fact that some of the richest countries have the highest population density without the associated infectious disease endemicity (Johansson, 2008). The economic wealth that fulfills the physical needs of the community is a protective factor against disease transmission, however, socio cultural practices can have more influence on the occurrence and spread of parasitic diseases (Ukoli, 1984). Poor nutrition is known to interfere with the ability of children to benefit from educational programs which can lead to other socio economic status issues and is a major cause of morbidity and death (United Nations, 1991). Controlling any enteric parasite means dealing with at least two populations, the pathogen infesting the host and the infective stages in the environment. Providing nutritional supplement and mass chemotherapy may help to decrease morbidity and mortality rates within the host population but it does nothing to stop the transmission stages. There are disagreements in the literature about the bene fits of sanitation interventions, similar to those of the results of water improvement studies. In fact, a number of researches have evidenced the failure of improved safe water supply and excreta disposal to sustainably combat infectious diseases (Schulz and Kroeger, 1992). That is, improvements in sanitation facilities may significantly reduce prevalence of infection, however, morbidity problems may linger (Asaolu et al. 2002). The threshold saturation theory (see Figure 2.6 ) has been used to explain t his counterintuitive finding (Shuval et al. 1981). The theory states that in communities with very low socio

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34 economic status, the health of members will not respond to any improvements in the sanitation infrastructure, resulting in an initial lag phase or threshold. The rationale is that there are so many transmission routes for disease and the personal hygiene and nutritional status of members are so low that these interventions will not succeed in eliminating enough to have a significant impact. As individuals and communitys socio economic status increases the community is able to respond to improvements in the physical environment, but at some point further improvements show diminishing return on investment (Asaolu et al. 2002). Figure 2 6 : Thr eshold saturation theory (Shuval et al. 1981) In addition to the probability of failure to decrease disease morbidity and mortality, simply providing latrines or drilling wells does not increase the social or economic capital of the community. That is, even if members help in construction, the process does not strengthen the social structure and encourage the community to solve its own problem. A simple latrine does not make use of a valuable resource that can be

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35 recycled to crop production. With the hi gh economic and ecological cost of chemical fertilizers, recycling excreta will in a single move, improve both nutritional and fiscal status. This type of integrated approach has been shown to work (Brentlinger et al. 2007; Checkley et al. 2004; Jensen e t al. 2005; Meddings et al. 2004; Root, 2001; Shuval et al. 1981; WHO, 2002). For example, in malaria eradication programs it has been found that bed net programs are more sustainable when distribution is coordinated through local shopkeepers (Brentling er et al. 2007; Goodman et al. 2007). Motivated by a business opportunity, shopkeepers were encouraged to keep up supply, thus health promotion was channeled through a social structure that was already well integrated into the local community (Foster, 1991; Goodman et al. 2006). The synergistic interactions among the factors discussed above imply that interventions targeting any one social service are likely to be wasted unless comprehensive and coordinated actions are undertaken. In addition, education and training programs are also essential in improving nutritional practices, especially in instruction of low income women on the value of breast feeding and on the preparation of balanced and uncontaminated food for infants and children (United Nation s, 1991). 2.9 Summary and conclusions History has shown that parasitic diseases, inadequate sanitation and poor nutrition with their associated morbidity and mortality can be resolved. The question that remains therefore is whether sustainable solutions can be found for these challenges in a rural and developing community setting. The Modified Wheel epidemiological model was employed as a framework to elucidate the controlling mechanisms in the host parasite relationship that lead to endemicity and the key interventions found in the

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36 literature that have been shown to have some measure of success in controlling adverse effects. The overarching goal of this dissertation is to propose economically viable, culturally sensitive and ecologically sustainable solutions for controlling fecal oral transmitted infectious diseases in a rural and developing community. By definition, sustainability is development that efficiently utilizes present resources to fulfill current needs, while facilitating the ability of future generations to meet their own needs (Wright, 2002). An implicit deduction is that for every challenge there are available resources and, if wisely applied, such solutions can be integrated within the social fabric of a community, such that future generati ons will be able to independently maintain them. To satisfy these criteria, disease control must be integrated with other aspects of land use and development, improvement in agricultural practice, and education. That is, a broad spectrum resource improv ement program which will generate the capacity in the people to seek solutions to future problems. This research is proposing a systems approach that will establish links among the various aspects of ecology, engineering and agriculture, human behavior, education and culture for sustainably breaking the host parasite environment continuum.

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37 3 METHODOLOGY 3.1 Background There are at least twenty species of pathogenic microorganisms that are found exclusively in the human intestines and are passed out with fec es to contaminate the environment to cause diarrhea and parasitic infections in others or the host (Curtis and Cairncross, 2003a). These microbes have a variety of developmental and transmission stages, but all have similar biological characteristics that determine the persistence of their relationship with the host. Ascaris plays dual roles of clinical as well as environmental indicator organism (Muller et al. 1989). Medically, the presence of eggs in fecal samples is indicative of an established worm population (Peng et al. 2003). In addition, because Ascaris tend to occur simultaneously with other infectious agents, its presence may point to poly parasitism (Fleming et al. 2006). Eggs found in environmental samples such as yard soil definitively v erify fecal contamination (Uga et al. 1995) While the mode of transmission (eggs, larvae or arthropod vector), life cycle (direct versus indirect), and propagation (cyclo developmental or cyclo propagative) for Ascaris do not mirror exactly what occu rs with all gastrointestinal infectious disease pathogens, the conditions under which these organisms and their transmission stages exist and flourish, and their routes of infection are similar (Curtis and Cairncross, 2003a). Thus, a fundamental assumption of this research project is that creating the conditions that sustainably control Ascaris will in effect facilitate the suppression of other infectious diseases. This is in part due to the fact that compared to parasitic infections caused by

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38 viruses and bacteria, Ascaris is very resistant to control strategies (Anderson and May, 1982). Research has shown that the stability of any microbial population depends on the life cycle stages that is most affected by density constraints, analogous to a rate deter mining step in a chemical reaction (Churcher et al. 2006) The first step towards proposing sustainable solutions to the challenges described in Chapter 1 is therefore to detail the life cycle of Ascaris. Ascaris epitomizes a macroparasite with a direct life cycle (see Figure 3 1 ) (Crompton, 2001). That is, the organism does not use an intermediate host in its developmental cycle (Heymann, 2004). Their eggs undergo obligatory development in the soil and are therefore referred to as soil transmitted helm inthes (Cairncross and Feachem, 1983; Curtale et al. 1998). While in the soil, fertilized eggs moult to second stage larva, which is the infective stage (Brown, 1928). This process takes about 2 4 weeks depending on the environmental conditions such as temperature, moisture and solar insolation (Croll et al. 1982). When infective eggs are ingested, they hatch and develop while journeying through the body as described in Section 2.4.1, a process that takes about 2 months (Murrell et al. 1997). The sexually mature worms mate and consequently produce eggs that pass out into the environment.

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39 Figure 3 1 : Life cycle of Ascaris (Ukoli, 1984) Based on the density dependent constraint principle mentioned above, the establishment of the worm population and egg production are the rate determining steps in the infection cycle (Churcher et al. 2006). However, the longevity of the eggs in the soil provides a continual source of reinfection that can dominate the influence of those processes in determining di sease entrenchment (Anderson and May, 1992; Churcher et al. 2006). Therefore the proposed strategy is to interrupt the developmental cycle of the pathogenic organisms with interventions that target these leverage points (Webber and Rutala, 2001). This inc ludes periodic mass treatment, crop production, hygiene education, and inactivating eggs in soil and excreta (Komiya and Kunii, 1964). Worm establishment is a function of the hosts immune resistance to the invading parasite (Churcher et al. 2006). Thus, providing adequate protein energy will assist the immune system in suppressing the number of larvae that survive the journey through the body and ultimately reduce worm density (Bradley and Jackson, 2004; King et al. 2005). Since the worms cannot surviv e outside the host, expelling them by mass chemotherapeutic treatment will instantaneously remove the entire populations, offering

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40 the hosts immediate relief from disease symptoms (Watkins and Pollitt, 1996). However, because there is a population of eggs still in the environment reinfection will occur. Research has shown that after one mass chemotherapy intervention pre control prevalence and intensity levels were achieved within 1 year and egg production restarted in as little as 2 3 months (Kightling er et al. 1995; Soeripto, 1991; Thein Hlaing et al. 1987). Therefore repeated applications with concurrent sanitation and hygiene programs are necessary (Arfaa, 1984). The three main transmission routes for infective eggs are from feces contaminated surfaces and materials, from fields that have been fertilized with night soil to workers and by consumption of uncooked plants grown in these fields (Feachem et al. 1983). Providing water and training in hygiene practices in washing surfaces, container s and hands would likely eliminate the first route. Inactivating the eggs in excreta before it is used in crop production will over time reduce the other two transmission routes. Therefore the excreta needs to be safely contained to prevent further environmental contamination and then treated to obtain a parasite free product. In summary, mass chemotherapy, Solar Latrine with treatment and crop production with treated excreta are proposed. Individual and integrated simulations of these interventions are being used to explore the minimum length of time needed to reduce the risk of reinfection in the community. Mass chemotherapy offers immediate relief to community members and stops the flow of eggs into the soil reservoir. Since there is a store of infective eggs already in the soil it is expected that reinfection is going to occur. Therefore mass chemotherapy will be repeated ad hoc. The Solar Latrine will require the addition of soil which more than likely will come from the area surrounding the homes that is known to have the highest concentrations of eggs. Infective eggs will therefore be deactivated over time. Recycling treated excreta to soybean cultivation will

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41 provide protein rich crops to strengthen the hosts immune system (defenses) and thus enable them to resist future infections. In addition this will improve soil structure and fertility. Hygiene education is also essential to interrupt the fecal oral transmission routes. 3.2 Objectives and subtasks As discussed in Chapter 1 above, the overall aim is to model the conditions that are required to eradicate parasitic infection in order to compare the sustainability of the systems approach versus traditional vertical intervention approach. This is will be accomplished through a variety of objectives and s ubtasks as listed below. 3.2.1 Objective 1 Dynamical modeling of systems components in STELLA: Model human parasite population dynamics, Model parasite infection dynamics in response to mass chemotherapy control measures, and Model crop production using t reated humanure as a form of excreta management. 3.2.2 Objective 2 Develop integrated models : Develop nutrition, sanitation and mass chemotherapy strategies, Determine the best complement to sustainably control infectious diseases in community.

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42 3.2.3 Objective 3 Design and model a high rate Solar Latrine: Design a Solar Latrine that treats fecal material using energy from the sun to deactivate microbes by increasing temperature of the product, Calculate hourly solar insolation for the selected site using EXCE L Using data from solar tables and acquired average weather conditions, model the heating, and deactivation processes in COMSOL to determine the extent to which pathogens can be predictably deactivated in human excreta. 3.3 Study design 3.3.1 Systems approach A collection of components that work together to produce a unique quality is called a system (Fisher, 2005). Systems theory is based on the assumption that all types of systems have common characteristics regardless of their unique internal structures (Skyt tner, 2005). That is, communities characterized by parasite endemicity have similar sets of interdependent controlling processes even if the behavior of individual hosts and the structure of the specific locality are different. Systems approach consists of systems thinking and systems dynamics. Systems thinking is a methodology used to identify and solve phenomena operating in and arising out of a larger environment (Shiflet and Shiflet, 2006). The interrelationships are conceptualized using causal loop mapping and parts integration techniques as opposed to the traditional linear cause effect isolation approach (Richmond and Peterson, 2001). Systems dynamics is using computer simulations to model the global dynamics of the systems components to understand rather than predict

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43 the behavior of the system over time (Ford, 1999; Shiflet and Shiflet, 2006). This approach is considered more realistic and valuable because it can reveal emergent properties that result from nonlinear interactions among systems com ponents and subsequent feedback mechanisms, which are not readily obvious during piecewise investigations. Thus, systems thinking and dynamical modeling can explore critical leverage points, effectiveness, as well as the unintended and counterintuitive eff ects of public health interventions. Considering the lifecycle of Ascaris, the interactions occurring among the host microbe environment are very complicated, however this characteristic complexity emerges from a small number of controlling mechanisms s uch as biological and population processes described in Section 2.4 above (Boccara, 2004; Holling, 2001). For this research the key factors found in literature that adequately describe the structures that hinder or promote parasite endemicity are modeled s eparately and simultaneously in STELLA to identify and understand the general dynamics of the system. From these simulations, an optimal complement of interventions can be derived that will successfully and sustainably control infectious disease. Once acc omplished, the successful solutions can be applied across different communities with similar systems emergence attributes or tailored to facilitate disparities unique to a given location (Novick et al ., 2008). 3.3.2 STELLA The STELLA software is specifically designed for modeling the dynamics of highly interdependent systems (Hannon and Ruth, 2001). The software allows one to represent complex systems conceptually through a series of simple building blocks that represent the controlling processes operating to produce an emergent behavior (Ford, 1999). An icon based graphical interface in the form of Stock and Flow diagrams is used to represent the concepts of systems thinking. The model equations are

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44 automatically generated and made accessible beneath the m odel layer (see Figure 3.2 and T able 3 1 ). All generated equations for the STELLA models presented are made available in the Appendix B. Figure 3 2 : Systems thinking representation of host dynamics in STELLA Table 3 1 : Automatically generated model equations in STELLA Hosts(t) = Hosts(t dt) + (births natural_deaths death_by_parasites) dt INIT Hosts = 150 {host} INFLOWS: births = growth_rate Hosts {host/time} OUTFLOWS: natural_deaths = growth_rate Hosts Hosts / carrying_capacity {host/time} death_by_parasites = Parasites host_death_rate_by_parasites {host/time} carrying_capacity = 200 {host} growth_rate = host_birth_rate host_natural_death_rate {host/host/time} host_birth_rate = 3 {1/time} host_death_rate_by_parasites = 0.5 { host/parasite/time} host_natural_death_rate = 1 {1/time} Hosts births host birth rate natural deaths death by parasites host natural death rate host death rate by parasites Parasites carrying capacity growth rate

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45 3.3.3 COMSOL The microbial inactivation in the Solar Latrine was modeled using the multi physics, Finite Element Method (FEM) software COMSOL. The multi physics capability of COMSOL means that it can handle partial differential equations describing different physical processes such as those governing heat transfer, evaporation and microbial inactivation and is able to solve them simultaneously over a given domain or geometry. In the FEM the partial differential equation is transformed into an integral expression and, the domain and boundary conditions are divided into elements resulting in a mesh (see Figure 3 3 ) with a number of nodal points (Hughes, 2000; Zienkiewicz, 1983). Numerical approximati on of the integral provides an approximate solution over each finite element and its contribution summed at each node (Hughes, 2000). The advantages of FEM are its ability to handle any arbitrary geometry, general, constant or varying boundary conditions and heterogeneous materials (Akin, 1994). Figure 3 3 : Finite element mesh in COMSOL for a rectangular geometry

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46 3.4 Site selection The following criteria were used to select the country and ultimately the study community: Human excreta and/or sludge reuse in agriculture, Currently cultivated or have the ability to grow soybean, Infection disease endemicity, Poor sanitation, and Practice agricultural sun drying. 3.4.1 Study village The village of Paquila, Guatemala was chosen as the model site because it was cons idered representative of this region and the above criteria. It is about 10 km2 and located about 1 hours south of QuetzaItenango and 2 hours west of the capital, Guatemala City (see Figure 3.4 ). Geographically, Guatemala is located in Central America and is bordered by El Salvador, Honduras, Belize and Mexico. The climate is predominantly tropical with very little temperature variation throughout the year. The rainy season is from May to October with average annual rainfall of about 1,300 mm. It is the most densely populated country in Central America with about 75% of the population living in rural areas (CIA, 2008).

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47 Figure 3 4 : Map of Guatemala showing village of Paquila (see star below Coatepeque) (CIA 2008) After the 1976 earthquake, several excreta disposal programs were undertaken to bring latrines to rural areas (Strauss et al. 1990). At first simple latrines were installed, however, they were socially rejected because they were difficult to construct on rocky underground and in areas with high groundwater table. The pits would flood during the raining season, the contents would smell and attract flies. The community members went back to open defecation. Following this initial failure, a double vault latrine with urine separation call Dry Alkaline Fertilizer Family (DAFF) was introduced and recycling latrine contents was encouraged (Plenty, 2008). Also in 1976, Plenty International, a non governmental organization based in Tennessee went to Guatemala to help with the rebuilding efforts. In an effort to sustainably reduce malnutrition, they started a soybean farm extension program that provided technical and financial assistance for economically disadvantaged families and

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48 organizations who were interested in learning how to grow soybeans and other dry legumes in rotation with traditional staples, improve family nutrition and food security and, increase annual cash income. This led to the construction of a Mayan owned and operated soy dairy (Alimentos San Bartolo) in the village of San Bartolo, Solola, about 50 miles north of Paquila. Today this facility is managed by the Mayan community development organization, ADIBE, employs eight people and produces a reliable and inexpensive source of protein in the form of soy milk, ice cream, tofu and other products for sale locally and nationally (Plenty, 2008). There is no specific development program for housing, road construction and environmental sanitation being carried out in the area. In February of 2003 two Christian missionaries, Jim and Dianne Thompson, moved from Asheville, North Carolina and started a base clinic in Paquila (Boca Costa Medical Mission, 2004). Before 2004, only about half the village had access to clean water. An extensive water project by the Thompsons in the summer of 2004 brought access to piped water the rest of the community. Today, there are about four other satellite clinics that serve over 45 villages in The Boca Costa de Solola area of Southwestern Guatemala and a developing referral relationship with a hospital of fering 24 hours emergency care 45 minutes away in Mazantenango. Over 30% of the patients are seen for gastrointestinal parasitic infections with the highest proportion suffering with intestinal worms (see Figure 3.5 and Table 3.2 ).

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49 Figure 3 5 : Breakdown of the disease diagnosis at area clinics (Boca Costa Medical Mission, 2004) Table 3 2 : Breakdown of the disease diagnosis at area clinics (Full table in Appendix A) Number code Disease diagnosis Percentage of patients diagnosed 11 Bacterial dysentery 1.40 22 Skin infection (fungal) 4.50 23 Gastritis 5.00 24 Amebic dysentery / Giardia 9.00 25 Other: general pain, vitamins, only 10.83 26 Respiratory infections 16.64 27 Intestinal worms 20.24 3.4.2 Study population The population of Paquila is about 3500 indigenous Mayan. The primary language is Quiche with Spanish secondary. It has one of the highest infant and maternal mortality rates, with 50% of infants dying before age 5. Paquila is a typical agricultural villag e and relatively isolated, with an extended family unit structure. The people of the villages are mostly subsistence farmers who grow coffee, banana, sugar 0 5 10 15 20 25 Percentage of patients diagnosedDisease diagnosis

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50 cane, corn, rice, root and vegetable crops, and rubber. Children usually start working in the fields by age 5 years and are encouraged to farm a small plot of land next to the main field of their household by age 14. The typical house is a single room hut that is primarily used for sleeping. It is constructed of mud wall, thatched roof with dirt floor. T he preceding information was acquired from the Boca Costa Missions website or through personal communication with the Thompsons. Due to the relative isolation of the community, infections can be assumed to occur only by intra community transfers and not from the imported infective stages. Sun drying of agricultural products and brick mean that relevant skills needed to utilize a proposed Solar Latrine are in place. The clinic ensures primary health care and has helped to engender the trust of the communi ty. The successful soybean project in the neighboring community creates potential for inter community transfer of technology. Villages like Paquila are prime candidates for successful and sustainable control and eradication of Ascariasis and other infect ious disease (Arfaa, 1984; Komiya and Kunii, 1964; Thein Hlaing et al. 1984).

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51 4 EPIDEMIOLOGICAL MODE L 4.1 Introduction This chapter covers the host parasite relationship that formed the core of the Modified Wheel Epidemiological conceptual framework discussed in Section 2.2.2. Moore (2002) agreed with this strategy of first establishing population dynamics before attempting to propose solutions to environmental health challenges. That is, it is important to first determine the reproduction and transmission rates, life expectancy, and pathogencity of the parasite within the human community before suitable control methods can be prescribed (Boes and Helwigh, 2000). To review, the establishment of a parasite in a community and its subsequent entrenchm ent result from a number of inherent biological and population processes that are detailed by organisms lifecycle (see Section 3.1). While endemicity emerges from the confluence of host parasite environment interactions, it is the proximate factors su ch as, female fecundity and longevity, environmental resistance of infective stages, density dependent constraints on parasite population, and nonlinearity associated with parasite induced host deaths that directly influence the stability of the host p arasite relationship (Anderson and May, 1982). The overall goal is to simulate population dynamics and to determine how to prevent, reduce or eliminate infection hazard, morbidity and mortality to community members. The specific objectives include: Model the host parasite dynamics, Determine the conditions that influence stability, and

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52 Determine the effects of chemotherapeutic control measures on parasite endemicity. Consequently, this chapter has three main sections. The chapter begins with a review of general population dynamics that occur in nature with special attention to predator prey interactions on which the proposed model is based. The model is then translated into STELLA to determine stability and optimal leverage points for interventions. Finally, a model simulating mean worm burden in response to mass chemotherapy is developed to determine eradication requirements. Parasite population biology and ecology have been extensively modeled (Anderson and May, 1978; Bradley and May, 1978; Churcher et al. 2006; Crofton, 1971; Dobson, 1988; Macdonald, 1961; Pielou, 1969; White and Grenfell, 1997). However, there is a lack of conformity in the use of notations, their definitions and dimensions. Through out the literature, equations are presented with a plethora of symbols representing the same variable, units not specified and/or inconsistent units even by the same authors. For example, Anderson (1980b) used the symbol ( ) to represent density dependent constraint on host mortality. While in the sa me year used it to mean the contact rate between hosts and parasitic infective stages (Anderson, 1980a). More recently (Kretzschmar and Adler, 1993) used the same notation to represent host birth rate. Table 4.1 gives a list of the nomenclature adopted in the proposed Human Ascaris model. Similar tables are located throughout the chapter to represent variables as they are introduced in those sections to create clarity and transparency, and reduce confusion.

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53 Table 4 1 : Nomenclature and definitions used in Human Ascaris model Symbol Description Units H Magnitude of host population at time, t host P Magnitude of worm population at time, t worm W Magnitude of infective egg population at time, t egg M Population mean (ratio of the average number of adult worms to each host) at time, t worm/host Host growth rate (birth rate natural death rate) host/host/time Village carrying capacity of the host population host Host natural death rate host/host/time Host mortality rate due to worm induced death host/worm/time Worms natural death rate worm/worm/time ( ) Probability that a host contains ( ) number of worms [ ] Egg production rate by adult worms egg/worm/time Proportion of eggs ingested by individuals in a given time interval; contact rate between infective eggs and hosts egg/egg/host/time Rate of inactivation of eggs in the environment; (d2/time) egg/egg/time d1 Number of ingested eggs that hatch and survive to adulthood worm/egg d2 Proportion of eggs that survive environmental conditions to become infective egg/egg Proportion of female worms in a metapopulation; all worms in all hosts [ ] Probability that a female worm will mate in an infrapopulation; worms in one host [ ] Negative binomial clumping parameter, denotes worm dispersion among host population worm/host

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54 4.2 Population dynamics 4.2.1 General population dynamics Table 4 2 : Nomenclature and definitions used in Section 4.2.1 Symbol Description Units Magnitude of species population at time, t species Species/Prey/Host population growth rate (birth rate death rate) 1/time Carrying capacity of area species The population growth rate of a species in a given area is normally generalized by the following mathematical function (Lotka, 1956): = ( ) [4.1] 4 1 Where ( ) is the number of a given species living in the area at time, (t) and whose future value is a function of the current state of the population (Bartlett, 1960; Boccara, 2004). For natural population growth (due to death and birth processes only, assuming n o immigration or emigration), the simplest model for ( ) is the Verhulst logistic equation, for which detailed derivation and rationale can be found in (Hutchinson, 1978; Pielou, 1969): = 1 [4.2] 4 2 The model satisfies the following assumptions (Hutchinson, 1978): Each individual has at least one parent like itself, and If the area occupied by the individuals is finite and there is no adverse event to cause extinction, the population will increase at a rate ( = birth rate death rate) up to the carrying capacity, ( ) which is determined by environmental resistance. ( ) is the biotic potential of the organisms, that is, the maximum

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55 growth where neither scarcity ( ) nor intra species crowding ( 2) limits reproduction (Pielou, 1969). 4.2.2 Predator prey dynamics Table 4 3 : Nomenclature and definitions used in Section 4.2.2 Symbol Description Units 1 Magnitude of prey population at time, t prey 2 Magnitude of predator population at time, t predator Death rate of predators 1/time Contact rate between predator and prey 1/predator/time Conversion efficiency of eaten preys to new predators predator/prey Equation [ 4 2 ] describes the population dynamics of a single species, however in nature, organisms of different species do not live in isolation but interact with each other in two main ways; competition for common environmental resources or one use the other as a food source (Leslie and Gower, 1960). This work advances the latter relationship, commonly generalized as the predator prey model. The Lotka Volterra equations are the simplest deterministic representation of the predator prey interaction (Maynard Smith, 1974; Pielou, 1969). Equations [ 4.3] are modified versions of the origin fo rmulation, accounting for density and resource constraints (1 ) on the prey population: 1 = 1 1 1 1 2 2 = 1 2 2 [4.3] Where ( ) is the growth rate of the prey ( 1), ( ) is the contact rate between predator ( 2) and prey deaths resulting from predation is given by ( 12). ( ) is the

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56 death rate of the predator while birth rate is directly proportional to prey predator interaction ( 12), with the prey to predator offspring conversion efficiency ( ). A unique characteristic of this model is that of damped population oscillations around a fixed equilibrium (Lapage, 1963). That is, when the prey population increases predator prey contact goes up with concomitant increases in predation and predator birth rates. This feeds back negatively to reduce host numbers with subsequent slowing in the growth of the predator population. The derivation of this system of equations is based on a number of simplifying assumptions, as follows (Maynard Smith, 1974): If prey s are able to avoid predation, their population growth is determined by the logistic model in equation [ 4 2 ], Both species move and interact randomly, similar to molecules in a chemical reactions, The predators feeding time is much smaller than the time between feeding, so it is reasonable to assume that the rate at which a prey gets eaten is proportional to their population density ( 12), Eaten preys are instantaneously converted to new predators. That is, there are no developmental time delays, Time i s a continuous variable since successive generations overlap allowing the use of differential equations to represent dynamics (Anderson and May, 1978), and The population densities of both species are only functions of time, not the age, sex or genotype of their members. Thus, the rate of change of population densities of predator and prey can be represented by ordinary differential equations (May and Mclean, 2007).

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57 This model is analogous to the collision theory in chemical kinetics (Lotka, 1956). This conceptualization only crudely represents the predator prey dynamics because predators tend to deliberately seek out preys and there is a time lapse between eating a prey, metabolic assimilation and subsequent birth of an offspring. The deterministic nature of these equations also makes them ecologically unrealistic (Maynard Smith, 1968). For example, a fundamental assumption is that the population size must be infinite (detailed in Section 4.2.5 below), which is not possible in a finite area (Bartlett, 1957). In addition, they ignore random fluctuations characteristic to biological and population processes (Boccara, 2004; Maynard Smith, 1974). In spite of these limitations, however, the predator prey model is valuable as a point of departure that can be cu stomized to more accurately mirror biological interactions of the host parasite population dynamics. The following sections will detail modifications to the system of equations in [ 4.3] to make them more representative of the biological and population pr ocesses that occur in host parasite relationships. 4.2.3 Host parasite dynamics The host parasite relationship is a unique manifestation of the predator prey model and is considered to be mathematically equivalent (Anderson and May, 1978; Pielou, 1969). An increase in the host population results in increased host parasite contac t, which leads to higher rates of infection and average parasite burden per host. As the number of parasite per host increases, the rate of infection induced host deaths also increases creating negative feedback to reduce the parasite population, resulting in population oscillations characteristic of predator prey dynamics (Pielou, 1969).The encounters are similarly not random, but are functions of host and parasite behavioral patterns. A minor difference in the two systems is manifested in the absolute numbers of the analogous population members. That is, preys are normally the more abundant of

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58 the two species in the predator prey relationship. In the host parasite model, parasites, which are the predators, tend to have population sizes much larger than their hosts. 4.2.4 Deterministic host parasite dynamics In general, parasites have two types of life cycles, indirect (more than one hosts) and direct (one host). Ascaris epitomizes parasites with direct life cycles (see Figure 4.1). The parasite has two distinct populations, the adult worms infesting human hosts and eggs dispersed in the environment (Usher and Williamson, 1974). Figure 4 1 : Flow chart of human Ascaris population dynamics

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59 4.2.4.1 Deterministic host population equations Table 4 4 : Nomenclature and definitions used in Sections 4.2.4.1 and 4.2.4.2 (Boccara, 2004) Symbol Reference Symbol* Description Units H H Magnitude of host population at time, t host P P Magnitude of worm population at time, t worm s Host mortality rate due to worm induced death host/worm/time Parasite population growth rate 1/time c Worm carrying capacity of each host worm/host *Reference Symbol: notation used by the reference cited in the table heading The prey population of equation [ 4.3 ] is adopted here to represent the host population in the host parasite model. As before, in the absence of parasites, the host is assumed to growth logistically, limited only by the availability of environmental resources. For parasitic infection not every encounter results in death of the host. Thus, the contact rate, ( ) is now redefined as parasite induced host death rate, ( ), which is assumed constant for the deterministic representation. In reality death only occurs at high worm burdens, which in turn depends on the probability distribution of the worms among community members. This is accounted for in the stochastic model presented in Section 4.2.5.1 below. The host dynamics from equation [ 4.3 ] is now: = 1 [4.4] 4 3 4.2.4.2 Determ inistic parasite population equations The predator population dynamics in equation [ 4.3 ] assumes a constant per capita death rate given by ( 2) and a birth rate that is proportional to the availability of preys leading to ( 12). However, in reality density (number of worms per organ) is limited by physical capacity of the host, infrapopulation competition for available

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60 resources of resources and the hosts immunological response which increases with infection intensity (Anderson, 1998; Englund, 1988; Loukas et al. 2000). To account for these constraint, a logistic type model similar to equation [ 4 2 ], has been proposed where the carrying capacity of an individual host, analogous to ( ) is given by ( ) and intra species competition given by ( 2) (Boccara, 2004): = 1 [4.5] 4.2.4.3 System of deterministic equations for host parasite dynamics The system of equations representing the host parasite dynamics is represented in equation [ 4 5 ]. These equations are just two of many variations possible, through combining different terms and making other assumptions about the ecology of the species. = 1 = 1 [4.6] 4.2.5 Stochastic host parasite population dynamics Table 4 5 : Nomenclature and definitions used in Section 4.2.5 (Maynard Smith, 1974) Symbol Description Units P Magnitude of parasite population at time, t parasite Po Initial magnitude of parasite population at time, t = 0 parasite Average parasite population parasite The preceding discussion was limited to deterministic representations of the host parasite population dynamics and are therefore subjected to the inherent limitations of

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61 that class of models (Maynard Smith, 1974). For example, consider the deterministic model for an exponentially growing parasite population: = [4.7] The number of individuals at time ( ) is thus given by the well known solution: = [4.8] The deterministic assumption is that a fraction of ( dt ) individuals are born over a short time interval, ( dt ) (Maynard Smith, 1974). The corresponding stochastic model assumption is, for the time period ( ), an individual produces one offspring with probability, ( dt ) and no offspring with probability ( 1 dt ) (Bartle tt, 1960). Therefore whole instead of fractional individuals are reproduced at each time step. The mean number of individuals ( ) and the variance of ( ) can then be calculated at time ( ) by (May, 1974): = ( ) = 2 ( 1 ) [4.9] The resulting population mean ( ) is the analogue of the solution for the deterministic model in equation [ 4 7 ] for replicate populations with initial size ( ). The variance of ( ) measures any differences in the population sizes after a time step. The coefficient of variation ( ); ratio of the standard deviation to the mean, is the best method for comparing dispersion among populations and is given by (Bradley and May, 1978): = ( ) = 2 ( 1 ) lim 1 [4.10]

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62 Thus, if ( ) is large, there is very little deviation among the population means, which tend to the mean in equation [ 4 8 ]. Since the stochastic and deterministic means are equivalent, it can be concluded that for infinitely large ( ) both models are equally representative of the population dynamics (Bartlett, 1960; May, 1974). In order for deterministic models to more accurately describe the host parasite relationship, more complicated equations are required. One method to ov ercome this limitation is to develop hybrid models consisting of deterministic models while allowing for stochastic variations (Anderson and May, 1978; Pielou, 1969). These models can then be developed to maintain the ecological and biological fidelity of the populations. This approach has been adopted for the Ascaris human population dynamics based on the predator prey model in equation [ 4.3 ] presented here and is described in the following sections. 4.2.5.1 Stochastic host population equation Table 4 6 : Nomenclature and definitions used in Section 4.2.5.1 Symbol Description Units Worm burden worm/host ( ) Probability of a host containing parasites [ ] ( ) Death rate among hosts with parasites host/worm/time For the host population ( ) dynamics (Anderson, 1978, 1980a, 1982; Anderson and May, 1978, 1992; May and Anderson, 1978): As a first approximation, there is no density dependent constraint on the growth rate ( ), leading to exponential instead of logistic reproduction similar to equation [ 4 6 ]. Instead, the host population is assumed to be regulated by parasitic activities (Anderson, 1980a).

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63 The rate of parasite induced host mortality is a function of the worm burden, ( ). That is, the more worms a host harbors the more likely death will result due to parasite induced complications such as abdominal obstruction, which is especially true for children ( Thein Hlaing and Myat Lay, 1990). If ( ) is the probability that a given host contains ( ) number of worms, then the death rate among those with ( ) parasites is given by ( ) The death rate will therefore depend on the number of parasite per host and the assumed probability distribution of ( ) The total parasite induce deaths among host is given by: ( ) ( ) = 0 [4.11] The host equation from [ 4.3] then becomes: = ( ) ( ) = 0 [4.12] 4.2.5.2 Stochastic worm population equation Table 4 7 : Nomenclature and definitions used in Section 4.2.5.2 Symbol Description Units Magnitude of egg population at time, t egg 1 number of ingested eggs that become established worms worm/egg 1 Time period between egg ingestion and established worm egg production; prepatent period time Contact rate between host and infective eggs; hosts ingestion rate of infective eggs egg/egg/host/time Death rate of host due to cause other than parasites host/host/time ( ) Death rate of parasites as a function of infrapopulation competition worm/worm/time

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64 For the worm population ( ) dynamics (Anderson, 1978, 1980a, 1982; Anderson and May, 1978, 1992; May and Anderson, 1978): When infective eggs of Ascaris are ingested only a portion ( 1) will survive the prepatent period ( 1), time between infection and when the larva finally return to the small intestine and develop to reproductive maturity. Assuming that the number of worms established in all host ( ) is a linear function of the number hosts ( ), and infective eggs in the environment ( ), then the total number of established worm s is given by equation [ 4 12 ]: 1 [4.13] The rate of change of the worm population is the difference between number of worms established in the human population and the losses due to various death processes. Parasite mortalities have three components; natural deaths of worm and host, and host deaths as a result of high parasite burdens (Anderson and May, 1978). These are discussed in turn below. Losses due to parasite natural host deaths at a rate of ( ). That is, when individuals die, the worms di e with them, assuming that the worm burden is not high enough to cause these deaths. The total number of worms lost in this manner is: . ( ) = 0 [4.14] Losses due to parasite induced deaths. From equation [ 4 10] the number of host dying as a resu lt of high worm burden was given by ( ) ( ) = 0. Therefore the product of the number host dying and the average worm burden per host ( / ) gives the total number of worms dying with them:

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65 ( ) ( ) = 0 [4.15] Losses due to worms dying naturally due to worms being spent or hosts immunological responses. The natural life expectancy for an average Ascaris worm is about 1 year. However, as the worm burden increase, the host immunological response is heightened whi ch results in a higher mortality rate ( ) among the parasites. As a first approximation ( ) is considered constant and is given by ( ). This is a reasonable assumption, since as the number of worms increases the likelihood of host death increases, which is accounted for in equation [ 4 14]. Total worm death due to natural causes is given by: [4.16] The parasite equation from [ 4.3] then becomes: = 1 ( ) = 0 ( ) ( ) = 0 [4.17]

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66 4.2.5.3 Stochastic egg population equation Table 4 8 : Nomenclature and definitions used in Section 4.2.5.3 Symbol Description Units Magnitude of egg population at time, t egg ( ) Rate of egg production as a function of parasite density egg/worm/time Proportion of female worm; assume to be 1:1 ratio [ ] Probability that female worm will mate [ ] 2 Time period between eggs exiting host and developing to become infective to host time 2 Proportion of eggs produced that survive environmental conditions to become infective egg/egg Inactivation rate of eggs in the environment; (d2/time) egg/egg/time The infective egg population ( ) dynamics (Anderson, 1978, 1980a, 1982; Anderson and May, 1978, 1992; May and Anderson, 1978): The rate of change of infective eggs in the environment is a function of the fecundity of the established worm population, ingestion by host and the rate of inactivation as a result of harsh ambient conditions. Research as shown that egg production ( ) affected by the worm burden ( ) of the host (Croll et al. 1982). In addition because Ascaris is dioecious (both sexes required for infective egg production) and polygamous (a single male will mate with multiple females), the fertility rate depends on the proportion o f female worms in the population, ( ) and probability that a given female will mate, (Haukisalmi et al. 1996). Egg production for the entire established worm population in the host is given by : . ( ) ( ) = 0 [4.18]

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67 The eggs are not immediately infective when released into the environment but require a developmental period ( 2) before they are able to cause disease in the host population. During this time, the developing embryo is particularly vulnerable and many die from exposure to harsh ambient conditions such as direct exposure to sunlight and desiccation. Therefore only a proportion ( 2) will survive to become pathogenic. Losses are due to environmental inactivation at a rate ( ), and ingestion by host ( ) as describe in equation [ 4 16]. The rate of change of eggs in the environment is given by: = 2 . ( ) ( ) = 0 [4.19] 4.2.5.4 System of stochastic equations for host parasite dynamics The three populations are represented in equation [ 4 19] below. The following discussion will involve further explanation of the various population and biological processes involved in parasite host dynamics and how these lead to stability and subsequent disease endemicity. This analysis will then be applied to evaluating the effects of various control strategies on the dynamics of the parasitic population in this and ensuing chapters. = ( ) ( ) = 0 = 1 ( ) = 0 ( ) . ( ) = 0 = 2. ( ) ( ) = 0 [4.20]

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68 4.2.5.5 Statistical distribution and spatial pattern of worms among hosts Table 4 9 : Nomenclature and definitions used in Section 4.2.5. 5 Symbol Description Units Mean worm burden worm/host t ( ) First moment define a mean worm burden, M worm/host t ( 2 ) Second moment define as variance, ( ) by (Bliss and Fisher, 1953) worm/host Clumping parameter of the negative binomial distribution worm/host D = Scanning power of infective eggs; number of host acquiring infection by (Macdonald, 1965) host From the three governing equations above, the number of worms per host ( ) is an important variable, whose value depends on the statistical distribution of its frequency. In general discrete ecological data are observed to fall into three categories; underdispersed (evenly dispersed), random and overdispersed. These spatial patterns are represented by the positive binomial, Poisson and negative binomial probability distributions respectively (Anderson, 1980a). The latter two distributions are particularly relevant to parasitic organisms and will be discussed further here. Consider a community endemic for Ascaris with each individual carrying ( ) number of worms, ( = 0, 1, 2, ). If each worm were randomly and independently assigned to a host, then their dispersion would be considered random. A sample from this host population would show that the number of worms per host is a Poisson variable (Pielou, 1969). This distribution as sumes that the maximum density (number of worm in small intestine) is the same for each host and that each host has the same probability of being infected by a worm (Maynard Smith, 1968). Thus, the mean and the variance of the observed frequency distributi ons of the number of worms per host are equal for this

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69 distribution (Bhattacharyya, 1977). The mean and variance of the Poisson distribution is given by (Anderson and May, 1978): t ( ) = ( ) [4.21] However, certain segments of the host population are more at risk for acquiring infection and higher worm burdens due heterogeneous distribution of infective eggs, differential habits and susceptibility to infection among community members (Wakelin, 1987). For example, older hosts are physiologicall y able to carry more worms and children are more likely to be infected because of behavioral habits such as playing in dirt. From field studies of Ascaris infections, the variance of the observed frequency distribution of the number of worms per host is us ually much greater than the mean and a clumped pattern of both infection incidence and egg location is typically observed (May, 1977; Wong et al. 1991). That is, a minority of the host population is infested with the majority of the worm population, refer red to as wormy people in Norman Stolls 1947 seminal work (Stoll, 1999); reprinted. This means that the greater proportion of the worm population is exposed to severe crowding effects (Anderson and May, 1992). Population processes such as parasite mo rtality and fecundity are greatly influenced by parasite burden, which has been shown to regulate parasite transmission and establishment (Churcher et al. 2006; Medica and Sukhdeo, 2001; Uznanski and Nickol, 1980). Overdispersed or aggregated distribution, therefore, has important implications for host parasite stability and by extension parasite endemicity (Boes et al. 1998). The degree of aggregation is measured by the parameter ( ), when the intensity has a negative binomial distribution. ( ) is an intrinsic property of the clumping pattern of the worms that is independent of mean worm burden. For example, in general, the

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70 worms natural death rate is greatest in hosts with higher worm densities as resources become limiting in the small intestine. However, unless these hosts are also dying, they will still have higher than average worm burdens due to their higher risk behaviors. Thus, the overall population mean ( / ) is reduced but the spatial arrangement denoted by ( ) is unchanged. In terms o f measuring the success of an intervention, it will be shown later in this chapter that because of this phenomenon, morbidity may be greatly reduced but disease prevalence and incidence remain unchanged. The mean and variance of the negative binomial distr ibution is given by Bliss and Fisher (1953) : t ( ) = ( ) t ( 2 ) M + M 2 k = 1 + [4.22] Low values of ( k ) indicate very high variance or dispersion from the population mean, that is, pronounced worm aggregation. The opposite is true for high values. It is interesting to note that as ( k ) becomes infinitely large the variance equals the mean (equation [4.23]) ; that is the frequency distribution of the worm burden becomes Poisson. lim + 2 ( ) M = [4.23] 4.2.6 Simplifying host, worm and egg population dynamics The birth, death and transmission processes described by the equations of [ 4 19] exhibit random characteristics and are subjected to density dependent constraints. These features are captured by the worm burden and its probability distribution among individuals in the host population as discussed in Section 4.2.5.5 above. The

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71 overdispersed distribution was chosen because it most accurately mirrored the biological and population processes of parasitic organisms. However, an important departure from the most influential models found in literature will first be dealt with. 4.2.6.1 Units inconsistency in Anderson and May ( 1978) Table 4 10 : Nomenclature and definitions used in Anderson and May (1978) and May and Anderson (1978) Reference symbol Equivalent symbol* Description Units from reference a r =(a ) Host birth rate /host/time b [host/host/time] Host natural death rate /host/time [host/worm/time] Host mortality rate due to worm induced death /host/time [ egg/worm/time ] Egg production rate by adult worms /worm/time [worm/worm/time] Worms natural death rate /worm/time = D = [host] Transmission efficiency constant/Scanning power unspecified [worm/host] Mean worm burden worm/host t ( ) [worm/host] First moment define a mean worm burden, M worm/host t ( 2 ) see below see [ 4.22 ] above Second moment; mean square number of parasites per host worm/host k k [worm/host] Clumping parameter of the negative binomial distribution unspecified [egg/egg/host/time] Egg transmission rate per host /host/time *Notation and units used in proposed Human Ascaris model of this work In their ground breaking work, Anderson and May (1978) proposed a system of equations that are foundational to this work and countless others over the past 30 years. However, on closer inspection there are fundamental flaws. For example, as proposed, the units are inconsistent. Consider equation (7) from their paper: = ( ) [4.24]

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72 D imensionally equation [ 4 23] is as follows using the units in Table 4.10 : = 1 1 [4.25] T hat is, ( ) has units of worm/time instead of the required host/time to ensure unit consistency. Similarly equation (9): = + ( + + ) 2 [4.26] Dimensionally equation [ 4 25] is as follows: = [ 1 1 ] . 1 1 2 [4.27] Unit inconsistencies occur in two places, + having units of egg/time and 2 units of worm2/host/time, when the correct units should be worm/time. These inconsistencies will be addressed in the proposed models in the following sections. 4.2.6.2 Hybridized equations for host population The parasite pathogencity rate ( ) is defined as a function of the worm burden. This relationship is assumed to linear for this work because previous works have determined that nonlinear representations do little to improve the accuracy (Crofton, 1971). Therefore, ( ) = . By d efinition ( ) = 0 is defined as the expected number of ( ) at time ( ) or the population mean worm burden and is denoted by t( ) Substituting both these values into the host equation of [ 4 19] simplifies to equation [4.27] where t( ) depends on the spatial distribution of the worms among the hosts. = . t ( ) [4.28]

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73 For overdispersed distributions, t( i ) = P H Equation [ 4 27 ] now becomes: = [4.29] Dimensionally equation [ 4 28] is as follows: = 1 / [4.30] 4.2.6.3 Hybridized equations worm population Assuming constant egg productivity rate ( ) independent of density constraints as a first approximation and substituting ( ) = and the identity t( ) the infective egg population equation of [ 4 19 ] becomes: = 2 [4.31] Unit consistency check: = . 1 / . [4.32] The life expectancy of the host, worm and egg populations differ significantly by several orders of magnitudes as shown in Table 4.11 below. Thus, density of the infective stages in the environment can be assumed to equilibrate instantaneously, relative to the variations in the other populations, to dW dt = 0. Rearranging equation [4.30] to solve for number of infective eggs in the environment, ( ) gives: = 2 + [4.33]

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74 Table 4 11 : Relative lifespans of human, worm and egg populations in the lifecycle of Ascaris (CIA 2008) Population Lifespan (years) Human 69 Adult worm 1 Ascaris egg 0.1 Macdonald (1961) introduced the concept of scanning power which when applied to Ascaris, is the number of host that infective eggs will succeed in coming into contact with and surviving to adulthood. The scanning power, ( ) is define as the ratio of the mortality rate of the eggs, ( ) and proportion of eggs ingested by human hosts, ( ). Substituting D = into equations [4.32] gives: = 2 + [4.34] Substituting equation [4.33] into the worm population equation of [4.19] gives: = 1 2 + ( ) = 0 ( ) . ( ) = 0 [4.35] From above the parasite induced host deaths was assumed to be ( ) = . The total death rate among hosts caused by heavy worm burden is given by: ( ) . ( ) = 0 P t ( 2 ) [4.36] If the worms natural mortality rate, ( ) is assumed to be proportional to the worm burden, then ( ) = Substituting this identity and equation [ 4 35] into [ 4 34] gives: = 1 2 + t ( ) t ( 2 ) [4.37]

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75 Anderson and May (1978) defined the second moment t( 2) as the mean square number of worms per host. For overdispersed distribution t( 2) was defined as: t ( 2 ) + 2 + 1 [4.38] Thus giving equation (13): = + ( + + ) 2 + 1 [4.39] Resulting in similar inconsistencies from equation [ 4 26 ]: = [ 1 1 ] . 1 1 2 [4.40] However, Bliss and Fisher (1953) in their equally seminal work define the second moment of the negative binomial as given in equation [ 4 21] above, where t( 2) +2 Thus, equation [ 4 36 ] becomes : = 1 2 + + + 2 2 = 1 2 + + + , 2 2 [4.41] I n terms of units, equation [ 4 40] becomes: = / . 1 / 2 2 [4.42]

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76 4.2.6.4 System of hybridized equations for host parasite dynamics The three populations represented in equation [ 4 19] are now simplified to two equations given by [ 4 42 ]. These will be translated to STELLA for further analysis and the results presented in Section 4.3 below. = = 1 2 + + + , 2 2 [4.43] 4.2.7 Population dynamics in terms of mean worm burden, Epidemiological interventions are interested in determining and reducing parasite reproduction, infection transmission, average worm burden, and ultimately disease incidence and prevalence in the entire human population. In the above discussion the host parasite dynamics were repres ented by the absolute values of population members, total host ( ) and parasite ( ). In reality, one cannot determine the total number of worms in the host population without treating everyone to induce parasite expulsion. Instead a sample of host is usu ally chosen and their worm burden determined (usually indirectly by counting the number of eggs in the hosts feces). From this, the average parasite prevalence, given an assumed probability distribution (say the negative binomial), is ascertained and the appropriate steps are then taken. For a chemotherapy intervention, these steps include choosing the type of mass treatment strategy, target population, medication delivery frequency and time period, and the proportion of persons to receive medication at each treatment. These decisions are therefore best made in terms of the host populations mean worm burden ( ). Expressing equation [ 4 19] in terms of ( / ) gives:

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77 = 1 ( ) = 0 ( ) . ( ) = 0 = 1 ( ) = 0 ( ) . ( ) = 0 [4.44] From the above assumptions, equation [ 4 43] can be rewritten as: = 1 t ( ) t ( 2 ) = 1 ( + ) t ( 2 ) [4.45] Setting the egg population equation from [ 4 18] to zero, assuming the negative binomial distribution and solving for ( ) gives: = 2 . ( ) ( ) . ( ) = 0 = 0 = 2 ( ) . ( ) . ( ) = 0 + [4.46] It is common to assume a 1:1 sex ratio, so ( = 1 2 ) (Croll et al. 1982). Substituting in equation [ 4 45] for ( ) = 0 with ( ) and ( ) with ( ) = 0 where ( ) is a measure of the density dependent constraint on reproduction and ( 0 ) is the maximum eggs production without those constraints gives(Anderson, 1982): = 1 2 2 ( ) . 0 + [4.47] Substituting equation [ 4 46] into equation [ 4 44] gives: = 1 1 2 2 ( ) . 0 + ( + ) t ( 2 ) [4.48]

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78 Substituting D = as in equation [ 4 33] above give: = 1 1 2 2 ( ) . 0 + ( + ) t ( 2 ) [4.49] Ascaris worms are dioecious and polygamous, therefore, the likelihood of worms in a given host mating to produce fertilized eggs, denoted by the mating function ( ( ) ), depends on the number of worms ( ) present and is its probability distribution ( ) (And erson and May, 1992). Assuming negative binomial distribution: ( ) = 1 1 + 2 ( 1 + ) [4.50] Substituting equations [ 4 49] and t( 2) +2 into [ 4 47 ] gives equation [ 4 50 ]: = 1 2 2 1 1 1 + 2 ( 1 + ) . 0 + ( + ) 2 + [4.51] In terms of units: / = . / 1 . / 2 + [4.52] 4.2.7.1 Basic reproductive rate Ascaris has a complex lifecycle with many distinct developmental stages and by extension many population determining rate processes. The overall aim of any interventions is to somehow reduce the reproductive or transmission potential of the

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79 parasite. For example, a nutrition program may increase the hosts immunity to invading parasites, which lowers the number of established worm which subsequently reduces egg production and ultimately the rate of infection. In the same way, mass chemotherapy, remove the adult worm population and ceases egg production, at least temporarily. The basic reproductive rate ( 0) captures all these reproductive and transmission processes into one parameter and is defined as the expected number of sexually mature female offsprings that one female will produce in her lifetime in the absence of density dependent constraints on th e infrapopulation (Anderson, 1985; Thomas and Weber, 2001). For a fertilized female Ascaris worm, ( 0) is a function of the net output of transmission stages which depends on her fecundity ( ) and the array of developmental and death processes the offsp rings are subjected to. For example, only a proportion, ( 2) of produced eggs are embryonated upon exit from the host and are able to survive the 2 3 week development in the environment before they become infective. The rate of ingestion is a function o f the rate of infective egg mortality ( ) and their rate of contact with the host population ( ). Once ingested, again only a portion of the larvae, ( 1) are able to withstand the hosts immunological defenses to make it back to the small intestine. Whi le in the intestine, the worms are subjected to various density independent death processes such as dying of natural causes ( ), and dying when the host dies of other causes except parasite induced ( ). Rearranging equation [ 4 50] gives:

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80 = ( + ) 1 2 2 1 . 1 1 + 2 ( 1 + ) 0 ( + ) ( + ) 1 ( + ) 2 + [4.53] The basic reproductive rate is therefore given by: 0 = 1 2 2 1 . 1 1 + 2 ( 1 + ) 0 ( + ) ( + ) [4.54] Substituting equation [ 4 53] into [4 52] gives: = ( + ) ( 0 1 ) 2 + [4.55] In practice, the basis reproductive rate is used as a measure of parasite stability in the host community. That is, when 0= 1 each female worm replaces itself in the next generation and the parasite is said to be endemic ( Thein Hlaing et al. 1991 ). Below this threshold, the organism is unable to maintain itself and is subsequently eradicated. In the field, ( 0) is usually approximated using models similar to equation [ 4 54 ] and estimates of the required variables (e.g. ) obtained as a result of mass chemotherapy (Anderson and May, 1992). ( 0) is therefore a very useful bench mark to measure an interventions success and will be adopted for this work.

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81 4.2.8 Control by chemotherapy Table 4 12 : Nomenclature and definitions used in Section 4.2.8 Reference Symbol Description Units Excessive worm deaths due to chemotherapy 1/time Number of community member treated at each application host/time Cure rate of drug per dose; proportion of worms expelled worm/worm/host Basic reproductive rate [ ] A chemotherapeutic intervention is the administration of medication to expel the adult life stages of the parasite from the human hosts. There are three main types; mass treatment (random application to a proportion or all community members), targeted treatment (administration to a specific group such as school aged children) and selective treatment (say to individuals with high fecal egg count) (Anderson, 1989). Due to the availability of increasingly effective, cheap and safe drugs, this is one of the most widely employed method of controlling parasitic infections (Anderson and May, 1985). In addition, it is the quickest method of preventing and reducing morbidity associated with helminth infections and has been recognized by the World Health Assembly who recommended frequent treatment of school aged children (Keiser and Utzinger, 2008). The following sections will consider interventions that subscribe t o mass treatment where at each administration the drug is given to a group of randomly selected individuals from among community members. The total number of worms expelled, ( ) is given by (Anderson and May, 1992): = ln ( 1 ) [4.56] Where ( ) is the number of persons treated per treatment interval and ( ) is the drug efficacy. The proportion of worms expelled in a single treatment for four of the most common drugs used to treat soil transmitted helminthes are listed in Table 4.13:

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82 Table 4 13 : Proport ion of host's worm burden kill by drug in a single treatment (Keiser and Utzinger, 2008) Drug Cure rate, (%/host) Albendazole (400mg) 93.9 Mebendazole (500mg) 96.5 Pyrantel pamoate(10mg/kg) 87.9 Levamisole (2.5mg/kg) 91.5 Including this new worm death rate into equation [ 4 50] gives: = 1 2 2 1 1 1 + 2 ( 1 + ) . 0 + ( + ) 2 + [4.57] Rearranging as before to obtain a form of the basic reproductive rate Ro: = 1 2 2 1 1 1 + 2 ( 1 + ) . 0 + ( + + ) 2 + [4.58] Let be a new basic reproductive rate in terms the excess worm deaths, c: = 1 2 2 1 1 1 + 2 ( 1 + ) . 0 ( + + ) ( + ) [4.59] Then equation [ 4 58 ] becomes: = ( + + ) 1 2 + [4.60] As before for the parasite to be eradicated < 1

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83 = 1 2 2 1 1 1 + 2 ( 1 + ) . 0 ( + + ) ( + ) < 1 1 2 2. 1. 1 1 + 2 ( 1 + ) . 0 ( + ) < ( + ) + [4.61] Rearranging in terms of c gives: 1 2 2 1 1 1 + 2 ( 1 + ) . 0 ( + ) ( + ) < 1 + ( + ) [4.62] The left hand side is actually ( ), therefore the number of worms expelled during chemotherapy must be greater than a critical number for eradication to occur: > ( 1 ) ( + ) [4.63] Therefore, the critical proportion of persons that must be treated at each treatment interval is obtained by solving for ( ) in equation [ 4 55] and substituting for ( ) from equation [ 4 63] to give: = 1 = 1 ( 1 ) ( + ) [4.64] Another important epidemiological parameter is the disease prevalence, number of persons infected with worms in the community. For the negative binomial distribution, disease prevalence ( ) is given by (Guyatt et al. 1990): = 1 1 + [4.65]

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84 4.3 Dynamical modeling in STELLA 4.3.1 Step 1: Reproducing host parasite trajectories from literature The first stage of the modeling process was to reproduce the trajectories from (Anderson and May, 1978) and compare the results obtained after translating into STELLA. Table 4.14 and Table 4.15 give the initial population and parameter values obtained from Figure 4 of the article. Figure 4.2 and Figure 4.3 illustrate the STELLA representation of the population equations given by [ 4.65] and [ 4.66 ] respectively. These equations are equivalent to equations (7) and (13) (Anderson and May, 1978) but rewritten in terms of the notations used in this work, the corresponding symbols used by those authors are also given in the tables. The results and discussion of this first step is given in the subsection following. Table 4 14 : Population parameters for host model (Anderson and May, 1978) Description Symbol Value Units Reference symbol Hosts H 100 host H Parasites P 200 worm P Host birth rate a 3.0 host/host/time a Host natural death rate 1.0 host/host/time b Host mortality rate due to parasite induced death 0.5 host/worm/time

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85 Figure 4 2 : STELLA representation of host's equation = , [4.66] Table 4 15 : Population parameters for parasite equation (Anderson and May, 1978) Description Symbol Value Units Reference Parasites P 200 worm P Egg production rate by adult worms 6.0 egg/egg/time Parasite carrying capacity 2 + 1 worm2/host/time 2 + 1 Clumping parameter 2.0 unspecified Parasite natural death rate 0.1 worm/worm/time Transmission efficiency 10 host Ho Parasites host deaths Hosts host births host birth rate host deaths by parasites host natural death rate parasite induced host death rate

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86 Figure 4 3 : STELLA representation of worm's equation = + + + , 2 + 1 [4.67] 4.3.1.1 Step 1 results and discussion: reproducing trajectories from literature The STELLA output compared well with the graph presented in the article with defining features such as the characteristic oscillations in the populations occurring in similar locations. Minor differences, such as the value of the maximums might be due to the fact that the initial values were estimated as they were not explicitly stated by the authors and could have been different from those used in their work. An interesting finding was that while host and parasite maximums occurred simultaneously, the maximum parasi te burden occurred a time step later, see Table 4 16 and Figure 4 4 below. Parasites production egg production rate transmission efficiency losses predator carrying capacity parasite natural death rate host natural death rate parasite induced host death rate Hosts clumping parameter

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87 Table 4 16 : STELLA output population values for host parasite equation from Anderson and May (1978) Time (years) Hosts Parasites Mean parasite burden 0 100.00 210.00 2.10 1 108.27 606.44 5.60 2 37.61 218.73 5.82 3 24.82 98.49 3.97 4 30.20 105.06 3.48 5 35.98 139.56 3.88 6 34.81 145.51 4.18 7 32.24 131.77 4.09 8 32.05 126.77 3.96 9 32.90 130.22 3.96 10 33.17 132.91 4.01 11 32.92 132.23 4.02 12 32.76 131.07 4.00 13 32.81 131.05 3.99 14 32.88 131.47 4.00 15 32.88 131.58 4.00 Figure 4 4 : STELLA reproduction of Figure 4 from Anderson and May (1978) with population mean added 4.3.2 Determining conditions for parasite dynamics in Paquila The next step was to model the study population using the system of equations developed in [ 4 42]. Once established, what if scenarios were conducted to determine

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88 the effects of varying variables that represent key parasite population processes on worm burden and disease prevalence i n the host community. The values chosen for the variables were either taken from literature in similar study sites or are values known to be true for Paquila through personal communications with Dianne and Jim Thompson; missionaries in the village. For those values taken from articles the appropriate reference is given in the population parameter tables below. Croll et al. (1982) found that the average worm burden for an agricultural village similar to Paquila had a mean worm burden ( ) of 22 worms/host. For this exercise, a mean worm burden of 20 worms/host was chosen instead to mimic the 2:1 parasite to host ratio from the Step 1, resulting in an initial parasite population of 7000. The host birth and death rates were estimated from the countrys populat ion values. There is some concern for committing an ecological fallacy (applying global results to local level), however, it could be argued that since the majority of the population lived in rural areas, these population rates are weighted towards those g roups of persons ( CIA, 2008 ; Oleckno, 2002). In lieu of actual values for pathogencity of Ascaris, the parasite induced host death rate was used for hookworm, another soil transmitted helminth (Anderson, 1980b). The fecundity of the female Ascaris worm is legendary with proposed average daily production of up to 200,000 eggs (Brown and Cort, 1927; Jungersen et al. 2000). However, these values were obtained from only two cases and without differentiating the fertilized status of the eggs (Brown and Cort, 1927). Fertilized eggs are more epidemiologically important and a tremendous amount of the eggs that exit the host are unfertilized (Peng et al. 2003). Thus for this model a conservative value of 20 fertilized eggs per day per female worm was chosen, which is reasonable since the average person comes in contact (ingests) 9 20 infective eggs annually (Wong et al. 1991).

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89 Anderson and Gordon (1982) define the transmission efficiency as the number of newly born cohort in host population, as such the number of live births in this community was used to estimate ( ) for this study. This is a reasonable assumption since in disease endemic areas infection is recycled continually with new incidence occurring only within newborns. Table 4 17 : Host population par ameters for Paquila Description Symbol Value Units Reference Hosts H 3500 host Parasites P 7000 worm (Croll et al. 1982) Host birth rate a 29/1000 host/host/year (Cia, 2008)* Host natural death rate 5.27/1000 host/host/year (Cia, 2008)* Host mortality rate due to parasite induced death 5 e05 host/worm/year (Anderson, 1980b) *This value is that for country of Guatemala = = 1 2 + + + , 2 2 [4.43] Figure 4 5 : STELLA representation of host's equation for Paquila (equation [ 4 43]) Parasites host deaths Hosts host births host birth rate host deaths by parasites host natural death rate parasite induced host death rate

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90 T able 4 18 : Parasite population parameter for Paquila Description Symbol Value Units Reference Parasites P 7000 worm Fertilized egg production rate by adult female worms 7300 egg/egg/year Parasite natural death rate 1.0 worm/worm/year (Croll et al. 1982) Transmission efficiency 100 host (Anderson and Gordon, 1982)* Parasite carrying capacity 2 worm/year Egg survival 1 0.01 egg/egg (Larsen and Roepstorff, 1999) Egg hatching 2 0.02 worm/egg (Wong et al. 1991) Egg production transmission 1 2 1/year Saturation + *These authors define transmission efficiency as newly born cohort of host Figure 4 6 : STELLA representation of parasites equation for Paquila (equation [4.43]) Parasites production egg production rate egg production transmission transmission efficiency egg survival saturation losses predator carrying capacity parasite natural death rate host natural death rate parasite induced host death rate worm deaths Hosts clumping parameter egg hatching Hosts

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91 4.3.2.1 Step 2 results and discussion: host parasite dynamics A model similar to the host parasite model simulated in Step 1 above was developed for the village of Paquila as shown in Figure 4.5 and Figure 4.6. However this was based on the system of equations listed in equation [4.43] using the default values presented in Table 4.17 and Table 4.18. The result is given in Figure 4.7. There is some parasite regulation of host population but not with the s everity seen in the article by Anderson and May (1978) This is in part due to the much lower parasite induced host death rate seen in human populations compared to smaller species that the article modeled. Figure 4 7 : Host parasite dynamics for Paquila 4.3.2.2 Step 2 results and discussion: varying egg survival, Under moist shady conditions Ascaris eggs are known to survive at least 7 years in the soil with a maximum of up to 15 years reported (Black et al. 1982). However, on average only about 1% survive the developmental period to become infective, the majority being inactivated by sunlight or desiccated due to high temperatures (Larsen

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92 and Roepstorff, 1999). The model was run for varying egg survival rates to determine the response of the mean worm burden of the host population. From Table 4.20 and Figure 4.7 a mere 10% increase in the deactivation rate (or 10% decrease in egg survival) decreases the potential max imum mean worm burden from 44 to 9 worms/host at year 15. A further 10 % decrease reduced the worm intensity to 50% of what it was at the beginning of the simulation. This simulation is mimicking what occurs in a sanitation treatment system such as a Solar Latrine which will be explored in Chapter 6. The following are of note ; the nonlinearity of the responses (small changes can create big results), results occur over time, and changing one variable may not be enough to eradicate parasite sustainably from community. Table 4 19 : Mean worm burden of Paquila in response to varying egg survival rates Time (years) Mean worm burden 2 = 0 008 Mean worm burden 2 = 0 009 Mean worm burden 2 = 0 01 0 2.00 2.00 2.00 1 1.92 2.21 2.54 2 1.84 2.44 3.24 3 1.76 2.69 4.12 4 1.69 2.98 5.25 5 1.62 3.30 6.68 6 1.56 3.65 8.49 7 1.50 4.04 10.78 8 1.44 4.48 13.62 9 1.39 4.97 17.08 10 1.34 5.51 21.21 11 1.29 6.11 25.91 12 1.24 6.77 30.98 13 1.20 7.51 36.05 14 1.16 8.32 40.70 15 1.12 9.21 44.60

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93 Figure 4 8 : Mean worm burden of Paquila in response to varying egg survival rates 4.3.2.3 Step 2 results and discussion: varying worm natural death rate, The adult worms of Ascaris are very long lived with life spans up to 2 years with 1 being the average (Crompton, 2001). The model was run for 25% and 50% decreases in worms average li fe expectancy. The latter simulation showed that it is possible to eradicate the parasites (mean worm burden < 1) in about 7 years, as seen in Table 4 20 and Figure 4 9 As a point of clarification, a mean worm burden of 1 leads to production of unfertiliz ed eggs (if the 1 worm present were female) since at least 2 worms are needed to successfully mate (Churcher et al. 2005). This begs the question, what practical intervention can be sustainably applied for 7 years to achieve this level of success? Increas ing the rate at which the adult worms die can be done by fortifying the hosts immune system via nutritional supplement (Chapter 5) or through chemotherapy (Section 4.3.3 below).

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94 Table 4 20 : Mean worm burden of Paquila in response to varying worm life ex pectancies Time (years) Mean worm burden = 1 0 Mean worm burden = 1 25 Mean worm burden = 1 5 0 2.00 2.00 2.00 1 2.96 2.30 1.79 2 4.37 2.65 1.61 3 6.45 3.06 1.44 4 9.51 3.52 1.30 5 13.94 4.07 1.17 6 20.18 4.69 1.05 7 28.48 5.42 0.95 8 38.38 6.26 0.86 9 48.36 7.23 0.77 10 56.45 8.34 0.70 11 61.76 9.61 0.63 12 64.72 11.06 0.57 13 66.23 12.70 0.52 14 66.97 14.53 0.47 15 67.34 16.56 0.42 Figure 4 9 : Mean worm burden of Paquila in response to varying worm life expectancies

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95 4.3.2.4 Step 2 results and discussion: varying parasite induced host death rate, Parasite induced host deaths is a measure of the pathogencity of the worms, that is, the number of worms needed to cause death in an average host. Thus, for the same host population size a small (say 5e 6) means that a large number of worms are required. While for a large (say 5e 3) represents a very lethal parasite. This is illustrated in the results below. The drastic difference in the mean worm burden at year 15 is predominantly attributable to host population dying (see Table 4.22). All species have an average pathogencity. However, host factors such as compromised immunity (due to nutritional deficiencies ) can increase an organisms ability to cause mortality.

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96 Table 4 21 : Mean worm burden of Paquila in response to varying parasite pathogencity Time (years) Mean worm burden = 5 e 6 Mean worm burden = 5 e 5 Mean worm burden = 5 e 3 0 2.00 2.00 2.00 1 2.54 2.54 2.44 2 3.24 3.24 2.91 3 4.13 4.12 3.40 4 5.27 5.25 3.85 5 6.73 6.68 4.25 6 8.59 8.49 4.56 7 10.98 10.78 4.79 8 14.03 13.62 4.96 9 17.94 17.08 5.06 10 22.91 21.21 5.13 11 29.22 25.91 5.18 12 37.16 30.98 5.21 13 47.01 36.05 5.22 14 58.97 40.70 5.23 15 73.03 44.60 5.24 Table 4 22 : Host population of Paquila in response to varying parasite pathogencity Time (years) Host = 5 e 6 Host = 5 e 5 Host = 5 e 3 0 3,500.00 3,500.00 3,500.00 1 3,584.01 3,583.64 3,544.59 2 3,670.02 3,669.17 3,581.53 3 3,758.08 3,756.60 3,610.12 4 3,848.24 3,845.91 3,630.33 5 3,940.53 3,937.09 3,642.85 6 4,035.01 4,030.12 3,648.94 7 4,131.70 4,124.92 3,650.07 8 4,230.65 4,221.41 3,647.64 9 4,331.90 4,319.48 3,642.77 10 4,435.48 4,418.98 3,636.31 11 4,541.40 4,519.78 3,628.85 12 4,649.69 4,621.74 3,620.76 13 4,760.35 4,724.80 3,612.29 14 4,873.38 4,828.97 3,603.61 15 4,988.76 4,934.38 3,594.80

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97 Figure 4 10 : Host population of Paquila in response to varying parasite pathogencity 4.3.2.5 Step 2 results and discussion: clumping parameter, The clumping parameter represents the degree to which worm numbers are aggregated or clumped in the host population. Compared to viral and bacterial disease, helminth offsprings a re not immediately infectious yet are able to persist in communities that have low population densities unlike their pathogenic counterparts (Anderson, 1982). This is in part attributable to their high transmission efficiencies and tendency for a large por tion of the worm population to aggregate in a small number of human host, ensuring a continual and abundant supply of infective stages (Macdonald, 1965). This can have unexpected implications for mean worm burden and disease prevalence as is seen from the result of running the model for varying clumping factor. From the results below, large changes in average worm intensity resulted in very little impact on the actual number of persons infected in the community, that is, there was little impact on disease prevalence in the community. For example, a 75% change in mean worm burden had a corresponding 1% change in disease prevalence. As the

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98 clumping factor becomes larger (more random distribution), large swings in worm intensities resulted in higher changes in prevalence. This has been corroborated by various researchers (Anderson and May, 1992; Croll et al. 1982). Thus, depending on the aggregation of worms among community members, an intervention program may be very successful at reducing morbidity and mortal ity, but have very little impact on the number of infected persons. Table 4 23 : Mean worm burden and disease prevalence in Paquila for varying clumping parameter, Time (years) Mean worm burden = 5 7 e 3 Prevalence* = 5 7 e 3 Mean worm burden = 5 7 e 1 Prevalence* = 5 7 e 1 0 20.00 0.05 20.00 0.87 1 7.93 0.04 24.37 0.88 2 6.49 0.04 29.15 0.89 3 5.92 0.04 34.03 0.90 4 5.64 0.04 38.64 0.91 5 5.49 0.04 42.65 0.92 6 5.41 0.04 45.86 0.92 7 5.37 0.04 48.26 0.92 8 5.34 0.04 49.95 0.92 9 5.33 0.04 51.10 0.92 10 5.33 0.04 51.88 0.92 11 5.33 0.04 52.40 0.92 12 5.33 0.04 52.75 0.92 13 5.34 0.04 52.99 0.92 14 5.34 0.04 53.16 0.93 15 5.35 0.04 53.30 0.93 *Prevalence was calculated using equation [ 4.64 ]

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99 Figure 4 11 : Mean worm burden in Paquila for varying clumping parameter, 4.3.3 Modeling population mean with chemotherapy From the simulation in Section 4.3.2.3 above reduction in the life expectancy of the adult worms can significantly reduce mean worm burdens. One me thod of accomplishing this reduction is through administering medication en masse to the host population. The resulting population mean was modeled according to equation [ 4 67]. The model variables as they appear in the STELLA model are presented in Table 4 24 with their corresponding values and/or equations. The model was first simulated with varying values of the basic reproductive rates. Various what if scenarios were then conducted by modifying the proportion of persons receiving medication at each t reatment interval, the drug cure rates, frequency of treatment and the length of the intervention. The results of the response of the population mean worm burden are presented in the sections below. = ( + ) ( 0 1 ) 2 + [4.68]

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100 Table 4 24 : Model parameters for the chemotherapy simulation Description Symbol Value Units Reference Population mean 20 worm/host Basic reproduction rate 0 1.5 Ro1 0 1 Clumping factor 0.57 Host natural death rate 5.27/1000 host/host/year (Cia, 2008)* Host mortality rate due to parasite induced death 5 e05 host/worm/year (Anderson, 1980b) Parasite natural death rate 1 worm/worm/year Proportion treated 0.27 host/host/time Drug efficacy, cure rate worm/worm see Table 4.13 Treatment frequency tf 4 times /year chemo = IF(TIME < 2) THEN(Population__Mean PULSE(chemo_rate,0,treatment__frequency)) ELSE(Population__Mean 0) {worm/host/time} Excess death rate due to chemotherapy chemo_rate = LOGN(1 drug_efficacy proportion_treated) {1/time}; equation [ 4.63] Figure 4 12 : STELLA representation of chemotherapy model for equation [ 4 6 8 ] Population Mean acquiring basic reproductive rate losing host natural death rate parasite natural death rate Ro1 parasite induced host death rate clumping parameter chemo chemo rate proportion treated drug efficacy treatment frequency

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101 4.3.3.1 Step 3 results and discussion: mean worm burden as a function of As discussed above when the value of 0 = 1 the parasite is unable to maintain its population and the mean worm burden decreases exponentially as shown in Figure 4 13. It should be noted that this does not occur rapidly (it took 15 years for an average 6 worms/person reduction). This is in part due to the store of infective eggs in the environment. Therefore, chemotherapy and nutrition may be used to reduce ( 0) however if eggs in the environment are not deactivated the disease will persist. A relative ly small increase in the worms basic reproductive rate resulted in a significant increase in the average worm burden (see Figure 4 14 ). Figure 4 13 : Variation of mean worm burden when Ro = 1

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102 Figure 4 14 : Mean worm burden dynamics for different values of Ro 4.3.3.2 Step 3 results and discussion: using different drugs The average treatment efficacies of four of the most commonly used anti helminthes are given in Table 4 13. The cure rates range from 88 97%. Three runs were made using 88, 93 and 97% f or intervention periods of 2 and 5 years with drug administration occurring every 3 months to 27% of community members. Four treatments per year was used as the default interval because the transmission cycle of Ascaris form egg production to soil developm ent to infection to sexual maturity requires a minimum of 3 months ( WHO, 1967 ). For all trials, mean worm burden increased and exceeded pre control levels after treatment stopped (Figure 4 15 ). It has been hypothesized that exposure to repeated infection during early life may induce some level of protective immunity, but this is quickly lost when the individual is worm free such as during anti helminthic interventions resulting in post treatment burdens that are greater than endemic levels (O'Lorcai n and Holland, 2000).

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103 For the least potent drugs this recovery time is usually equal to the length of the treatment period (2 or 5 years). However, as the efficacy of the drugs increases mean worm burden is suppressed for longer periods. When treatment co ntinued for 2 years and then stopped, the ultimate worm burden at the end of 15 years was the same for all drugs regardless of the cure rate. For longer a treatment period drug efficacy had a more significant effect on the final infection intensity; that i s, a 97% kill rate kept reinfection substantially lower relative to other schemes (see Table 4.25 ). Figure 4.15 shows the dynamics of the mean worm burden if the program were run for all 15 years. Under this scheme the parasite burden decreased below 1 wor m/host after about 5 6 years for all 3 drugs. Figure 4 15 : Chemotherapy application for treatment period s of 2 and 5 years with different drugs

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104 Table 4 25 : Chemotherapy application for treatment period s of 2 and 5 years with different drugs Time (years) Mean worm burden = 88 % Mean worm burden = 93 % Mean worm burden = 97 % Mean worm burden = 88 % Mean worm burden = 93 % Mean worm burden = 97 % Treatment time = 2 years Treatment time = 5 years 0 20.00 20.00 20.00 20.00 20.00 20.00 1 11.30 10.41 9.72 11.30 10.41 9.72 2 6.50 5.53 4.83 6.50 5.53 4.83 3 11.10 9.44 8.25 3.77 2.95 2.41 4 18.74 16.01 14.03 2.19 1.58 1.20 5 30.82 26.62 23.50 1.27 0.84 0.60 6 47.44 42.05 37.76 2.18 1.45 1.03 7 64.32 59.61 55.35 3.73 2.48 1.77 8 74.98 72.57 70.03 6.39 4.25 3.03 9 79.17 78.35 77.42 10.91 7.27 5.19 10 80.41 80.19 79.92 18.44 12.39 8.86 11 80.75 80.69 80.62 30.36 20.86 15.05 12 80.83 80.82 80.80 46.86 33.97 25.12 13 80.86 80.85 80.85 63.86 51.18 40.02 14 80.86 80.86 80.86 74.76 67.19 57.65 15 80.86 80.86 80.86 79.09 76.27 71.44 Figure 4 16 : Mean worm burden dynamics for treatment period of 15 years using different drugs

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105 4.3.3.3 Step 3 results and discussion: varying proportion treated The chemotherapy scheme chosen is based on ad hoc random selection individuals at the time of each treatment application. The critical percentage of persons that must be treated in order to eradicate the parasite is given by equation [4.64] above. From tha t equation the required number of person to be randomly chosen at each treatment are 45, 42 and 41% for medication with cure rates of 88, 93 and 97% respectively. For this simulation 27, 45 and 50% were chosen to be treated for 2 years at 4 treatments per year. For all simulations the mean increased again after treatment stopped. However the times to re acquire pre control levels were different. For example the time taken for the mean to get back to 20 worms/host was 2, 7 and 9 years for proportion treated at 27, 45 and 50%, respectively. Within 2 years the mean worm burden was reduced to less than 1 worms/host when 45 and 50% of the population was treated. Figure 4 17 : Mean worm burden dynamics for varying proportion of population treated

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106 Table 4 26 : Mean worm burden dynamics for varying proportion of population treated Time (years) Mean worm burden g = 27 % Mean worm burden g = 45 % Mean worm burden g = 50 % 0 22.00 22.00 22.00 1 11.96 3.27 1.91 2 6.66 0.50 0.17 3 11.36 0.86 0.29 4 19.17 1.47 0.50 5 31.47 2.52 0.86 6 48.22 4.31 1.47 7 64.95 7.38 2.53 8 75.27 12.57 4.33 9 79.26 21.15 7.41 10 80.44 34.40 12.62 11 80.75 51.67 21.22 12 80.84 67.55 34.51 13 80.86 76.42 51.79 14 80.86 79.62 67.63 15 80.86 80.54 76.45 4.3.3.4 Step 3 results and discussion: varying treatment length and frequency In previous simulations the default number of treatments was taken as every 3 months (4 times per year). Fallah et al. (2002) recommended intervals of 2 months but cautioned that drug resistance and inabil ity to sustainably implement such a strategy on a large scale may lead to failure, compromising instead with every 4 (3 times per year) or 6 months (twice per year).To determine the level of response to frequency and length of treatment, the model was run for 4, 2 and 1 times per year, and 2 and 5 years respectively. At each trial, only 27% of the population was treated. The results are presented in Figure 4.18 and Table 4.27. For all treatment trials the mean increased to and above pre control levels aft er treatment stopped. All treatments returned to the same mean worm burden at year 15 except when the population was treated every treated every 3 months for 5 years. Also only this treatment achieved a mean worm burden below 1 worm/host. The rapidity of

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107 t he observed return differed most markedly for the number of treatments per year. Thus, for those receiving four treatments per year the mean infection intensity returned to 20 worms/host 3 6 years depending on the treatment period and in less than 1 year for twice per year frequency. When treatment occurred once per year the mean never fell below the initial value regardless of how long the intervention continued. Figure 4 18 : Mean worm burden dynamics for varying treatment period and frequency

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108 Table 4 27 : Mean worm burden dynamics for varying treatment period and frequency Time (years) Mean worm burden = 4 Mean worm burden = 2 Mean worm burden = 1 Mean worm burden = 4 Mean worm burden = 2 Mean worm burden = 1 Treatment time = 2 years Treatment time = 5 years 0 20.00 20.00 20.00 20.00 20.00 20.00 1 10.23 18.41 24.70 10.23 18.41 24.70 2 5.34 17.03 30.01 5.34 17.03 30.01 3 9.13 28.21 46.43 2.80 15.81 35.65 4 15.50 44.13 63.49 1.47 14.72 41.21 5 25.82 61.52 74.58 0.78 13.75 46.19 6 40.97 73.59 79.04 1.33 23.04 63.30 7 58.59 78.71 80.38 2.28 37.12 74.49 8 71.99 80.29 80.74 3.91 54.66 79.01 9 78.15 80.71 80.83 6.69 69.59 80.37 10 80.13 80.82 80.86 11.41 77.25 80.74 11 80.67 80.85 80.86 19.26 79.87 80.83 12 80.81 80.86 80.86 31.60 80.60 80.86 13 80.85 80.86 80.86 48.39 80.80 80.86 14 80.86 80.86 80.86 65.08 80.85 80.86 15 80.86 80.86 80.86 75.33 80.86 80.86 *tf means treatments per year 4.3.3.5 Cost effectiveness of best and worst case scenarios The drug of choice for Paquila is Albendazole (Boca Costa Medical Mission, 2004). It is chewable, has relatively few side effects and cost effective. Cost is about US$0.20 per dose (1 tablet), which is about 4 10 times the cost for individual diagnosis and is therefore recommended for en masse instead of selective treatment (WHO, 2002) Assuming there are on average about 4216 persons in Paquila over the next 15 years, then the cost for treating 25% of the population (1139 persons) over 5 years once per year is about US$ 1139. It will cost almost eight times as much to treat 50% of the same community 4 times per year for 5 years. However the disease would be eradicated in 2 years and mean worm burden would not increase immediately after treatment stopped (see Figure 4.19), while in the former case the money would have been poorly spent since there is little result to show for it. This is similar to recommendation in

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109 literature that for a chemotherapy intervention to be successful, treatment must be given t o a proportion of the population above that indicated by the critical value as calculated by equation [4.64], for a greater than the maximum life expectancy of the longest lived developmental stage, which for Ascaris is the adult worm and is on average 2 y ears (Anderson and May, 1992). Figure 4 19 : Comparing effectiveness of two possible treatment strategies 4.4 Summary and conclusions The aim of epidemiological modeling is to determine who is affected, and how to prevent, reduce or eliminated the risk of infection. This was covered when modeling for the conditions that promote parasite endemicity in Step 2. In Step 3 the aim was to determine how long it takes to eradicate worms using mass chemotherapy only. In general, there the response of the mean worm burden was characterized by nonlinearity to changes in the variables governing the population processes, small changes cause big results, after treatment stopped the hosts are rapidly reinfected and large changes in worm burden does not necessitate commensu rate reductions in

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110 disease incidence and prevalence in the community. Egg survival, parasite induced host deaths and natural parasite deaths seemed to be the rate determining processes in the life cycle of the parasite. The following are conclusions that a re more specific to each simulation: Population processes There is some degree of parasite regulation on the host population, A treatment system that deactivates greater than 20% of infective eggs is required to sustainable eradicate the parasite, A 50% de crease in adult worm life expectancy must be maintained for about 7 years to suppress the mean worm burden below unity, If parasite pathogencity is high enough, a significant swing in mean disease intensity can be a result of host rather than worms dying and, When the distribution of the number of worms per host is highly aggregated large changes in mean worm burden produces very little changes in disease prevalence. Sustainability and success of chemotherapy program There are a variety of drugs use to treat parasitic infections and each has a different level of efficacy. While reinfection occurred after all trials stopped, drugs that had high cure rates suppressed post control rebound more, The longer the treatment time and the higher the cure rate of the medicine being applied the more successful the intervention, The higher the number of persons treated in each interval the longer post control rebound is suppressed and the more likely the intervention to eradicate disease,

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111 Treatment every 3 months fo r 5 years was the best scheme, however this was the most expensive and, Applying treatment once per year did not affect mean worm burden, prevalence and thus morbidity. Therefore, treatment must be administered at regular intervals, in systematic manner, over an economically viable time scale and must be accompanied by other control measures for sustainable eradication to occur.

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112 5 NUTRITION MODEL 5.1 Background Parasitic organisms are mainly transmitted via the fecal oral route: from feces contaminated surfaces, fields that have been fertilized with unsanitized excreta, and by consuming under cooked or raw plants grown in these fields (Curtis and Cairncross, 2003a; Feachem et al. 1983; Santiso, 1997). The poor nutritional status of those affected exacer bates their, susceptibility to infection, duration and degree of morbidity, and likelihood of mortality (Gendrel et al. 2003; Santiso, 1997). Every day each human being produces between 20 1500 g (wet weight basis) of fecal matter containing up to 8 g of nitrogen, 2 g phosphorus and 3 g of potassium as well as various micronutrients, assuming urine is collected separately (Feachem et al. 1983; Schouw et al. 2002b). Annual nutrient production is equivalent to the amount of commercial fertilizer needed to cultivate 250 kg of cereal, the approximate yearly per capita required food intake ( Heinonen Tanski and Van Wijk Sijbesma, 2005; WHO, 1985). It is only logical therefore to recycle excreta to crop production. However, the average person also excretes 1010 1015 microbes per gram of fecal material, some of which can be pathogenic (Vinneras et al. 2003a ). Therefore, excreta must be treated to ensure microbial quality before it can be safely reused. This chapter will cover the production of fecal matt er and its use to supply the agronomic requirements during soybean cultivation as part of a nutrition program. Microbial inactivation of humanure will be dealt with in Chapter 6.

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113 5.1.1 Protein nutrition and parasitic infections Protein calorie malnutrition is the most common and significant cause of immune deficiency in developing countries and is usually associated with parasitic infections (Gendrel et al. 2003; Woodruff and Wright, 1984). The malnutrition infection interaction, however, is not confined to a linear, one way causal relationship. That is, a diet with protein deficiencies facilitates the growth and establishment of parasites which in turn create nutritional imbalances due to increased energy requirements to fight them, deceased food intake, a nd interference with protein absorption and metabolism (Boes and Helwigh, 2000; Stephenson et al. 2000; Venkatachalam and Patwardhan, 1953). On the other hand, as the host becomes more malnourished, worm burden and fecundity may be reduced as nutrients become unavailable (Bundy and Golden, 1987). Studies have shown that when a diet high in protein (skimmed milk) is administered almost all parasitic infections are eradicated (Bundy and Golden, 1987; Venkatachalam and Patwardhan, 1953). 5.1.2 Soybean In proposing soybean, it should be noted that this is not a promotion for monoculture (an image normally associated with this crop), with its attendant ecological shortcomings, but rather crop rotation and intercropping with traditional staples. Such practices are wel l known to be a more sustainable method of agricultural production. In addition, soybean is being used here as a nutrient equivalent (a sort of nutrient indicator organism). That is, if it is not possible to cultivate soybean, then the calculations prese nted can be translated to a more culturally and ecologically appropriate protein dense crop. Nevertheless, soybean was chosen for this project because it has several

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114 qualities that makes it ideal for a protein nutrient intervention.The rationales for choosing soybean are: Due to its position as the worlds primary source of protein, it has been extensively studied and therefore detailed information is readily available for model input (Liu, 1997; Smith and Circle, 1978; University of Nebrask a Lincoln, 2007), It is the only known complete source of protein among plant based food; contains all the essential amino acids that must be provided because of the bodys inability to synthesize them and then some (Liu, 1997), Direct use is a form of primary consu mption (diet based on vegetation), which is more efficient in terms of energy conversion and utilization; a significant amount of energy is wasted at each trophic level change (Moore, 2002), Food and Agricultural Organization of the United Nations and the World Health Organization (FAO/WHO) have used egg and milk as bench marks for protein nutrition. However, 75% of Guatemalan Mayans are lactose intolerant (Boca Costa Medical Mission, 2004; Plenty, 2008; WHO and FAO, 1973, 1985 ). In addition Ascaris infecti on is know to exacerbate this condition (Carrera et al. 1984), The crop was introduced to a neighboring community over 20 years ago and has been woven into their social fabric, as well as technical support through extension services is available (Plenty, 2008), Soybean is a legume and therefore fixes nitrogen. It passes this benefit along when intercropped or rotated with traditional staples (Ghosh et al. 2004; Smith and Circle, 1978), and

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115 Agronomic retention time (planting to harvesting) is relatively sh ort; about 3 4 months (Liu, 1997; Plenty, 2008; Smith and Circle, 1978). 5.1.3 Goals and objectives The main goal of this chapter is to simulate the response of the population mean worm burden to a nutritional intervention. Unless otherwise cited, model input s and recommendations for agricultural and nutrition planning were obtained from: Plenty, (2008), University of Nebrask Lincoln (2007), and WHO and FAO (1973, 1985). The specific objectives are: Model soybean cultivation, Model the effect of protein nut rition on the parasite induced host death rate in the population mean worm burden dynamics, and Model effect of nutrition and chemotherapy on population mean worm burden. 5.2 Excreta model development 5.2.1 Excreta and nutrient production In rural areas of developing countries, the average adult daily excreta output approximately 0.35 kg feces and 1.2 kg urine (Feachem et al. 1983). Strictly speaking, excreta refers to urine production but is generally used to mean both together, but for this project it is used to mean fecal material only. Typical nitrogen content is approximately 5% (dry weight bases), of which a third is released yearly (Heinonen Tanski and Van Wijk Sijbesma, 2005) The nitrogen content of urine is significantly higher than that of fec es ( Heinonen Tanski and Van Wijk Sijbesma 2005; Schouw et al. 2002a), however, this work focuses on the latter for the following reasons:

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116 Nitrogen losses associated with urine storage are much higher, producing high concentrations of ammonia which sig nificantly reduces its shelf life ( Heinonen Tanski and Van Wijk Sijbesma 2005), Soybean requires a high organic matter content that is absent from urine (Plenty, 2008; University of Nebraska Lincoln, 2007 ), Organic matter is known to improve soil s tructure, increase the soils ability to resist drought and erosion and promote salt tolerance of plants (Chambers et al. 2003), and The nitrogen in feces becomes available over time, thus reducing the potential for groundwater contamination upon applicat ion (Melse and Verdoes, 2005). 5.2.2 STELLA excreta simulation For this simulation, Latrine Content refers to the combined total capacity of all the latrines in the community assuming each household has and uses this facility (see Figure 5.1). Based on rate o f production and capacity of the latrine and solar vaults (details in Chapter 6), it is expected that the latrine will be emptied every 4 months. Excreta that is not immediately used for soybean production is stored for later use. The simulation result is given in Figure 5.2. The graph shows that fecal matter will be removed from latrine vaults to the solar vault every 4 months, with a four month offset separating the vaults. Thus, for the first year, processed excreta will not be harvested in time for th e soybean planting season which occurs around May.

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117 Figure 5 1 : STELLA representation of excreta production Figure 5 2 : Result of excreta production and processing in solar and latrine vaults 5.3 Soybean model development 5.3.1 Nutrient requirements of hosts When dietary protein is derived from a single vegetable source such as soybean, the daily recommended intake is 1.1 g per kg of body weight. Assuming a 70 kg person the yearly protein intake would be 28 kg (1.1 70* 365). In general the recommended range is 0.8 1.5 g/kg/d and 0.66 g/kg/d for basal metabolic maintenance. For maintenance: 0.66 g/kg/d for adults and 0.67 g/kg/d for children. Latrine Content Solar Vault Excreta producing emptying latrine content excreta production rate latrine retention time emptying solar vault content Hosts solar vault retention time Excreta Storage

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118 Dried soybeans contain on average 40% protein by weight of which only about 70% is biologically available depending on preparation (National Soybean Research Lab, 2008). So for a 70 kg person with intake of 1.1 g/kg/d, 100 kg soybean will cover his 28 kg protein yearly requirement (28/0.4 kg soybean). Table 5 1 : Protein and soybean requirements Metabolic requirement P rotein requirement Daily (g/kg/d) Yearly (kg/year)* Soybean equivalent* Maintenance 0.66 16.9 60 Lower limit 0.80 20.4 73 Single veg. source 1.10 28.1 100 Maximum 1.50 38.3 137 *Assuming a 70 kg person 5.3.2 Land requirement Assuming available land is fixed, the arable land determines the carrying capacity of the village. The village sits on an area of about 10.36 km2, therefore using the percentage arable land for Guatemala, approximately 1.37 km2 (13.22%) can be used for crop production (CIA, 2008). The average crop yield for soybean in Guatemala is 39 kg of soybean for every 1 kg seed planted (28 kg seeds produced 1089 kg soybeans per acre (4*103 km2)). Thus, each person requires about 2.6 kg (100 kg soybean/person / 39 kg soybean/1 kg seed) seeds planted on his behalf resulting in total requirement of 102.6 kg soybeans per year (20% factor of safety is added to 100 kg requirement during simulation). From the planting rate of 28 kg seeds produced 1089 kg soybeans per acre (4*103 km2) each person re quires 3.7*104 km2. The total carrying capacity of the village is then approximately 3700 persons (1.37 km2/3.7 104 km2/person). The

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119 number of seeds per kg of soybean depends on the variety; for this work 1 kg of soybean is taken have 5280 seeds. 5.3.3 Nit rogen demand requirement from humanure For the yield given above, crop nitrogen demand over the entire growing season is 35910 kg of N/km2 (see Table 5.2). Since it is a legume, soybean will fulfill 75% of this from soil nitrogen (existing soil nitrogen and mineralized soil organic matter nitrogen), acquiring the rest through fixation. However, applying more than 50% of the required total demand is counterproductive as this prevents the nodules from fixing atmospheric nitrogen, increases the likelihood of nitrogen contamination due to excess residual nitrates at the end of the growing season, and has been shown to increase plant susceptibility to certain diseases ( University of Nebraska Lincoln, 2007). Typical nitrogen fraction in excreta is about 11% on a dry weight basis and only a third is bio available each year ( Heinonen Tanski and Van Wijk Sijbesma, 2005; Tarkalson et al. 2006). In manure application it is typical to expect 15 35% losses due to ammonia volatilization (Sogaard et al. 2002). However, conditions in the latrine vaults can be reasonably assumed to be anaerobic and pH around 7, hence in the presence of urease, urea is converted to the ammonium ion ( NH4 +) (Montangero and Belevi, 2007). Table 5 2 : Soybean nutrient uptake at 1089 kg soybeans per acre (4*103 km2) yield Nutrient Seed Stover* Total N (kg/km2) 21432 14478 35910 *Stover: leaves, stalks and pods left in field after harvest The results from Table 5.3 show that in the early stages humanure may have to be supplemented by chemical fertilizer depending on the ambient nitrogen content of the village soil. However, after successive crop seasons the nitrogen fixed from the air,

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120 mine ralized from soil organic matter from previous seasons and continued available excreta from the human population will cover the required demand. Table 5 3 : Percentage soybean nitrogen demand fulfilled by humanure Variable Minimum Maximum Hosts 3500 4990 Excreta production, kg 447,125 637,473 Area under cultivation, km 2 1.28 1.37 Required nitrogen demand (35910 kg N/km2), kg N 45,965 49,197 Recommended excreta application (up to 50%), kg N 22, 983 24,598 Available nitrogen in excreta in 1st year, kg N 16,820 23,981 Percent demand fulfilled by humanure 37% 49% 5.3.4 STELLA soybean simulation The host and parasite model is similar to those presented in Chapter 4, only now the parasite induced death rate is being modified by a multiplier which modifies the normal parasite induced death rate over time based on the ratio of available to desired nitrogen (see Figure 5.3). The assumption is, as the amount of nitrogen increases in the hosts diet, his ability to fight infection is strengthened and the pathogencity of the worms against the host is reduced (Anderson et al. 1979). To simulate this, the planting rate was varied to produce different amounts of soybean per host. It was assumed that currently the host population is getting just enough protein for maintenance which results in the default pathogencity used in Chapter 4.

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121 Figure 5 3 : STELLA representation of host population illustrating effect of nutrition on hosts survival Figure 5 4 : STELLA representation of parasite population illustrating effect of nutrition on parasites survival Parasites host deaths Hosts host births host birth rate host deaths by parasites host natural death rate parasite induced host death rate ~ effect of soybean on parasite induced host death rate normal parasite induced host death rate Parasites production egg production rate egg production transmission transmission efficiency egg survival saturation losses predator carrying capacity parasite natural death rate host natural death rate parasite induced host death rate worm deaths Hosts clumping parameter egg hatching Hosts

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122 Figure 5 5 : Soybean production cycle with effect of supplying nutrient Table 5.4 shows that the results of providing nutrition for metabolic maintenance are similar to those seen in Chapter 4. As nutrition is increased more hosts are surviving, an almost 300 hosts difference by the end of the 15 year run. When replanting was removed the mean worm burden increased drastically but was suppressed for the nutri tion interventions (see Table 5.5). A counterintuitive observation can be seen with the increase of mean worm burden with increasing nutrition. The possible reasons for this is, nutrition was assumed to affect only the hosts ability to resist death from t he parasite but did not change the natural death rate of the parasite. Hence, nutrition by itself will increase the life expectancy of the host population but chemotherapy is needed to reduce the mean worm burden. Seedlings Soybean Seeds maturing consumption carrying capacity available soybean per person per year desired soybean seed per person normal soybean consumption per person per year per capita land requirement Hosts Soybean Seeds replanting maturing fraction planting rate arable land seeds per pod pods per plant maturing fraction rate seed production maturing rate ~ effect of soybean on parasite induced host death rate actual available soybean per person per year ~ effect of soybean supplyon consumption per year actual consuption per person per year

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123 Table 5 4 : Host population at different l evels of protein interventions Time (years) Hosts default from Chapter 4 Hosts base protein Hosts minimum protein Hosts required protein Hosts maximum protein 0 3,500.00 3,500.00 3,500.00 3,500.00 3,500.00 1 3,582.59 3,562.39 3,562.39 3,562.39 3,562.39 2 3,655.87 3,623.19 3,623.77 3,624.97 3,626.63 3 3,714.39 3,682.41 3,684.40 3,688.55 3,694.26 4 3,772.43 3,740.29 3,744.81 3,754.27 3,767.42 5 3,831.36 3,797.36 3,805.83 3,823.74 3,848.17 6 3,891.19 3,854.40 3,868.55 3,898.95 3,929.78 7 3,951.95 3,912.39 3,934.27 3,978.62 4,012.38 8 4,013.65 3,972.43 4,004.45 4,058.33 4,096.17 9 4,076.31 4,035.68 4,080.69 4,138.17 4,181.50 10 4,139.93 4,103.30 4,157.19 4,218.34 4,268.83 11 4,204.53 4,176.45 4,233.20 4,299.20 4,358.76 12 4,270.14 4,251.14 4,309.09 4,381.16 4,451.98 13 4,336.76 4,325.35 4,385.30 4,464.71 4,549.27 14 4,404.41 4,399.53 4,462.29 4,550.30 4,651.59 15 4,473.10 4,474.15 4,540.48 4,638.34 4,760.14 Table 5 5 : Mean worm burden for different levels of protein interventions Time (years) Mean worm burden no intervention Mean worm burden base protein Mean worm burden minimum protein Mean worm burden required protein Mean worm burden maximum protein 0 2.00 2.00 2.00 2.00 2.00 1 21.20 2.47 2.47 2.47 2.47 2 133.58 3.03 3.03 3.03 3.04 3 164.12 3.67 3.68 3.70 3.73 4 164.59 4.40 4.43 4.50 4.59 5 164.64 5.21 5.29 5.45 5.69 6 164.69 6.08 6.24 6.62 7.01 7 164.74 7.01 7.33 8.05 8.57 8 164.79 8.00 8.59 9.66 10.38 9 164.83 9.07 10.12 11.40 12.44 10 164.88 10.28 11.71 13.22 14.77 11 164.92 11.69 13.26 15.05 17.42 12 164.97 13.14 14.68 16.85 20.49 13 165.01 14.42 15.95 18.60 24.18 14 165.05 15.51 17.05 20.33 28.92 15 165.10 16.41 18.01 22.06 35.68

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124 5.4 STELLA integrated population dynamics 5.4.1 Chemotherapy and nutrition The STELLA model for the hosts population is similar to that of Figure 5.3 above. Figure 5.6 illustrates an additional pathogen loss through chemotherapy. The best chemotherapy strategy was found to be treating 50% of the population, every 3 months for 5 years with a drug that was 94% efficacious. This program was adopted for this simulation; only the treatment period was reduced to 2 years. The results in Tables 5.6 and 5.7 show that an additional 219 lives, over the maximum achieved in the above simulation, were s aved and that the worms are virtually eradicated without the rebound seen with chemotherapy alone. It should be noted that the ultimate populations for all types of intervention were similar; this is due to the fact that the carrying capacity has been exce eded as people are living longer and so saturation occurs. This has been observed in malaria eradication programs (Barlow, 1967). Thus it is necessary to promote family planning in conjunction with these interventions. Figure 5 6 : STELLA representation of parasite population illustrating nutrition and chemotherapy

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125 Table 5 6 : Host population at different levels of protein interventions with chemotherapy Time (years) Hosts no intervention Hosts base protein Hosts minimum protein Hosts required protein Hosts maximum protein 0.00 3,500.00 3,500.00 3,500.00 3,500.00 3,500.00 1.00 3,575.52 3,575.52 3,575.52 3,575.52 3,575.52 2.00 3,660.83 3,660.86 3,660.87 3,660.88 3,660.90 3.00 3,748.46 3,748.49 3,748.50 3,748.51 3,748.53 4.00 3,838.17 3,838.21 3,838.22 3,838.24 3,838.27 5.00 3,930.01 3,930.08 3,930.09 3,930.12 3,930.16 6.00 4,024.05 4,024.14 4,024.16 4,024.20 4,024.24 7.00 4,120.31 4,120.44 4,120.47 4,120.53 4,120.58 8.00 4,218.85 4,219.05 4,219.09 4,219.17 4,219.23 9.00 4,319.72 4,320.01 4,320.07 4,320.17 4,320.23 10.00 4,422.97 4,423.38 4,423.47 4,423.58 4,423.65 11.00 4,528.62 4,529.22 4,529.34 4,529.46 4,529.55 12.00 4,636.73 4,637.59 4,637.74 4,637.87 4,637.98 13.00 4,747.32 4,748.55 4,748.72 4,748.87 4,749.00 14.00 4,860.43 4,862.15 4,862.34 4,862.52 4,862.69 15.00 4,976.08 4,978.46 4,978.67 4,978.88 4,979.10 Table 5 7 : Mean worm burden for different levels of protein interventions with chemotherapy Time (years) Mean worm burden no intervention Mean worm burden base protein Mean worm burden minimum protein Mean worm burden required protein Mean worm burden maximum protein 0 2.00 2.00 2.00 2.00 2.00 1 0.07 0.07 0.07 0.07 0.07 2 0.00 0.00 0.00 0.00 0.00 3 0.00 0.00 0.00 0.00 0.00 4 0.00 0.00 0.00 0.00 0.00 5 0.00 0.00 0.00 0.00 0.00 6 0.01 0.01 0.01 0.01 0.01 7 0.01 0.01 0.01 0.01 0.01 8 0.01 0.01 0.01 0.01 0.01 9 0.01 0.01 0.01 0.01 0.01 10 0.01 0.01 0.01 0.01 0.01 11 0.02 0.02 0.02 0.02 0.02 12 0.02 0.02 0.02 0.02 0.02 13 0.03 0.03 0.03 0.03 0.03 14 0.04 0.04 0.04 0.04 0.04 15 0.05 0.05 0.05 0.05 0.05

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126 5.5 Summary and conclusions The aim of this chapter was to model the human population in response to various nutrition regimes and compare vertical interventions of nutrition or deworming, with an integrated program. The following is a summary of the results obtained: Excreta produc tion and nutrient recycling Excreta production provides enough nitrogen to meet the demand of soybean cultivation, and In the first year chemical fertilizer may have to be used to start the project, depending on the fertility of the soil. Nutrition interv ention In the first year, a feeding program will be necessary while the soybean crop matures, Depending on the level on nutrition provided, up to 300 lives can be saved, Nutrition significantly reduces worm burden but was not able to eradicate the worms fr om among the host population, and (Stephenson, 1980) found that when protein deficient hosts were dewormed, growth rates increased 20 35. The simulation found that number of host surviving increase about 11% when supplied with protein. Sustainability and success of integrated program A further 219 lives were saved with the introduction of the chemotherapy program, Compared to chemotherapy only a shorter treatment period is necessary for eradication, for example, only 2 years compared to the 5 previously r ecommended, and

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127 As these programs achieve success the population will expand. To avoid unsustainable population growth, family planning education is also necessary, Eradicating parasitic infection from a community is a balancing act among community resourc es, health and living status. As the nutritional status is improved and worm burden decreased, the population will expand beyond its carrying capacity, which can feed back to cause excess deaths due to scarcity. Thus, in addition to chemotherapy and nutrit ional programs, family planning must also be promoted. While the mean worm burden did not rebound as previously seen in Chapter 4, there was some reinfection (starting in year 6) due to the presence of infectious eggs in the environment. Thus, a latrine intervention is necessary

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128 6 SOLAR HIGH RATE LATRINE 6.1 Background As seen in Chapter 5, fecal material is a valuable resource that can be recycled to lifesaving crop production. However, improper handling and disposal facilitate the transmission of parasitic organisms, which are the cause of approximately 1.5 billion bouts of infectious diarrhea and 3 million deaths annually in children alone (Kosek et al. 2003; Meddings et al. 2004). Therefore, before fecal matter can be used in cr op cultivation, its microbial quality must first be assured. In developing countries the most common methods of excreta sanitation are the drop and store options of latrines, addition of chemicals, and composting (Jimenez, 2007; Langergraber and Muellegg er, 2005; Vinneras et al. 2003a). 6.1.1 Excreta treatment in developing countries Traditionally, pit latrines consisted of an unlined hole in the ground surrounded by a simple cover to provide privacy (Grimason et al. 2000). The Ventilated Improved Pit (VIP) latrine consists of a prefabricated concrete floor over the drop zone, a superstructure, and a ventilation pipe to reduce odor and prevent fly infestations (Cairncross and Feachem, 1983). The latter is being widely promoted and installed in response to the Millennium Development Goal (MDG) of globally reducing the proportion of persons currently without adequate sanitation from 50 to 25% by 2015 (Jimenez et al. 2006; Langergraber and Muellegger 2005). In these systems microbial inactivation is a function of storage time, based on the assumption that most microorganisms die

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129 naturally upon exiting their host and are exposed to harsh environment conditions (Corrales et al. 2006; Jimenez, 2007). However, these systems can become transmission loci where proper hygiene is not practiced resulting in higher incidence of diseases than where open defecation is practiced, can contaminate ground water sources and do not allow for reuse due to high effluent concentrations of resistant pathogens (Banks et al. 2002; Jensen et al. 2005; Vinneras et al. 2003b). Ash or lime is usually added to latrine contents to enhance microbial die off during storage by increasing the pH ( Capizzi Banas et al. 2004 ). While more effective than simply storing, the efficacy of the ashes is contingent on the source of the wood, which limits quality control ( Vinneras et al. 2003a). Effluent quality is more predictable when lime is used, where pH above 12 is guaranteed, but its use can be economically challenging due to high cost ( Cap izzi Banas et al. 2004 ). Sustained temperatures of up to 70 oC, which will deactivate most pathogens, can be achieved in composting systems, but for them to work, specific carbon to nitrogen ratio, moisture contents and aeration rates must be achieved and maintained, that are not possible without specialized knowledge ( Heinonen Tanski and Van Wijk Sijbesma, 2005; Redlinger et al. 2001). In addition, as much as 40% nitrogen and 60% organic carbon can be loss during processing (Fares et al. 2005). 6.1.2 So lar Latrines Most developing countries are located in warm humid climates and receive up to 3000 hours of sunshine per year ( Eggers Lura, 1979). Solar Latrines are therefore particularly suited for countries in the tropics. Solar Latrines are modified VI P latrines which utilize the thermal energy from sunlight to inactivate microbes and were introduced in Central America in the early 1990s. Over the years several updates have been introduced because the systems were not able to achieve and maintain the

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130 el evated temperatures required for inactivation due to several design flaws (Corrales et al. 2006). Earlier versions were poorly oriented to the sun, were constructed under trees which blocked solar insolation, and had vault covers that were opaque to energ y rich light rays (metallic cover that does not allow visible light through). In addition, there has not been a rigorous analysis of the heat transfer that results from solar flux into the vault. 6.1.3 Goals and objectives This portion of the research has two main goals with several accompanying objectives as follows: Design a Solar Latrine and develop a multi physics model for simultaneous heating of and microbial inactivation in latrine contents based on Fouriers and Ficks Laws Propose a new latrine design, Develop solar tables for the study village, and Model heating of latrine contents using Finite Element Method package, COMSOL, to determine if effluent excreta can meet US EPA Class A Biosolids quality standards. Simulate the population response t o a latrine intervention Develop STELLA model to represent latrine intervention, and Model population mean worm burden to combined interventions of chemotherapy, soybean and latrine.

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131 6.2 Solar Latrine design and modeling 6.2.1 Current design description Current S olar Latrines are similar to other VIP designs; in that the liquid fraction of excreta is separated from solids using a urine diverting toilet bowl (see Figure 6 1 ). Urine diversion reduces the emptying frequency and leaching hazard to the ground and sur face waters, and produces effluent with lower moisture contents ( Heinonen Tanski and Van Wijk Sijbesma, 2005 ). Typically, the foundation, envelopes of the vaults and superstructure are made from standard concrete blocks and poured concrete. The latrine and solar vaults are above ground, which reduces the risk of groundwater contamination through seepage. A vent pipe carries off excess odors and prevents fly infestations. Excreta accumulate in a pile in the drop zone and must be manually pushed and shov eled, if access is provided at all. Once a substantial pile builds up, the material is pushed back towards the solar vault for thermal processing. Therefore, both vaults are open to each other, which leads to parasitic heat losses through the toilet pedest al and vent pipe. Sunlight is made up of several types of electromagnetic radiations (Goswami et al. 2000). Thermal radiation is one portion of the radiation spectrum and consists of infrared, visible and ultraviolet wavelengths, and heat up objects on co ntact or is emitted when matter is heated (Ync et al. 1987). Metallic materials are opaque to light in the visible range and incident energy heats first the material before energy is emitted. These energy conversions have associated heat losses. Thus the metallic covers of the current Solar Latrine models are not very efficient at heating the fecal material in the vault below.

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132 Figure 6 1 : Current Solar Latrine design 6.2.2 New Solar Latrine design The proposed design is a modification of the Solar Latrine in Figure 6.1. The major changes included: addition of a drum under the drop zone to collect fecal matter, closing off the solar vault from the drop zone, replacing the metal solar panel with a lig ht transparent glazing, and addition of a water collection system for a hygiene station. Figure 6 2 shows an isometric cut away view of the entire arrangement.

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133 Figure 6 2 : Isometric cut away view of new Solar Latrine design The proposed design has new several features: A 1/8 thick single polycarbonate glazing with shading coefficient of 0.98 (opaque to only 2% of incoming solar energy) was chosen to replace the metal vault panel, is inclined at 29.53o (latitude + 15o) resulting in greater insolat ion

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134 throughout the year ( ASHRAE, 1997 ; Jain and Jain, 2004; Kreider and Kreith, 1981). The solar vault is completely blocked off from the drop zone, instead an access door is constructed thru the side of the latrine vault. The vent pipe is split into a Y entering both vaults (see Figure 6 3 ). The potion entering the solar vault Ts off, running along the entire width and is perforated to prevent short circuiting of air flow over the material being processed. This portion can be removed and the orif ice capped during the heating phase of processing. A 55 gallon cylindrical drum is placed in the drop zone to store excreta during the filling phase, which is removed for treatment and replaced with an empty one once capacity is reached. This promotes sa fer handling of the potentially hazardous material. Once removed from the drop zone, the drum can be opened to form two semicircular troughs; hence it is given the name Solar Processing Trough (SPT). Details are provided in Figure 6 4 A drum cart is provided for easier transfer of SPT from latrine to solar vault. Taking advantage of the high rainfall of the area, a rain collection system is provided for hand washing (after toilet use and SPT handling). This system features a novel PVC chain link water guide, which eliminates the need for cleaning associated with traditional gutters (see Figure 6 5 ). Gravel resulting from concrete construction on the latrine can be placed in the solar vault to form a rock bed to provide heat when the sun is not shining (Fi gure 6 6 ). A rock bed is uni directional heat exchanger, that is, during the day it takes in energy and at night (or sunless days) releases it (Kreider, 1989).

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135 Figure 6 3 : Section view thru new Solar Latrine design Figure 6 4 : Detail view of Solar Processing Trough (SPT)

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136 Figure 6 5 : Side view showing details of water collection system

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137 Figure 6 6 : Plan view of new Solar Latrine showing perforated vent pipe in solar vault 6.2.2.1 Solar Processing Trough (SPT) capacity requirement calculations In rural areas of developing countries, the average adult daily excreta output is 350 g feces and 1.2 kg (0.32 gallons) urine (Feachem et al. 1983). For 4 adult equivalents (2 adult and 4 children) total production is 168 kg (370 lbs) assuming latrine harves ting is carried out every 4 months. Fecal matter is about 80 95% water so the density was taken as 1000 kg/m3. Thus, the volume required is 0.168 m3 (44 gallons). A standard 0.21 m3 (55 gallons) drum was chosen, providing 20% extra volume to allow for addition of ash, soil or other desiccating materials. Using the Manufacturers Standard Gauge for steel sheet (41.82 lbs/ft2/in thickness), a 20 gauge (0.0359 in thick) 55 gallon metal drum weighs approximately 13 kg (28.5 lbs) resulting in total at capac ity weight of 181 kg (398 lbs) which can be readily lifted by two adult men. Based on 0.32 gallon output and allowing for hand washing, the 5 gallon waste water tank needs to be emptied about every 3 days.

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138 6.2.3 Determination of the total instantaneous radiati on on vault glazing Table 6 1 : Symbols used in developing solar tables Symbol Description Units Solar declination angle deg Total instantaneous solar radiation incidence on glazing W/m2 Direct beam radiation W/m2 Diffuse radiation W/m2 Ground reflected radiation W/m2 Beam radiation normal to suns rays W/m2 Extraterrestrial solar radiation W/m2 Solar constant W/m2 Area of vault glazing (solar transparent cover) m2 Ground reflectance [ ] Optical depth [ ] Sky diffusion factor for a given month [ ] The day number [ ] Latitude of the location deg Solar altitude deg Solar azimuth deg Solar hour angle deg Orientation angle of the solar vault deg Angle of incidence of beam radiation on glazing deg Angle of tilt of solar vault panel deg *Standard angular measurements applied, e.g. north is considered positive. The total instantaneous solar radiation () incidence on the vault glazing of area (), is a function of the vault location latitude (), the solar declination (), solar altitude (), solar azimuth (), angle of incidence of beam radiation ( Cos ), ground reflectance (), and weather conditions. Equations and the following discussion can be obtained from any standard solar engineering text and unless otherwise stated were s cI c b I c dI, c rI, N bI, I oI cA ok C n L sa sh wa cIcA L s sa

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139 acquired from Davidson and Chavez (1996), Duffie and Beckman (1974, 1980) Goswami et al. (2000), Kreider and Kreith (1981), Kreider (1989), Kreider and Joint (1975), Kreith and Kreider (1978), Wieder, (1982), Wu et al. ( 1975), and Ync et al. (1987). A conceptual model is presented in Figure 6.7 Figure 6 7 : Conceptual model of solar insolation on a horizontal or inclined surface The total instantaneous solar radiation () incidence on solar panel of area () is given by: [6.1] Where () is the direct beam radiation and is given by: [6.2] Where () is the angle of incidence of the direct beam radiation on the panel is calculated as follows: cIcA c r c d c b cI I II, , c bI, N b c bI Cos I,

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140 [6.3] Where () is the orientation angle of the vault, (when vault is facing south, = 0 ), () is the solar azimuth angle (angle formed on the horizontal plane of the earths surface as it moves across the sky and is measured from the south) and is given as follows: [6.4] Where () is the solar altitude angle at a given time of the day and is computed from the following equation: [6.5] Where () is the latitude of the location under consideration, () the declination angle, which is given by: [6.6] ( ), the solar hour angle and is given by: [6.7] From equation [6.1] (), is the instantaneous solar beam radiation normal to suns rays, given by: [6.8] Where () is the clearness number, () the optical depth, (both a function of weather conditions), () the extraterrestrial solar radiation, which is computed as follows: [6.9] Sin Sin Sin a aCos Cos Cosw s ) ( wawa sa Cos h Sin Cos a Sins s s s s sh Cos Cos L Cos Sin LSin Sin L s ) 284 ( 365 360 45 .23 n Sino s sh ) ( 15 noon solar from hours hour hs N bI, sin / ,ok n N bI C I nC ok I 25 365 360 034 0 1n Cos I Io

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141 Where = 1367 W/m2 is the solar constant (total energy intensity measured just outside the earths atmosphere) and () is the day number corresponding to the date under consideration. Example for January 1st, = 1. From equation [6.1], is the diffused radiation and is given by: [6.10] Where () is the sky diffusion factor for the month in question (function of weather conditions), () is the tilt angle (angle of inclination) of the solar vault glazing (recommended: Latitude of area + 15o). From equation [6.1] () is the ground reflected solar radiation and is given by: [6.11] Where () is the ground reflectance and depends on the surrounding vegetation. Therefore using equations [6.1 6.11] the total solar radiation on the vault can be calculated for every hour of every day of the year, for any location in the world. 6.2.3.1 Solar insolation and climatic data for study village Solar tables were developed for Paquila, Guatemala (latitude 14.53 oN longitude 91.51 oS). An excerpt from solar tables showing hourly solar insolation f or 1 year on surfaces inclined at various angles and facing different directions that were developed in EXCEL using equations [6.1 6.11] is given in Figure 6 8 The calculations were compared with NASAs 22 years monthly averages for accuracy (NASA, 2008). Data for a south facing surface, inclined at 29.53o was abstracted from the tables, while temperature, cloud cover, number of clear sky and no sun days, and rainfall data were retrieved from the NASA website (NASA, 2008). From the data, it was det ermined that the months of May to August had the lowest average solar radiation, zero days of average clear sky days, the highest number of black days and highest rainfall amounts. oI n n c dI, ) 2 / (2 ,Cos IC IN b c d C c rI, ) 2 / (2 , Sin C Sin I IN b c r

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142 Average temperatures were not significantly different from the rest of the year. Data for this four month period were used for model simulation. The complete data set for solar insolation is given in the Appendix C Figure 6 8 : Excerpt from solar insolation tables for Paquila showing data for May 1 6.2.4 Heating and microbial inactivation model development and performance 6.2.4.1 Microbial quality requirements The microbial standard for Class A Biosolids from the US EPAs Part 503 Biosolids Rule was used as the bench mark for effluent quality. The rule requires that biosolids to be appl ied to land must undergo treatment that reduces pathogenic bacteria, enteric viruses and viable helminth ova ( US EPA, 1992 ). The microbial criteria for Class A Biosolids are listed in Table 6.2 and were chosen because once achieved there is no public entry or crop harvest restriction requirement after land application (Lewis and Gattie, 2002).

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143 Table 6 2 : Criteria for meeting Class A requirements (US EPA, 1992) Parameters Limit Units Total fecal coliform 1000 Most Probable Number (MPN)/g Total Solid (TS, dry weight) Salmonella 3 MPN/4g TS Enteric viruses <1 Plaque Forming Units (PFU)/4g TS Helminth/Protozoa <1 Ova/4g TS 6.2.4.2 Process criteria requirements The eggs of helminthes are very resistant to environmental insults (Verle et al. 2003). For example, research has shown that the eggs of Ascaris can withstand temperature ranges 60 65 oC and have been know to remain viable in soil for up to 15 years (Bird and Mcclure, 1976; Fairbairn, 1957; Komiya and Kobayashi, 1965; Wharton, 1979). Recommendations for excreta recycling from double vault latrines in Guatemala have been at least 18 months at temperatures 18 20 oC (Strauss, 1991). Ascaris was therefore the indicator organism of choice for this research. Under laboratory conditions heating to 60 oC for 3 5 minutes was shown to destroy all eggs (Arfaa, 1984). From Figure 6 9 it wa s determined that to achieve Class A requirement for this parameter, a minimum retention time should be about 1 month with a temperature 45 oC. Due to heterogeneity of latrine contents, uncertainty in weather conditions and diurnal variations in solar inso lation, a minimum processing time of 4 months with temperatures up to a maximum of 65 oC was targeted. The underlying assumptions are: these conditions are favorable for the inactivation of Ascaris eggs, if they are destroyed then other pathogenic organis ms will be too and thus, microbial quality of the humanure can be sufficiently assured for agricultural purposes.

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144 Figure 6.9: Processing time required to deactivate microorganisms at specific temperatures (Feachem et al., 1983) 6.2.5 Numerical methods The aim was to model the thermal sanitation of the excreta, to determine the temperature profiles and microbial concentration as a function of treatment time. The problem was set up as a 2D symmetrical transient heat conduction problem for temperature with tr ansport for the destruction of microbes. Two differential equations, connected by the temperature changes in the product, were solved simultaneously in the model, one for heat transfer (equation [6.12]) and one for microbial transport (equation 6.15]) usin g the Finite Element Method. To make use of the symmetry of the container, only half the length of the SPT was modeled (Figure 6 10). The boundary conditions were represented by the convective flux of solar radiation through the vault glazing. All other boundaries were considered to be insulated (Thorvaldsson and Janestad, 1999).

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145 Figure 6 10 : Solar Processing Trough as modeled in COMSOL showing finite e lement s mesh

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146 Table 6 3 : Nomenclature used in numerical modeling Symbols Description Units T Temperature of excreta in SPT K Thermal conductivity of drum material W/m/K Density of fecal matter kg/m 3 Specific heat at constant pressure of fecal matter J/kg/K Concentration of Ascaris eggs in fecal matter (# of microbes)/kg D Diffusivity of Ascaris eggs m 2 /s Microbial inactivation rate mol(#)/m3/s Activation energy kJ/mol R Gas constant J/K/mol Inward heat flux W/m2 Convective heat transfer coefficient of vault air W/m2/K Atmospheric temperature (outside vault) K Uo Overall coefficient of heat transfer W/m2/K A Overall area of the vault m2 6.2.5.1 Heat transfer Equation [6.12] was derived from Fouriers Law for heat conduction to determine the energy balance over a reference element in the product. The temperature T(r, z, t) at position (r, z) at time t was calculated as: = 1 + 2 2 [6.12] The following boundary conditions were applied: = + ( ) [6.13]

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147 The inward heat flux, ( ) is the net of the solar radiation through glazing and the convection gains or losses between vault envelope and ambient air due to temperature differences. This was determined from the following equation (see Table 6.4 below f or definitions): = ( ) + [6.14] 6.2.5.2 Microbial inactivation Equation [6.15] was derived from Ficks Law for mass diffusion to determine concentration of microbes over a reference element in the product. Ascaris eggs are non motile and thus their diffusivity was set to zero, and all boundaries are considered insulated towards diffusion. The microbial concentration c(r, z, t) at position (r, z) at time, ( t ) was calculated as: = 1 + 2 2 = 1 [6.15] 6.2.5.3 Model simulation 2D heat and mass transfer was modeled by solving equations [6.12 6.15] numerically using an unconditionally stable Finite Element Method, Implicit (backward) Euler (Thorvaldsson and Janestad, 1999). The total heating time was 4 months (2952 hours) with time step size 1 second (varying the time step did not cause significant deviations in the results). Input variables are listed in Table 6.4:

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148 Table 6 4 : COMSOL input variables Variable Definition Values T(to) Initial temperature of atmosphere and vault content 295 [K] 22 years of average hourly atmospheric temperature Text file [K] (N ASA 2008) Thermal conductivity of drum material 0.55 [W/m/K] Density of fecal matter 1000 [Kg/m3] Specific heat at constant pressure of material 4200 [J/Kg/K] Activation energy 1.6 *105 [KJ/mol] D Diffusivity of Ascaris eggs 0 [m2/s] R Gas constant 8.314 [KJ/mol/K] 1 Decay rate of microbes 2.31 x 10 21 [/s] Convective heat transfer coefficient 2.36 [W/m 2 /K] (Axaopoulos et al. 2001) SHGC Solar heat gain coefficient for glazing 0.85 [ ] ( ASHRAE 1997) solar_flux Hourly solar insolation on inclined surface, ( ) Text file [W/m2] Heat loss coefficient of concrete envelope of vault 0.44 [KW/m 2 /K] (Axaopoulos et al. 2001) A Area of vault envelope 1.44 [m2] 6.2.5.4 Results and discussion Figure 6 11 shows the temperature fronts at the end of the simulation. Temperatures ranged from 295 343 K (22 70 oC), with an average of 331K (55 oC) at location (0.3, 0.15) of SPT. The diurnal variation in the solar flux drove the temperature variation which is illustrated by Figure 6 12. There was a 2 day lag before required treatment temperatures (55 65 oC) wer e achieved. cI

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149 Figure 6 11 : Surface plot showing temperature fronts at time t = 2900 hours Figure 6 12 : Temperature variation at location (0.3, 0.15) of SPT

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150 At the temperatures that were achieved in the SPT it required at least 3 days before the organisms were totally inactivated and Class A status could be achieved as shown in Figure 6 13 The results of the above simulations indicate that the proposed design is able to safely contain and treat excreta to obtain a parasite free product. Quality a ssurance can be even better if ashes are also added when available. In Japan, where one of the most successful infectious disease program was implemented, sodium nitrite (ovicide) and calcium superphosphate are added to excreta (buffer and fertilizer) to i ncrease egg die off (Komiya and Kunii, 1964). Figure 6 13 : Concentration of microbes at (0.3, 0.15 ) as function of time One of the most effective methods of controlling infectious diseases is to interrupt the developmental cycle and transmission routes of the pathogenic organisms (Webber and Rutala, 2001). Safe stool disposal will keep parasites out of the domestic area fre quented by children, while treating excreta before it is used in crop production will

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151 overtime eliminate the other transmission routes. However, fulfilling this mandate is challenging due to high prevalence rates and the subsequently high concentrations of pathogens that must be inactivated before reuse is possible. In addition the installed systems need to be low cost, very easy and simple to operate in order to be sustainable. The proposed modified Solar Latrine design fulfilled these requirements: The pr ocess is economically sustainable because it utilizes a renewable and freely available source of energy. Compared to traditional pit latrine the investment is not significantly more and the system pays for itself both financially (reduced the need for co mmercial fertilizers) and socially (reduced morbidity and mortality) ( Eggers Lura, 1979 ), Makes use of a technology that is already being use, is embedded into the culture and is thus familiar to individuals. Reduces learning curve and cognitive dissonance associated with learning a new skill, and self efficacy is already in place, Tackles both public health issues to improve nutritional status while preventing infectious diarrheal diseases, The SPT significantly limits the contact between human beings and the hazardous material and makes for easy handling and transportation, This design can be retrofitted to existing latrines, that is, it can be used to update earlier models, In tropical climates there is on average three crop cycles throughout the year. This scheme matches the agronomic rates so farmers are less likely to use unsanitized humanure (Jensen et al. 2005), Innovation can be married to community economy which will increase the likelihood of success and sustainability (create a labor market f or excreta

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152 collection and storage, latrine construction, etc), From an economical perspective the process is virtually volume independent (Caslake et al., 2004), and Unlike synthetic fertilizers (which do not improve soil structure), the nutrients in night soil are slowly released over time, thereby reducing the likelihood of nitrogen and phosphorous groundwater contamination. It also contains an organic carbon fraction which improves soil structure (Jimenez et al. 2006). 6.2.6 Summary In general, however, lat rines are usually abandoned once filled (Simms et al. 2005). This has caused reintroduction of communities into the class of persons without access to improved sanitation and destruction of the latrines as farmers try to get to the contents (Jensen et a l. 2005). The results showed that there is an initial time lag of about 2 days before desired treatment temperatures (55 65 oC) were achieved. Under average solar insolation conditions, the microbial concentration in a familys 170 kg quarterly output can be lowered to US EPA Class A Biosolids levels. May to August is considered the worse solar insolation period and it is from this period that data was abstracted to input into the heating and inactivation model. A 4 month retention time is recommended due to uncertainties in weather conditions especially during the rainy season, which was modeled here. Even so, this is significantly less than the 12 18 months currently prescribed for other latrine systems.

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153 6.3 STELLA modeling of solar latrine and integrated intervention 6.3.1 Solar Latrine intervention Table 6 5 : Symbols used in modeling Solar Latrine intervention Reference symbol Description Units Excessive egg deaths due to latrine 1/time Number of community member using latrine over each retention time host/time Kill rate of latrine per dose; proportion of worms inactivated egg/egg/host 6.3.1.1 Evaluating the stationary egg population assumption In Chapter 4, the assumption that the infective egg population does not change over time because of the relative differences in the life expectancies among the three populations. As a result the differential equation for the egg population was subsumed into that of the parasite. For this simul ation each population is considered separately. Therefore the first trial was to determine if the assumption held. Figures 6.14 6.16 show the populations separated: Figure 6 14 : STELLA model of host population with all three populations separated Parasites host deaths Hosts host births host birth rate host deaths by parasites host natural death rate parasite induced host death rate

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154 Figure 6 15 : STELLA model of parasite population with all three populations separated Figure 6 16 : STELLA model of egg population with all three populations separated Parasites production egg production transmission transmission efficiency losses predator carrying capacity parasite natural death rate host natural death rate parasite induced host death rate worm deaths Hosts clumping parameter egg hatching Hosts contact rate inactivation in environment Infective Egg Population Infective Egg Population egg production loss to host egg production rate egg survival Parasites inactivation in environment Hosts environmental retention time contact rate

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155 6.3.1.2 Results and discussion of stationary egg population assumption From the results in Table 6.6, the final host and mean worm burden are very similar. In the early time periods, there were major differences, but over time equilibrium was established as the rate of change in the egg population goes to zero. Thus, the assumption was indeed accurate and thus previous interventions can be modeled using this method with comparisons possible. Table 6 6 : Comparison of the host population and mean worm burden dynamics in response to assumption Time (years) Host population assumption Mean w orm burden assumption Host population no assumption Mean worm burden no assumption Egg population 0 3,500.00 2.00 3,500.00 2.00 0 1 3,582.59 21.20 3,583.04 9.48 261878.03 2 3,655.87 133.58 3,665.83 31.61 891526.99 3 3,714.39 164.12 3,743.63 90.71 3000086.57 4 3,772.43 164.59 3,810.59 147.68 8420227.56 5 3,831.36 164.64 3,871.58 163.82 13418858.83 6 3,891.19 164.69 3,931.78 167.08 14935372.21 7 3,951.95 164.74 3,992.58 167.70 15245236.81 8 4,013.65 164.79 4,054.24 167.81 15302735.71 9 4,076.31 164.83 4,116.85 167.83 15313012.59 10 4,139.93 164.88 4,180.42 167.84 15314801.11 11 4,204.53 164.92 4,244.97 167.84 15315104.74 12 4,270.14 164.97 4,310.52 167.84 15315155.02 13 4,336.76 165.01 4,377.08 167.84 15315163.15 14 4,404.41 165.05 4,444.67 167.84 15315164.43 15 4,473.10 165.10 4,513.30 167.84 15315164.62 6.3.1.3 Solar Latrine intervention Modeling a Solar Latrine intervention in this manner is entirely new and there was no precedence in literature. Therefore, the effect of the latrine intervention was conceptualized in the following manner:

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156 The Solar Latrines vault is acting as a chemotherapeutic agent, but instead of worms, the target is the eggs, If people are assumed to use the latrine randomly (similar to choosing members to treat randomly), then the excess deaths among the egg population ( ) is given by an equation similar to that equation [4.56] for parasites. Where ( ) is the efficacy of the latrine in deactivating the eggs (assumed to be 99% effective) and ( ) is the number of persons using the latrine over a treatment period, = ln ( 1 ) [6.16] Therefore the solar rate (Figure 6 17 ) is analogous to the chemo rate used for parasites and is the rate at which the latrines remove infective eggs from the environment. Figure 6 17 : STELLA model of egg population with latrine intervention Infective Egg Population egg production loss to host egg production rate egg survival Parasites inactivation in environment Hosts environmental retention time contact rate solar rate latrine rate latrine efficacy proprotion of host using latrine latrine retention time

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157 6.3.1.4 Results and discussion of latrine intervention A variable environmental retention time was added to the model to indicate the life expectancy of the infective stage in the environment and was taken to be about 1 months (0.125). Previously, this was assumed to be 0.1 years, but due to software idiosyncrasies (time steps needing to be 1/2n), this value was chosen. The model was run with all the default values previously used, but for differing number of host using the system. From the results in Figure 6 18 and T ables 6.7 and 6.8, the minimum number of persons required to use the latrine system for eradication to be possible is about 70%, with significant changes in mean worm burdens occurring at 30%. This agrees with ( Muller et al. 1989) who found that at least 20% of household population needs to use latrine to make any difference in fecal contamination. Figure 6 18 : Infective egg, worm and host population and mean worm burden to latrine intervention

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158 Table 6 7 : Response of mean worm burden to different rates of population use in latrine intervention Time (years) Mean worm burden 0% using latrines Mean worm burden 10% using latrines Mean worm burden 30% using latrines Mean worm burden 50% using latrines Mean worm burden 70% using latrines Mean worm burden 90% using latrines 0 2.00 2.00 2.00 2.00 2.00 2.00 1 9.48 8.22 5.83 3.67 2.22 1.80 2 31.61 24.14 12.60 5.32 1.88 1.14 3 90.71 65.69 27.12 7.82 1.61 0.73 4 147.68 121.86 54.83 11.64 1.40 0.48 5 163.82 144.19 89.34 17.44 1.23 0.32 6 167.08 148.90 108.66 26.03 1.10 0.22 7 167.70 149.91 114.44 37.88 0.99 0.15 8 167.81 150.26 116.11 51.90 0.91 0.11 9 167.83 150.48 116.88 64.73 0.84 0.08 10 167.84 150.68 117.46 73.40 0.79 0.06 11 167.84 150.87 118.00 78.08 0.75 0.04 12 167.84 151.05 118.52 80.51 0.73 0.03 13 167.84 151.24 119.03 81.96 0.71 0.03 14 167.84 151.41 119.52 83.02 0.70 0.02 15 167.84 151.59 120.00 83.92 0.70 0.02

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159 Table 6 8 : Response of host population to different rates of population use in latrine intervention Time (years) Host 0% using latrines Host 10% using latrines Host 30% using latrines Host 50% using latrines Host 70% using latrines Host 90% using latrines 0 3,500.00 3,500.00 3,500.00 3,500.00 3,500.00 3,500.00 1 3,583.04 3,583.10 3,583.24 3,583.38 3,583.47 3,583.50 2 3,665.83 3,666.48 3,667.60 3,668.48 3,669.00 3,669.14 3 3,743.63 3,746.95 3,752.10 3,755.22 3,756.63 3,756.93 4 3,810.59 3,819.15 3,834.66 3,843.42 3,846.41 3,846.89 5 3,871.58 3,884.37 3,912.58 3,932.75 3,938.36 3,939.05 6 3,931.78 3,948.11 3,986.09 4,022.71 4,032.55 4,033.44 7 3,992.58 4,012.34 4,058.31 4,112.60 4,129.01 4,130.11 8 4,054.24 4,077.48 4,131.06 4,201.67 4,227.81 4,229.11 9 4,116.85 4,143.61 4,204.83 4,289.58 4,328.98 4,330.50 10 4,180.42 4,210.76 4,279.77 4,376.75 4,432.59 4,434.32 11 4,244.97 4,278.96 4,355.90 4,464.07 4,538.69 4,540.63 12 4,310.52 4,348.21 4,433.24 4,552.26 4,647.34 4,649.50 13 4,377.08 4,418.54 4,511.83 4,641.69 4,758.59 4,760.97 14 4,444.67 4,489.96 4,591.67 4,732.55 4,872.51 4,875.12 15 4,513.30 4,562.48 4,672.79 4,824.91 4,989.15 4,992.01 6.3.2 Simultaneous Solar Latrine and chemotherapy interventions The next step in the modeling process was to add chemotherapy. At first only 27% of the population was treated every 3 months with Albendazole (94% efficacy) for 2 years. The model was then simulated with the proportions of host using the latrine as given above. The results are given in Tables 6.9 and 6.10. The model was then run assuming 50% of the population was treated. These results were given in Tables 6.11 and 6.12.

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160 6.3.2.1 Results and discussion for simultaneous latrine and chemotherapy interventions When both interventions were employed the minimum number of persons required to use the latrine system for eradication to be possible is dropped from 70% to 50%, with significant changes in mean worm burdens again occurring at 30%, and total eradication oc curring in about 6 years at 90% toilet usage. When the number of hosts treated was increased to 50%, the required percent usage dropped to 30% from 50%, however, the ultimate worm burden rebounded to pre control levels. Total eradication was now possible at 70% toilet utilization in as little as 2 years. Significant changes in the number of hosts saved as a result of the addition chemotherapy occurred at lower usages. When the majority of the population started using the latrines, chemotherapy showed a sm aller impact on the hosts life expectancy.

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161 Table 6 9 : Response of mean worm burden to different rates of population use in latrine intervention with 27% of host receiving chemotherapy Time (years) Mean worm burden 0% using latrines Mean worm burden 1 0% using latrines Mean worm burden 30% using latrines Mean worm burden 50% using latrines Mean worm burden 70% using latrines Mean worm burden 90% using latrines 0 2.00 2.00 2.00 2.00 2.00 2.00 1 4.99 4.17 2.68 1.45 0.73 0.54 2 8.75 6.14 2.59 0.80 0.19 0.09 3 30.49 18.88 5.82 1.20 0.16 0.06 4 89.14 53.83 12.92 1.79 0.14 0.04 5 147.52 112.87 28.54 2.73 0.12 0.03 6 163.92 142.51 58.54 4.21 0.11 0.02 7 167.12 148.90 93.92 6.59 0.10 0.01 8 167.71 150.18 111.50 10.44 0.09 0.01 9 167.82 150.56 116.27 16.67 0.08 0.01 10 167.83 150.78 117.62 26.47 0.08 0.00 11 167.84 150.97 118.29 40.65 0.08 0.00 12 167.84 151.15 118.83 57.44 0.07 0.00 13 167.84 151.34 119.33 71.54 0.07 0.00 14 167.84 151.51 119.82 79.61 0.07 0.00 15 167.84 151.68 120.30 83.28 0.07 0.00

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162 Table 6 10 : Response of host population to different rates of population use in latrine intervention with 27% of host receiving chemotherapy Time (years) Host 0% using latrines Host 10% using latrines Host 30% using latrines Host 50% using latrines Host 70% using latrines Host 90% using latrines 0 3,500.00 3,500.00 3,500.00 3,500.00 3,500.00 3,500.00 1 3,583.34 3,583.39 3,583.48 3,583.58 3,583.64 3,583.66 2 3,668.18 3,668.47 3,668.95 3,669.31 3,669.50 3,669.54 3 3,753.08 3,754.42 3,756.20 3,757.11 3,757.45 3,757.51 4 3,833.00 3,838.37 3,844.62 3,846.91 3,847.51 3,847.60 5 3,901.74 3,914.72 3,933.05 3,938.71 3,939.74 3,939.85 6 3,964.18 3,982.62 4,019.11 4,032.47 4,034.18 4,034.31 7 4,025.82 4,048.12 4,099.84 4,128.06 4,130.89 4,131.04 8 4,088.06 4,113.94 4,176.01 4,225.28 4,229.92 4,230.09 9 4,151.20 4,180.65 4,251.13 4,323.71 4,331.32 4,331.52 10 4,215.30 4,248.39 4,326.92 4,422.68 4,435.16 4,435.38 11 4,280.39 4,317.17 4,403.83 4,521.17 4,541.49 4,541.73 12 4,346.49 4,387.01 4,481.95 4,618.09 4,650.37 4,650.63 13 4,413.60 4,457.94 4,561.31 4,713.11 4,761.85 4,762.14 14 4,481.75 4,529.97 4,641.94 4,807.13 4,876.01 4,876.32 15 4,550.96 4,603.12 4,723.86 4,901.46 4,992.91 4,993.25

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163 Table 6 11 : Response of mean worm burden to different rates of population use in latrine intervention with 50% of host receiving chemotherapy Time (years) Mean worm burden 0% using latrines Mean worm burden 10% using latrines Mean worm burden 30% using latrines Mean worm burden 50% using latrines Mean worm burden 70% using latrines Mean worm burden 90% using latrines 0 2.00 2.00 2.00 2.00 2.00 2.00 1 2.16 1.69 0.90 0.35 0.11 0.06 2 1.64 1.01 0.29 0.05 0.00 0.00 3 6.15 3.27 0.67 0.07 0.00 0.00 4 21.12 9.93 1.50 0.10 0.00 0.00 5 67.59 29.97 3.39 0.16 0.00 0.00 6 136.64 79.98 7.77 0.24 0.00 0.00 7 161.86 132.02 17.91 0.38 0.00 0.00 8 166.79 147.37 40.25 0.61 0.00 0.00 9 167.66 150.22 77.74 0.99 0.00 0.00 10 167.81 150.84 107.28 1.63 0.00 0.00 11 167.83 151.09 116.71 2.71 0.00 0.00 12 167.84 151.29 118.92 4.59 0.00 0.00 13 167.84 151.46 119.70 7.87 0.00 0.00 14 167.84 151.64 120.23 13.62 0.00 0.00 15 167.84 151.81 120.70 23.54 0.00 0.00

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164 Table 6 12 : Response of host population to different rates of population use in latrine intervention with 50% of host receiving chemotherapy Time (years) Host 0% using latrines Host 10% using latrines Host 30% using latrines Host 50% using latrines Host 70% using latrines Host 90% using latrines 0 3,500.00 3,500.00 3,500.00 3,500.00 3,500.00 3,500.00 1 3,583.57 3,583.60 3,583.66 3,583.73 3,583.76 3,583.77 2 3,669.21 3,669.32 3,669.50 3,669.63 3,669.69 3,669.70 3 3,756.58 3,756.96 3,757.41 3,757.61 3,757.68 3,757.69 4 3,844.50 3,845.97 3,847.31 3,847.69 3,847.78 3,847.79 5 3,929.29 3,934.84 3,939.12 3,939.93 3,940.04 3,940.05 6 4,003.53 4,019.29 4,032.55 4,034.36 4,034.51 4,034.53 7 4,068.82 4,093.83 4,126.83 4,131.03 4,131.25 4,131.27 8 4,132.30 4,162.33 4,220.13 4,229.98 4,230.31 4,230.32 9 4,196.23 4,230.14 4,309.06 4,331.23 4,331.74 4,331.76 10 4,261.04 4,298.69 4,391.55 4,434.80 4,435.61 4,435.62 11 4,326.84 4,368.26 4,470.91 4,540.66 4,541.96 4,541.98 12 4,393.66 4,438.90 4,550.37 4,648.71 4,650.87 4,650.89 13 4,461.50 4,510.63 4,630.87 4,758.73 4,762.39 4,762.41 14 4,530.39 4,583.48 4,712.62 4,870.29 4,876.58 4,876.60 15 4,600.35 4,657.45 4,795.67 4,982.54 4,993.51 4,993.53 6.3.3 Integrated Solar Latrine, chemotherapy and nutrition interventions The final step in the modeling process was to combine all three interventions. For the first iteration, 27% of the population was treated with anti helminthic medication and nutrition was provided at the required amount of 1.1 g/kg/d. The proportion of the population receiving treatment was then increase to 50% with all other variables except the proportion of persons using latrines remained constant. The results are given in Tables 6.13 and 6.14, and Tables 6.15 and 6.16 respectively.

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165 6.3.3.1 Results and discussion for simultaneous Solar Latrine, chemotherapy, and nutrition interventions Once resources became a limiting factor through the fixed area of arable land counterintuitive results occurred. For example, even while providing optimal nutrition, the worm burden increased above previous numbers for those not having any latrine intervention. This is as a result of hosts dying as the carrying capacity of the land was reached and surpassed. Thus mean worm burden was reduced below 1 worm/host at 50% toilet usa ge and with a reduction in absolute ultimate value (mean worm burden 83.28 to 39.89), however, over 300 more hosts died as a result compared to when intervention with only Solar Latrine and chemotherapy. When the chemotherapy rate was increased to 50% the worm burden decreased by about 100% saving the lives of 271 individuals at 50% latrine usage.

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166 Table 6 13 : Response of mean worm burden to different rates of population use in latrine intervention with 27% of host receiving chemotherapy and all having optimal protein supplement Time (years) Mean worm burden 0% using latrines Mean worm burden 10% using latrines Mean worm burden 30% using latrines Mean worm burden 50% using latrines Mean worm burden 70% using latrines Mean worm burden 90% using latrines 0 2.00 2.00 2.00 2.00 2.00 2.00 1 4.86 4.07 2.63 1.43 0.72 0.53 2 7.96 5.73 2.49 0.78 0.18 0.09 3 20.43 14.83 5.41 1.16 0.16 0.06 4 32.64 26.40 10.86 1.72 0.14 0.04 5 45.49 38.51 19.37 2.58 0.12 0.03 6 53.64 46.83 29.12 3.92 0.11 0.02 7 58.33 51.10 36.07 5.99 0.10 0.01 8 62.73 54.83 39.88 9.12 0.09 0.01 9 67.78 59.01 42.88 13.53 0.08 0.01 10 74.01 64.10 46.03 19.00 0.08 0.00 11 82.01 70.53 49.69 24.61 0.07 0.00 12 92.81 78.98 54.11 29.37 0.07 0.00 13 108.48 90.63 59.61 33.19 0.07 0.00 14 134.18 108.03 66.68 36.53 0.07 0.00 15 188.05 138.01 76.20 39.89 0.07 0.00

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167 Table 6 14 : Response of host population to different rates of population use in latrine intervention with 27% of host receiving chemotherapy and all having optimal protein supplement Time (years) Host 0% using latrines Host 10% using latrines Host 30% using latrines Host 50% using latrines Host 70% using latrines Host 90% using latrines 0 3,500.00 3,500.00 3,500.00 3,500.00 3,500.00 3,500.00 1 3,554.53 3,556.70 3,561.25 3,566.10 3,569.26 3,569.92 2 3,596.59 3,607.90 3,627.69 3,643.11 3,651.48 3,653.29 3 3,603.97 3,637.09 3,691.37 3,724.17 3,737.84 3,740.36 4 3,579.50 3,634.50 3,742.62 3,806.14 3,826.65 3,829.77 5 3,567.54 3,634.53 3,783.99 3,889.40 3,917.87 3,921.47 6 3,569.32 3,646.01 3,821.86 3,974.35 4,011.48 4,015.43 7 3,571.04 3,655.78 3,855.48 4,060.24 4,107.46 4,111.68 8 3,577.25 3,669.25 3,886.59 4,144.07 4,205.77 4,210.25 9 3,589.18 3,687.76 3,919.98 4,224.32 4,306.46 4,311.19 10 3,607.40 3,711.87 3,957.15 4,299.80 4,409.58 4,414.55 11 3,632.44 3,742.07 3,998.65 4,370.60 4,515.19 4,520.40 12 3,664.96 3,778.90 4,044.83 4,438.60 4,623.34 4,628.78 13 3,705.84 3,823.04 4,096.08 4,506.37 4,734.10 4,739.77 14 3,756.38 3,875.37 4,152.83 4,575.93 4,847.52 4,853.42 15 3,818.72 3,937.23 4,215.62 4,648.45 4,963.66 4,969.79

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168 Table 6 15 : Response of mean worm burden to different rates of population use in latrine intervention with 50% of host receiving chemotherapy and all having optimal protein supplement Time (years) Mean worm burden 0% using latrines Mean worm burden 10% using latrines Mean worm burden 30% using latrines Mean worm burden 50% using latrines Mean worm burden 70% using latrines Mean worm burden 90% using latrines 0 2.00 2.00 2.00 2.00 2.00 2.00 1 2.14 1.68 0.90 0.35 0.11 0.06 2 1.62 0.99 0.28 0.04 0.00 0.00 3 5.93 3.21 0.66 0.07 0.00 0.00 4 17.54 9.27 1.47 0.10 0.00 0.00 5 35.66 22.85 3.30 0.16 0.00 0.00 6 49.48 39.35 7.39 0.24 0.00 0.00 7 56.31 48.50 15.87 0.38 0.00 0.00 8 60.91 53.02 28.57 0.60 0.00 0.00 9 65.67 56.94 38.42 0.96 0.00 0.00 10 71.32 61.35 43.48 1.58 0.00 0.00 11 78.40 66.70 47.02 2.62 0.00 0.00 12 87.62 73.39 50.61 4.39 0.00 0.00 13 100.27 82.10 54.78 7.41 0.00 0.00 14 119.04 93.99 59.82 12.41 0.00 0.00 15 151.02 111.51 66.12 19.95 0.00 0.00

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169 Table 6 16 : Response of host population to different rates of population use in latrine intervention with 50% of host receiving chemotherapy and all having optimal protein supplement Time (years) Host 0% using latrines Host 10% using latrines Host 30% using latrines Host 50% using latrines Host 70% using latrines Host 90% using latrines 0 3,500.00 3,500.00 3,500.00 3,500.00 3,500.00 3,500.00 1 3,565.70 3,567.19 3,570.27 3,573.44 3,575.33 3,575.64 2 3,638.74 3,643.75 3,651.95 3,657.92 3,660.78 3,661.24 3 3,706.02 3,719.56 3,736.66 3,745.25 3,748.53 3,749.02 4 3,745.64 3,782.04 3,821.23 3,834.61 3,838.40 3,838.91 5 3,755.16 3,822.68 3,904.65 3,926.06 3,930.43 3,930.96 6 3,758.92 3,845.38 3,985.66 4,019.67 4,024.66 4,025.21 7 3,761.31 3,859.72 4,060.46 4,115.46 4,121.16 4,121.73 8 3,765.92 3,871.97 4,118.99 4,213.25 4,219.98 4,220.56 9 3,775.92 3,888.13 4,161.57 4,312.92 4,321.16 4,321.76 10 3,792.23 3,909.61 4,198.82 4,414.25 4,424.77 4,425.39 11 3,815.37 3,936.94 4,237.83 4,516.87 4,530.86 4,531.50 12 3,845.91 3,970.55 4,280.80 4,620.10 4,639.50 4,640.15 13 3,884.52 4,010.96 4,328.40 4,722.87 4,750.74 4,751.41 14 3,932.13 4,058.81 4,381.04 4,823.53 4,864.65 4,865.34 15 3,990.11 4,114.96 4,439.10 4,919.99 4,981.30 4,982.00

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170 6.4 Summary and conclusions The aim of this chapter was to design a Solar Latrine and model the heating and microbial inactivation process occurring within, and model the response of the host and mean worm burdens to various combinations of Solar Latrine, chemotherapy and nutrition interventions. The following is a summary of the results obtained and a proposition of the most sustainable intervention strategy found: Solar Latrine design and process model As designed, t emperatures of up to 55 65 oC can be achieved and sustained in the solar vault, and A four month retention time is enough to produce US EPA Class A Biosolids from human excreta even under the most solar unfriendly conditions. Vertical and integrated i ntervention strategies Vertical integration of individual strategies may not be enough to sustainably eradicate parasitic disease in an endemic community, Combining strategies does not necessarily produce positive additive effects, Eradication is possible if a least 50% of the host population were treated every 3 months for at least 2 years with a drug of at least 94% efficacy, latrine coverage and usage were at least 70%, and nutrition were provide at about 1.1 g protein per kg (human mass) per day, and Family planning must also be promoted simultaneously.

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171 7 CONCLUSIONS AND FUTURE STUDIES 7.1 Summary Preventable infectious diarrheal diseases claim the lives of and cause a tremendous amount of morbidity in many children living in rural areas of developing countries. These diseases are primarily caused by parasitic organisms transmitted via the fecal oral route. P oor protein nutrition weakens the immune system against infections and their associated morbidity. Given that these challenges have been successfully addressed in developed countries such as the United States, the main thrusts of this research were to determine if they might be similarly solved and what will it take to do so sustainably in the context of a developing community. Current stra tegies include single vertical interventions that address individual causes such as nutritional deficiencies, poor sanitation and the pathogenic organisms. A communitys health, however, results from a confluence of host parasite population and biologic al processes that are facilitated by the physical and social environment in which they occur. This project proposes a systems approach instead. Models representing single and combined interventions were developed to determine if a systems approach could more sustainably eradicate endemic parasitic diseases from a rural community whose livelihood centered on agriculture. That is, the resistance of the model parasite, Ascaris lumbricoides, to various insults (chemotherapy, sanitation and nutrition interventi on) was explored for Paquila, a rural and agricultural community located in the southwestern highlands of Guatemala.

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172 7.2 Limitations and assumptions The results produced here are limited by the scope and associated assumptions. These included: This study is limited to only those infectious disease that are transmitted via the fecal oral route and are cause by parasitic microorganisms, Ascaris was used as an indicator organism because given its ability to resist environmental conditions and association with ot her diarrheal agents. However, this organism has its own biological characteristics that may not be applicable to all diarrhea causing pathogens, It was assumed that all Solar Latrines have the same inactivation rates and performance, in reality this might not be the case, In addition to microorganisms humans also excrete other elements such as heavy metals and pharmaceuticals and personal care products (PCPPs). There is technology being developed that is able to sequester heavy metals using micro organis ms and natural plant extracts. With regards to PCPPs these occur in minute quantities, there limited plant uptake and has not show signs of bioaccumulation or concentration (WHO, 2006), As presented, this model does not allow for increases in land yield due to technological breakthroughs; better seeds, pesticides or new ways of farming. In reality the carrying capacity of arable land has increased due to these factors in recent years, Also the model does not consider that as food shortages occur, planting d ensity will likely increase which will lead to soil degradation and reduced fertility, The carrying capacity of the village was determined by the amount of arable land that was available for crop production only, in reality it is the sum of all the

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173 limiting factors that control the population in the defined area should be consider in the computation. This is therefore a conservative estimate, and For chemotherapy it was assumed that the persons to be treated would be drawn randomly from the population. The re is research that has suggested that treating those more heavily infected individuals may be more effective (Anderson, 1985). 7.3 Findings and conclusions From the STELLA models developed, various what if scenarios and sensitive analysis were conducted. T he major findings and conclusions from the simulations were as follows: The rate determining steps were: life expectancy of the adult worms, rate of egg production and the survival rate of eggs in the environment, T he rate of reinfection to levels observed before chemotherapy was very rapid. Thus, chemotherapy must be accompanied with other strategies and needed to be continually applied for at least 2 years (Croll et al. 1982) It will ideally take at least 2 5 years for dise ase to be sustainably cont rolled However, this is contingent on the ability and willingness of the community to acquire and accept the new skills respectively In general it takes about 1 2 generations for a major technical innovation to become a societal staple. This time can be significantly reduced and the probability of success increased if the intervention dove tails an already established process, such as sun drying of excess agricultural product and sun drying of latrine contents (Spencer et al. 1967).

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174 For the nutriti on intervention, it is important to note that feeding programs must be in place for the first year, independent of soybean cultivation, since it will take about a year before soybeans harvest and excreta production are synchronized, ( Fewtrell et al. 2005 ) found that point of use water availability was very effective in reducing disease incidence. The provision of water supply for washing hands could increase the success of the proposed program, The systems approach was shown to be more sustainable because of the cost effectiveness of utilizing an existing and abundant resources (sunlight), can be easily applied in tandem with current interventions, the community members are empowered by being able to contribute to the solution and by producing their own food, increases independence and socio economic status, and is easily integrated into the communitys social and cultural structure (Coreil et al. 2001) ( Muller et al. 1989) suggested that latrines must be used by at least 20% of the hosts population, which was confirmed by the simulations. H owever to ensure eradication it was observed that 70% usage was required and As the interventions succeed in eradicating the organisms, the population will increase over time, thus birth control methods must also be promoted (Barlow, 1967; Goodman et al. 2006) 7.4 Future studies The models developed in this work could be modified to produce age appropriate effective didactic tools, which could be used to teach students about the link between feces and being sick and how to prevent disease occurrence. The transparent solar vault could be used as an important talking point to start the conversation about fecal matter,

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175 its associated health risk and reuse benefits, a discussion that is currently taboo in many cultures. One very important variable not considered in this study is mat ernal education and its impact on disease and health status of household members. Research has shown that as maternal education increases the fertility rate decreases and the health of children increases drastically (Moore, 2002; United Nations, 1991). In addition this variable is closely linked with socioeconomic status as indicated by the Threshold theory in Chapter 2 (Gorter et al. 1998). It would of interest to determine the minimum level of economic empowerment necessary to encourage the community to address and sustainably solve their own health challenges Drying is an important part of excreta processing, however water and vapor diffusion were not considered here. These physics would help to represent the treatment process more realistically. F uture studies would address this The village of Paquila, Guatemala is ideal for the interventions presented here; has a primary health care system in place, water is available to all and it is in close proximity to the extension services required to start a so ybean program. Success in curtaining this highly visible disease could serve as an entry point into promoting and tackling other community challenges. A successful intervention program here could enable this village to serve as a model community for countl ess others with similar health issues and disease sustaining mechanisms. In addition an actual intervention would substantiate these findings and suggestions, which could then be tailored to the specific needs of a community.

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176 LIST OF REFERENCES Akin, J. E. (1994). Finite Elements for Analysis and Design. Academic Press, San Diego 548 p. Anderson, R. M. (1978). Regulation of Host Population Growth by Parasitic Species." Parasitology 76: 119 57. Anderson, R. M. (1980a). "Depression of Host Population Abundance by Direct Life Cycle Macroparasites." Journal of Theoretical Biology 82: 283 311. Anderson, R. M. (1980b). "The Dynamics and Control of Direct Life Cycle Helminth Parasites." Lecture Notes in Biomathematics 39: 278 322. Anderson, R. M. (1982). The Population Dynamics of Infectious Diseases: Theory and Applications." In: Population and Community Biology Anderson, R. M., R. M. May and P.E.M. Fine (eds.). Springer Verlag, New York, 368 p. Anderson, R. M. (1985). "Mathematical Model s in the Study of the Epidemiology and Control of Ascariasis in Man." In: Ascariasis and Its Public Health Significance Crompton, D. W. T., M. C. Nesh eim, and Z. S. Pawlowski (eds.). Taylor and Francis, Philadelphia, 289 p. Anderson, R. M. (1989). "Transm ission Dynamics of Ascaris Lumbricoides and the Impact of Chemotherapy." In: Ascariasis and Its Prevention and Control Crompton, D. W. T., M. C. Nesh eim, and Z. S. Pawlowski (eds.). Taylor and Francis, New York, 406 p. Anderson, R. M. (1998). "Complex Dynamic Behaviours in the Interaction between Parasite Populations and the Host's Immune System." International Journal for Parasitology 28: 551 66. Anderson, R. M., and D. M. Gordon. (1982). "Processes Influencing the Distribution of Parasite Numbers within Host Populations with Special Emphasis on Parasite Induced Host Mortalities." Parasitology 85: 373 98. Anderson, R. M., and R. M. May. (1978). "Regulation and Stability of Host Parasite Population Interactions: Regulatory Processes." Journal of Animal Ecology 47: 219 47. Anderson, R. M., and R. M. May. (1982). "Population Dynamics of Human Helminth Infections: Control by Chemotherapy." Nature, 297: 557 63.

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195 APPENDICE S

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196 Appendix A Table A 1: Complete breakdown of disease diagnosis at area clinics (Boca Costa Medical Mission, 2004) Disease diagnosis Patients seen/% Emergency 0.10 Encephalopathy 0.10 Hemorrhagia 0.10 Asthma 0.20 Diabetic 0.20 Hepatitis 0.40 Surgical (recommended) 0.40 Seizure disorder 0.60 Hypertension 0.70 Bacterial vaginitis 0.90 Bacterial dysentery 1.40 Ear infection 1.70 Yeast infection 1.80 Allergies 1.90 Preg n ant 2.00 Skin infection : fungal 2.80 Parasite skin (scabies / lice) 3.00 Dentist 3.50 Anemia 3.80 Urinary infection 3.90 Eye infection 4.40 Skin infection : bacterial 4.50 Gastritis 5.00 Amebic dysentery / Gia rdia 9.00 Other: general pain, vitamins, only 10.83 Respiratory infections 16.64 Intestinal (worms) 20.24

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197 Appendix B Table B 1: Host parasite STELLA generated equations from Anderson and May (1978) Hosts(t) = Hosts(t dt) + (host_births host_deaths host_deaths_by_parasites) dt INIT Hosts = 100 {hosts} INFLOWS: host_births = Hosts host_birth_rate {host/time} OUTFLOWS : host_deaths = Hosts host_natural_death_rate {host/time} host_deaths_by_parasites = Parasites parasite_induced__host_death_rate {parasite/time} Parasites(t) = Parasites(t dt) + (production losses predator_carrying__capacity) dt INIT Parasites = 210 {parasites} INFLOWS: production = (egg_production_rate Parasites Hosts) / (transmission_efficiency + Hosts) {parasite/time} OUTFLOWS: losses = (host_natural_death_rate + parasite_natural_death_rate + parasite_induced__host_death_rate) Parasi tes {parasite/time} predator_carrying__capacity = (parasite_induced__host_death_rate Parasites Parasites (clumping_parameter + 1))/ (Hosts *clumping_parameter) {parasites^2/host/time} clumping__parameter = 0.57 clumping_parameter = 2.0 egg_production_rate = 6 {1/time} host_birth_rate = 3.0 {1/time} host_natural_death_rate = 1.0 {1/time} mean_parasite_burden = Parasites/Hosts mean_worm_burden = Parasites/Hosts {worm/host} parasite_induced__host_death_rate = 0.5 {hosts/parasite/time} paras ite_natural_death_rate = 0.1 {1/time} prevalence = 1 (1 + (mean_worm_burden/clumping__parameter))^ clumping__parameter transmission_efficiency = 10 {hosts}

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198 Appendix B (Continued) Table B 2: Host parasite STELLA generated equations for Paquila Hosts(t) = Hosts(t dt) + (host_births host_deaths host_deaths_by_parasites) dt INIT Hosts = 3500 {hosts} INFLOWS: host_births = Hosts host_birth_rate {host/time} OUTFLOWS: host_deaths = Hosts host_natural__death_rate {host/time} host_deaths_by_parasites = Parasites parasite_induced__host_death_rate {host/time} Parasites(t) = Parasites(t dt) + (production losses predator_carrying__capacity) dt INIT Parasites = 7000 {parasites} INFLOWS: production = egg_production_transmission Para sites saturation {worm/time} OUTFLOWS: losses = (host_natural__death_rate + parasite_natural__death_rate + (worm_deaths Parasites)) Parasites {worm/time} predator_carrying__capacity = Parasites parasite_induced__host_death_rate (Parasites Parasites/(clumping__parameter *Hosts Hosts)) {worm/time} clumping__parameter = 0.57 {worm/host} egg__hatching = 0.05 {worm/egg} egg__survival = 0.01 {egg/egg} egg_production__rate = 7300 {egg/worm/year} egg_production_transmission = egg__hatching egg__su rvival egg_production__rate {worm/egg egg/egg egg/worm/time} host_birth_rate = 0.029 {1/year} host_natural__death_rate = 0.00527 {1/year} mean_worm_burden = Parasites/Hosts parasite_induced__host_death_rate = 0.00005 {host/worm/year} parasite_natural__death_rate = 1.15 {1/year} saturation = Hosts/(Hosts + transmission__efficiency) {host/(host+host)} transmission__efficiency = 100 {host} worm_deaths = parasite_induced__host_death_rate/Hosts {1/worm/time}

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199 Appendix B (Continued) Table B 3: STELLA generated equations for population mean with chemotherapy Population__Mean(t) = Population__Mean(t dt) + (acquiring losing chemo) dt INIT Population__Mean = 20 {worm/host} INFLOWS: acquiring = (host_natural_death_rate + parasite_ natural_death_rate) Ro1 Population__Mean {worm/host/time} OUTFLOWS: losing = parasite_induced_host_death_rate Population__Mean (((Population__Mean Population__Mean) /clumping__parameter) + Population__Mean) {worm/host/time} chemo = IF(TIME < 5) THEN(Population__Mean PULSE(chemo_rate,0,treatment__frequency)) ELSE(Population__Mean 0) {worm/host/time} basic_reproductive_rate = 1.5 chemo_rate = LOGN(1 drug_efficacy proportion_treated) clumping__parameter = 0.57 {worm/host} drug_efficacy = 0.9 {worm/worm} host_natural_death_rate = 0.00527 {1/time} parasite_induced_host_death_rate = 0.00005 {host/worm/time} parasite_natural_death_rate = 1.15 {1/time} proportion_treated = 0.27 {host/host} Ro1 = basic_reproductive_rate 1 treatment__frequenc y = 0.33 {every 3 months}

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200 Appendix B (Continued) Table B 4: STELLA generated equations for excreta production Excreta_Storage(t) = Excreta_Storage(t dt) + (emptying_solar_vault_content) dt INIT Excreta_Storage = 0 {kg excreta} INFLOWS: emptying_solar_vault_content = PULSE(Solar_Vault_Excreta, 0.66, solar_vault_retention__time) Hosts(t) = Hosts(t dt) + (host_births host_deaths host_deaths__by_parasites) dt INIT Hosts = 3500 {hosts} INFLOWS: host_births = Hosts host_birth_rate {host/time} OUTFLOWS: host_deaths = Hosts host_natural__death_rate {host/time} host_deaths__by_parasites = Parasites parasite_induced__host_death_rate {host/time} Latrine_Content(t) = Latrine_Content(t dt) + (producing emptying_latrine_content) d t INIT Latrine_Content = 0 {kg excreta} INFLOWS: producing = Hosts excreta_production_rate {kg excreta/year} OUTFLOWS: emptying_latrine_content = PULSE(Latrine_Content, 5/12, latrine__retention_time) Parasites(t) = Parasites(t dt) + (production los ses predator_carrying__capacity) dt INIT Parasites = 7000 {parasites} INFLOWS: production = egg_production_transmission Parasites saturation {worm/time} OUTFLOWS: losses = (host_natural__death_rate + parasite_natural__death_rate + (worm_deaths Parasites)) Parasites {worm/time} predator_carrying__capacity = Parasites parasite_induced__host_death_rate (Parasites Parasites/(clumping__parameter *Hosts Hosts)) {worm/time} Solar_Vault_Excreta(t) = Solar_Vault_Excreta(t dt) + (emptying_lat rine_content emptying_solar_vault_content) dt INIT Solar_Vault_Excreta = 0 {kg} INFLOWS: emptying_latrine_content = PULSE(Latrine_Content, 5/12, latrine__retention_time) OUTFLOWS: emptying_solar_vault_content = PULSE(Solar_Vault_Excreta, 0.66, solar_ vault_retention__time)

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201 Appendix B (Continued) Table B 4 (continued) clumping__parameter = 0.57 {worm/host} egg__hatching = 0.05 {worm/egg} egg__survival = 0.01 {egg/egg} egg_production__rate = 7300 {egg/worm/year} egg_production_transmission = egg__hatching egg__survival egg_production__rate {worm/egg egg/egg egg/worm/time} excreta_production_rate = 0.35 365 {kg excreta/person/day 365 day/year = kg excreta/year} host_birth_rate = 0.029 {1/year} host_natural__death_rate = 0.00527 {1/y ear} latrine__retention_time = 0.33 { 0.33DT = 4months or 1/3year} parasite_induced__host_death_rate = 0.00005 {host/worm/year} parasite_natural__death_rate = 1.15 {1/year} saturation = Hosts/(Hosts + transmission__efficiency) {host/(host+host)} solar_vaul t_retention__time = 0.33 {100% removal} transmission__efficiency = 100 {host} worm_deaths = parasite_induced__host_death_rate/Hosts {1/worm/time}

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202 Appendix B (Continued) Table B 5: STELLA generated equations for the effect of nutrition on hosts survival Hosts(t) = Hosts(t dt) + (host_births host_deaths host_deaths__by_parasites) dt INIT Hosts = 3500 {hosts} INFLOWS: host_births = Hosts host_birth_rate {host/time} OUTFLOWS: host_deaths = Hosts host_natural__death_rate {host/time} host_deaths__by_parasites = Parasites parasite_induced__host_death_rate {host/time} Parasites(t) = Parasites(t dt) + (production losses predator_carrying__capacity) dt INIT Parasites = 7000 {parasites} INFLOWS: production = egg_production_transmission Parasites saturation {worm/time} OUTFLOWS: losses = (host_natural__death_rate + parasite_natural__death_rate + (worm_deaths Parasites)) Parasites {worm/time} predator_carrying__capac ity = Parasites parasite_induced__host_death_rate (Parasites Parasites/(clumping__parameter *Hosts Hosts)) {worm/time} Seedlings(t) = Seedlings(t dt) + (replanting maturing) dt INIT Seedlings = Hosts replanting INFLOWS: replanting = IF(Hosts
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203 Appendix B (Continued) Table B 5 (continued ) actual_consuption_per_person_per_year = normal_soybean_consumption_per_person_per_year effect_of_soybean_supplyon_consumption_per_year arable_land = 1.37 {km^2} available_soybean_per_person__per_year = (Soybean_Seeds/ Hosts) {soybean seeds/person/year} carrying__capacity = arable_land/per_capita_land_requirement {host} clumping__parameter = 0.57 {worm/host} desired__soybean_seed_per_person = 528000 {soybean seeds/person/year} egg__hatching = 0.02 {worm/egg} egg__survival = 0.01 {egg/egg} egg_production__rate = 7300 {egg/worm/year} egg_production_transmission = egg__hatching egg__survival egg_production__rate {worm/egg egg/egg egg/worm/time} host_birth_rate = 0.029 {1/year} host_natural__death_rate = 0.00527 {1/year} maturing__fraction = 0.45 matur ing__fraction_rate = maturing__fraction/maturing_rate maturing_rate = 4/12 {years} mean_worm_burden = Parasites/Hosts normal_parasite_induced_host_death_rate = 0.00005 {host/worm/year} normal_soybean_consumption_per_person_per_year = 528000 {soybean seeds/ person/year} parasite_induced__host_death_rate = normal_parasite_induced_host_death_rate *effect_of_soybean__on_parasite_induced_host_death_rate {host/worm/year} parasite_natural__death_rate = 1.15 {1/year} per_capita_land_requirement = 3.661E 4 {km^2/host } planting_rate = 0 pods_per_plant = 35 {pods/plant} prevalence = 1 (1+(mean_worm_burden/clumping__parameter))^( clumping__parameter) saturation = Hosts/(Hosts + transmission__efficiency) {host/(host+host)} seed__production = pods_per_plant seeds_per_pod seeds_per_pod = 3 {seeds/pod} transmission__efficiency = 100 {host} worm_deaths = parasite_induced__host_death_rate/Hosts {1/worm/time} effect_of_soybean__on_parasite_induced_host_death_rate = GRAPH(actual_available_soybean_per_person__per_year / desired__soybean_seed_per_person) (0.00, 100), (0.2, 10.0), (0.4, 0.1), (0.6, 0.01), (0.8, 0.001), (1, 0.001), (1.20, 0.001), (1.40, 0.001)

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204 Appendix B (Continued) Table B 5 (continued ) effect_of_soybean_supplyon_consumption_per_year = GRAPH(actual_available_soybean_per_person__per_year / desired__soybean_seed_per_person) (0.00, 0.00), (0.2, 0.2), (0.4, 0.3), (0.6, 0.4), (0.8, 0.5), (1.00, 1.00), (1.20, 2.00), (1.40, 3.00), (1.60, 5.00), (1.80, 10.0), (2.00, 20.0)

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205 Appendix B (Continued) Table B 6: STELLA generated equations for the effect of nutrition and chemo on hosts survival Hosts(t) = Hosts(t dt) + (host_births host_deaths host_deaths__by_parasites) dt INIT Hosts = 3500 {hosts} INFLOWS: host_births = Hosts host_bir th_rate {host/time} OUTFLOWS: host_deaths = Hosts host_natural__death_rate {host/time} host_deaths__by_parasites = Parasites parasite_induced__host_death_rate {host/time} Parasites(t) = Parasites(t dt) + (production losses predator_carrying__capacity chemo) dt INIT Parasites = 7000 {parasites} INFLOWS: production = egg_production_transmission Parasites saturation {worm/time} OUTFLOWS: losses = (host_natural__death_rate + parasite_natural__death_rate + (worm_deaths Parasites)) Parasites {worm/time} predator_carrying__capacity = Parasites parasite_induced__host_death_rate (Parasites Parasites/(clumping__parameter *Hosts Hosts)) {worm/time} chemo = IF(TIME < 2) THEN(Parasites PULSE(chemo_rate,0,treatment _frequency)) ELSE(Parasites 0) {worm/time} Seedlings(t) = Seedlings(t dt) + (replanting maturing) dt INIT Seedlings = Hosts replanting INFLOWS: replanting = IF(Hosts
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206 Appendix B (Continued) Table B 6 (continued) OUTFLOWS: consumption = actual_consuption_per_person_per_year actual_available_soybean_per_person__per_year = min (available_soybean_per_person__per_year, desired__soybean_seed_per_person) {trees/person} actual_consuption_per_person_per_year = normal_soybean_consumption_per_person_per_year effect_of_soybean_supplyon_consumption_per_year arable_land = 1.37 {km^2} ava ilable_soybean_per_person__per_year = (Soybean_Seeds/ Hosts) {soybean seeds/person/year} carrying__capacity = arable_land/per_capita_land_requirement {host} chemo_rate = LOGN(1 drug__efficacy proportion_treated) clumping__parameter = 0.57 {worm/host } desired__soybean_seed_per_person = 528000 {soybean seeds/person/year} drug__efficacy = 0.94 {worm/worm} egg__hatching = 0.02 {worm/egg} egg__survival = 0.01 {egg/egg} egg_production__rate = 7300 {egg/worm/year} egg_production_transmission = egg__hatching egg__survival egg_production__rate {worm/egg egg/egg egg/worm/time} host_birth_rate = 0.029 {1/year} host_natural__death_rate = 0.00527 {1/year} maturing__fraction = 0.45 maturing__fraction_rate = maturing__fraction/maturing_rate maturing_rate = 4 /12 {years} mean_worm_burden = Parasites/Hosts normal_parasite_induced_host_death_rate = 0.00005 {host/worm/year} normal_soybean_consumption_per_person_per_year = 528000 {soybean seeds/person/year} parasite_induced__host_death_rate = normal_parasite_induce d_host_death_rate *effect_of_soybean__on_parasite_induced_host_death_rate {host/worm/year} parasite_natural__death_rate = 1.15 {1/year} per_capita_land_requirement = 3.661E 4 {km^2/host} planting_rate = 0 pods_per_plant = 35 {pods/plant} prevalence = 1 (1+ (mean_worm_burden/clumping__parameter))^( clumping__parameter) proportion_treated = 0.5 {host/host} saturation = Hosts/(Hosts + transmission__efficiency) {host/(host+host)} seed__production = pods_per_plant seeds_per_pod seeds_per_pod = 3 {seeds/pod} tra nsmission__efficiency = 100 {host} treatment_frequency = 0.25 {every 3 months}

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207 Appendix B (Continued) Table B 6 (continued) worm_deaths = parasite_induced__host_death_rate/Hosts {1/worm/time} effect_of_soybean__on_parasite_induced_host_death_rate = GRAPH(actual_available_soybean_per_person__per_year / desired__soybean_seed_per_person) (0.00, 100), (0.2, 10.0), (0.4, 0.1), (0.6, 0.001), (0.8, 0.001), (1, 0.001), (1.20, 0.001), (1.40, 0.001) ef fect_of_soybean_supplyon_consumption_per_year = GRAPH(actual_available_soybean_per_person__per_year / desired__soybean_seed_per_person) (0.00, 0.00), (0.2, 0.2), (0.4, 0.3), (0.6, 0.4), (0.8, 0.5), (1.00, 1.00), (1.20, 2.00), (1.40, 3.00), (1.60, 5.00), ( 1.80, 10.0), (2.00, 20.0)

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208 Appendix B (Continued) Table B 7: STELLA generated equations for all three populations separated Hosts(t) = Hosts(t dt) + (host_births host_deaths host_deaths_by_parasites) dt INIT Hosts = 3500 {hosts} INFLOWS: host_births = Hosts host_birth_rate {host/time} OUTFLOWS: host_deaths = Hosts host_natural__death_rate {host/time} host_deaths_by_parasites = Parasites parasite_induced__host_death_rate {host/time} Infective_Egg__Population(t) = Infective_Egg__Popul ation(t dt) + (egg_production loss_to_host inactivation_in__environment) dt INIT Infective_Egg__Population = 0 INFLOWS: egg_production = egg__survival*egg_production__rate*Parasites {egg/year} OUTFLOWS: loss_to_host = contact_rate*Infective_Egg__P opulation*Hosts inactivation_in__environment = egg__survival/environmental_retention__time Parasites(t) = Parasites(t dt) + (production losses predator_carrying__capacity) dt INIT Parasites = 7000 {parasites} INFLOWS: production = egg_production_t ransmission*Infective_Egg__Population*Hosts {worm/time} OUTFLOWS: losses = (host_natural__death_rate + parasite_natural__death_rate + (worm_deaths Parasites)) Parasites {worm/time} predator_carrying__capacity = Parasites parasite_induced__host_death_rate (Parasites Parasites/(clumping__parameter *Hosts Hosts)) {worm/time} clumping__parameter = 0.57 {worm/host} contact_rate = inactivation_in__environment/transmission__efficiency egg__hatching = 0.05 {worm/egg} egg__su rvival = 0.01 {egg/egg} egg_production__rate = 7300 {egg/worm/year} egg_production_transmission = egg__hatching* contact_rate {worm/egg egg/egg egg/worm/time} environmental_retention__time = 0.125 host_birth_rate = 0.029 {1/year} host_natural__death_rate = 0.00527 {1/year} mean_worm_burden = Parasites/Hosts parasite_induced__host_death_rate = 0.00005 {host/worm/year} parasite_natural__death_rate = 1.15 {1/year} transmission__efficiency = 100 {host} worm_deaths = parasite_induced__host_death_rate/Hosts { 1/worm/time}

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209 Appendix B (Continued) Table B 8: STELLA generated equations for hosts population response to latrine intervention Hosts(t) = Hosts(t dt) + (host_births host_deaths host_deaths_by_parasites) dt INIT Hosts = 3500 {hosts} INFLOWS: host_births = Hosts host_birth_rate {host/time} OUTFLOWS: host_deaths = Hosts host_natural__death_rate {host/time} host_deaths_by_parasites = Parasites parasite_induced__host_death_rate {host/time} Infective_Egg__Population(t) = Infective_Egg__Population(t dt) + (egg_production loss_to_host inactivation_in__environment solar_rate) dt INIT Infective_Egg__Population = 260610 INFLOWS: egg_production = egg__survival*egg_production__rate*Parasites {egg/year} OUTFLOWS: loss_to_host = contact_rate*Infective_Egg__Population*Hosts inactivation_in__environment = egg__survival/environmental_retention__time solar_rate = IF(TIME<15) THEN(Infective_Egg__Population*PULSE(latrine_rate,0,latrine__retention_time)) ELSE(Infective_Egg__Population*0) Parasites(t) = Parasites(t dt) + (production losses predator_carrying__capacity) dt INIT Parasites = 7000 {parasites} INFLOWS: production = egg_production_transmission*Infective_Egg__Population*Hosts {worm/time} OUTFLOWS: losses = (host_natural__death_rate + parasite_natural__death_rate + (worm_deaths Parasites)) Parasites {worm/time} predator_carrying__capacity = Parasites parasite_induced__host_death_rate (Parasites Parasites/(clumping__parameter *Hosts Hosts)) {worm/t ime} clumping__parameter = 0.57 {worm/host} contact_rate = inactivation_in__environment/transmission__efficiency egg__hatching = 0.05 {worm/egg} egg__survival = 0.01 {egg/egg} egg_production__rate = 7300 {egg/worm/year} egg_production_transmission = egg__hatching* contact_rate {worm/egg egg/egg egg/worm/time} environmental_retention__time = 0.125 host_birth_rate = 0.029 {1/year}

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210 Appendix B (Continued) Table B 8 (continued) host_natural__death_rate = 0.00527 {1/year} latrine__retention_time = 0.25 latrine_efficacy = 0.99 latrine_rate = LOGN(1latrine_efficacy*proprotion_of__host_using_latrine) mean_worm_burden = Parasites/Hosts parasite_induced__host_death_rate = 0.00005 {host/worm/year} parasite_natural__death_rate = 1.15 {1/year} proprotion_of__host_using_latrine = 0.4 {host/host} transmission__efficiency = 100 {host} worm_deaths = parasite_induced__host_death_rate/Hosts {1/worm/time}

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211 Appendix B (Continued) Table B 9: STELLA generated equations for hosts population response to latrine and chemo interventions Hosts(t) = Hosts(t dt) + (host_births host_deaths host_deaths_by_parasites) dt INIT Hosts = 3500 {hosts} INFLOWS: host_births = Hosts host_birth_rate {host/t ime} OUTFLOWS: host_deaths = Hosts host_natural__death_rate {host/time} host_deaths_by_parasites = Parasites parasite_induced__host_death_rate {host/time} Infective_Egg__Population(t) = Infective_Egg__Population(t dt) + (egg_production loss_to_host inactivation_in__environment solar_latrine) dt INIT Infective_Egg__Population = 260610 INFLOWS: egg_production = egg__survival*egg_production__rate*Parasites {egg/year} OUTFLOWS: loss_to_host = contact_rate*Infective_Egg__Population*Hosts inacti vation_in__environment = egg__survival/environmental_retention__time solar_latrine = IF(TIME<15) THEN(Infective_Egg__Population*PULSE(latrine_rate,0,latrine__retention_time)) ELSE(Infective_Egg__Population*0) Parasites(t) = Parasites(t dt) + (production losses predator_carrying__capacity chemo) dt INIT Parasites = 7000 {parasites} INFLOWS: production = egg_production_transmission*Infective_Egg__Population*Hosts {worm/time} OUTFLOWS: losses = (host_natural__death_rate + parasite_natural__death_r ate + (worm_deaths Parasites)) Parasites {worm/time} predator_carrying__capacity = Parasites parasite_induced__host_death_rate (Parasites Parasites/(clumping__parameter *Hosts Hosts)) {worm/time} chemo = IF(TIME < 2) THEN(Parasites PULSE(chemo_rate,0,treatment_frequency)) ELSE(Parasites 0) {worm/time} chemo_rate = LOGN(1 drug__efficacy proportion_treated) clumping__parameter = 0.57 {worm/host} contact_rate = inactivation_in__environment/transmission__efficiency drug__efficacy = 0.94 {worm/worm} egg__hatching = 0.05 {worm/egg}

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212 Appendix B (Continued) Table B 9 (continued) egg__survival = 0.01 {egg/egg} egg_production__rate = 7300 {egg/worm/year} egg_production_transmission = egg__hatching* contact_rate {worm/egg egg/egg egg/worm/time} environmental_retention__time = 0.125 host_birth_rate = 0.029 {1/year} host_natural__death_rate = 0.00527 {1/year} latrine__retention_time = 0.25 latrine_efficacy = 0.99 latrine_rate = LOGN(1latrine_efficacy*proprotion_of__host_using_latri ne) mean_worm_burden = Parasites/Hosts parasite_induced__host_death_rate = 0.00005 {host/worm/year} parasite_natural__death_rate = 1.15 {1/year} proportion_treated = 0.50 {host/host} proprotion_of__host_using_latrine = 0.4 transmission__efficiency = 100 {h ost} treatment_frequency = 0.25 {every 3 months} worm_deaths = parasite_induced__host_death_rate/Hosts {1/worm/time}

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213 Appendix B (Continued) Table B 10: STELLA generated equations for hosts population response to latrine, chemo and nutrition interventions Hosts(t) = Hosts(t dt) + (host_births host_deaths host_deaths_by_parasites) dt INIT Hosts = 3500 {hosts} INFLOWS: host_births = Hosts host_birth_r ate {host/time} OUTFLOWS: host_deaths = Hosts host_natural__death_rate {host/time} host_deaths_by_parasites = Parasites parasite_induced__host_death_rate {host/time} Infective_Egg__Population(t) = Infective_Egg__Population(t dt) + (egg_production loss_to_host inactivation_in__environment solar_latrine) dt INIT Infective_Egg__Population = 260610 INFLOWS: egg_production = egg__survival*egg_production__rate*Parasites {egg/year} OUTFLOWS: loss_to_host = contact_rate*Infective_Egg__Population*H osts inactivation_in__environment = egg__survival/environmental_retention__time solar_latrine = IF(TIME<15) THEN(Infective_Egg__Population*PULSE(latrine_rate,0,latrine__retention_time)) ELSE(Infective_Egg__Population*0) Parasites(t) = Parasites(t dt) + (production losses predator_carrying__capacity chemo) dt INIT Parasites = 7000 {parasites} INFLOWS: production = egg_production_transmission*Infective_Egg__Population*Hosts {worm/time} OUTFLOWS: losses = (host_natural__death_rate + parasite_natur al__death_rate + (worm_deaths Parasites)) Parasites {worm/time} predator_carrying__capacity = Parasites parasite_induced__host_death_rate (Parasites Parasites/(clumping__parameter *Hosts Hosts)) {worm/time} chemo = IF(TIME < 2) THEN(Parasites PULSE(chemo_rate,0,treatment_frequency)) ELSE(Parasites 0) {worm/time} Seedlings(t) = Seedlings(t dt) + (replanting maturing) dt INIT Seedlings = Hosts replanting

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214 Appendix B (Continued) Table B 10 (continued) INFLOWS: replanting = IF(Hosts
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215 Appendix B (Continued) Table B 10 (continued) mean_worm_burden = Parasites/Hosts normal_parasite_induced_host_death_rate = 0.00005 {host/worm/year} normal_soybean_consumption_per_person_per_year = 528000 {soybean seeds/ person/year} parasite_induced__host_death_rate = normal_parasite_induced_host_death_rate effect_of_soybean__on_parasite_induced_host_death_rate {host/worm/year} parasite_natural__death_rate = 1.15 {1/year} per_capita_land_requirement = 3.661E 4 {km^2/host} planting_rate = 11175 pods_per_plant = 35 {pods/plant} proportion_treated = 0.5 {host/host} proprotion_of__host_using_latrine = 0.4 seed__production = pods_per_plant seeds_per_pod seeds_per_pod = 3 {seeds/pod} transmission__efficiency = 100 {host} treatment_frequency = 0.25 {every 3 months} worm_deaths = parasite_induced__host_death_rate/Hosts {1/worm/time} effect_of_soybean__on_parasite_induced_host_death_rate = GRAPH(actual_available_soybean_per_person__per_year / desired__soybean_seed_per_person ) (0.00, 100), (0.2, 10.0), (0.4, 0.1), (0.6, 0.001), (0.8, 0.001), (1, 0.001), (1.20, 0.001), (1.40, 0.001) effect_of_soybean_supplyon_consumption_per_year = GRAPH(actual_available_soybean_per_person__per_year / desired__soybean_seed_per_person) (0.00, 0 .00), (0.2, 0.2), (0.4, 0.3), (0.6, 0.4), (0.8, 0.5), (1.00, 1.00), (1.20, 2.00), (1.40, 3.00), (1.60, 5.00), (1.80, 10.0), (2.00, 20.0)

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216 Appendix C Table C 1: Solar incidence radiation on the south facing Solar Latrine panel in Paquila, Guatemala for the months May to August Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 1 0 41 0 81 432 121 0 2 0 42 0 82 589 122 0 3 0 43 0 83 691 123 0 4 0 44 0 84 726 124 0 5 0 45 0 85 691 125 0 6 1 46 0 86 589 126 1 7 72 47 0 87 432 127 73 8 245 48 0 88 245 128 246 9 431 49 0 89 73 129 434 10 587 50 0 90 1 130 590 11 689 51 0 91 0 131 693 12 724 52 0 92 0 132 728 13 689 53 0 93 0 133 693 14 587 54 1 94 0 134 590 15 431 55 73 95 0 135 434 16 245 56 245 96 0 136 246 17 72 57 432 97 0 137 73 18 1 58 588 98 0 138 1 19 0 59 690 99 0 139 0 20 0 60 725 100 0 140 0 21 0 61 690 101 0 141 0 22 0 62 588 102 1 142 0 23 0 63 432 103 73 143 0 24 0 64 245 104 246 144 0 25 0 65 73 105 433 145 0 26 0 66 1 106 589 146 0 27 1 67 0 107 692 147 0 28 73 68 0 108 727 148 1 29 245 69 0 109 692 149 73 30 431 70 0 110 589 150 246 31 587 71 0 111 433 151 434 32 689 72 0 112 246 152 591 33 725 73 0 113 73 153 694 34 689 74 0 114 1 154 729 35 587 75 0 115 0 155 694 36 431 76 0 116 0 156 591 37 245 77 0 117 0 157 434 38 73 78 1 118 0 158 246 39 1 79 73 119 0 159 73 40 0 80 245 120 0 160 1

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217 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 161 0 201 436 241 0 281 73 162 0 202 593 242 0 282 1 163 0 203 696 243 0 283 0 164 0 204 731 244 0 284 0 165 0 205 696 245 0 285 0 166 0 206 593 246 1 286 0 167 0 207 436 247 73 287 0 168 0 208 247 248 248 288 0 169 0 209 73 249 437 289 0 170 0 210 1 250 595 290 0 171 0 211 0 251 698 291 0 172 0 212 0 252 734 292 0 173 0 213 0 253 698 293 0 174 1 214 0 254 595 294 1 175 73 215 0 255 437 295 73 176 247 216 0 256 248 296 249 177 435 217 0 257 73 297 439 178 592 218 0 258 1 298 597 179 695 219 0 259 0 299 701 180 730 220 0 260 0 300 736 181 695 221 0 261 0 301 701 182 592 222 1 262 0 302 597 183 435 223 73 263 0 303 439 184 247 224 248 264 0 304 249 185 73 225 436 265 0 305 73 186 1 226 594 266 0 306 1 187 0 227 697 267 0 307 0 188 0 228 732 268 0 308 0 189 0 229 697 269 0 309 0 190 0 230 594 270 1 310 0 191 0 231 436 271 73 311 0 192 0 232 248 272 249 312 0 193 0 233 73 273 438 313 0 194 0 234 1 274 596 314 0 195 0 235 0 275 699 315 0 196 0 236 0 276 735 316 0 197 0 237 0 277 699 317 0 198 1 238 0 278 596 318 1 199 73 239 0 279 438 319 74 200 247 240 0 280 249 320 250

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218 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 321 440 361 0 401 74 441 445 322 598 362 0 402 1 442 605 323 702 363 0 403 0 443 710 324 738 364 0 404 0 444 746 325 702 365 1 405 0 445 710 326 598 366 74 406 0 446 605 327 440 367 251 407 0 447 445 328 250 368 442 408 0 448 253 329 74 369 601 409 0 449 74 330 1 370 705 410 0 450 1 331 0 371 741 411 0 451 0 332 0 372 705 412 0 452 0 333 0 373 601 413 0 453 0 334 0 374 442 414 1 454 0 335 0 375 251 415 74 455 0 336 0 376 74 416 252 456 0 337 0 377 1 417 444 457 0 338 0 378 0 418 604 458 0 339 0 379 0 419 708 459 0 340 0 380 0 420 744 460 0 341 0 381 0 421 708 461 0 342 1 382 0 422 604 462 1 343 74 383 0 423 444 463 74 344 250 384 0 424 252 464 253 345 441 385 0 425 74 465 446 346 600 386 0 426 1 466 607 347 703 387 0 427 0 467 712 348 739 388 0 428 0 468 748 349 703 389 0 429 0 469 712 350 600 390 1 430 0 470 607 351 441 391 74 431 0 471 446 352 250 392 251 432 0 472 253 353 74 393 443 433 0 473 74 354 1 394 602 434 0 474 1 355 0 395 707 435 0 475 0 356 0 396 743 436 0 476 0 357 0 397 707 437 0 477 0 358 0 398 602 438 1 478 0 359 0 399 443 439 74 479 0 360 0 400 251 440 253 480 0

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219 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 481 0 521 75 561 451 601 0 482 0 522 0 562 613 602 0 483 0 523 0 563 719 603 0 484 0 524 0 564 755 604 0 485 0 525 0 565 719 605 0 486 1 526 0 566 613 606 0 487 74 527 0 567 451 607 75 488 254 528 0 568 256 608 258 489 447 529 0 569 75 609 453 490 608 530 0 570 0 610 617 491 713 531 0 571 0 611 723 492 750 532 0 572 0 612 759 493 713 533 0 573 0 613 723 494 608 534 0 574 0 614 617 495 447 535 75 575 0 615 453 496 254 536 255 576 0 616 258 497 74 537 450 577 0 617 75 498 1 538 612 578 0 618 0 499 0 539 717 579 0 619 0 500 0 540 753 580 0 620 0 501 0 541 717 581 0 621 0 502 0 542 612 582 0 622 0 503 0 543 450 583 75 623 0 504 0 544 255 584 257 624 0 505 0 545 75 585 452 625 0 506 0 546 0 586 615 626 0 507 0 547 0 587 721 627 0 508 0 548 0 588 757 628 0 509 0 549 0 589 721 629 0 510 0 550 0 590 615 630 0 511 75 551 0 591 452 631 75 512 255 552 0 592 257 632 258 513 448 553 0 593 75 633 455 514 610 554 0 594 0 634 618 515 715 555 0 595 0 635 725 516 751 556 0 596 0 636 761 517 715 557 0 597 0 637 725 518 610 558 0 598 0 638 618 519 448 559 75 599 0 639 455 520 255 560 256 600 0 640 258

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220 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 641 75 681 458 721 0 761 75 642 0 682 622 722 0 762 0 643 0 683 729 723 0 763 0 644 0 684 766 724 0 764 0 645 0 685 729 725 0 765 0 646 0 686 622 726 0 766 0 647 0 687 458 727 76 767 0 648 0 688 260 728 261 768 0 649 0 689 76 729 460 769 0 650 0 690 0 730 626 770 0 651 0 691 0 731 733 771 0 652 0 692 0 732 770 772 0 653 0 693 0 733 733 773 0 654 0 694 0 734 626 774 0 655 75 695 0 735 460 775 75 656 259 696 0 736 261 776 261 657 456 697 0 737 76 777 461 658 620 698 0 738 0 778 627 659 727 699 0 739 0 779 735 660 764 700 0 740 0 780 772 661 727 701 0 741 0 781 735 662 620 702 0 742 0 782 627 663 456 703 76 743 0 783 461 664 259 704 261 744 0 784 261 665 75 705 459 745 0 785 75 666 0 706 624 746 0 786 0 667 0 707 731 747 0 787 0 668 0 708 768 748 0 788 0 669 0 709 731 749 0 789 0 670 0 710 624 750 0 790 0 671 0 711 459 751 75 791 0 672 0 712 261 752 260 792 0 673 0 713 76 753 459 793 0 674 0 714 0 754 625 794 0 675 0 715 0 755 733 795 0 676 0 716 0 756 770 796 0 677 0 717 0 757 733 797 0 678 0 718 0 758 625 798 0 679 76 719 0 759 459 799 75 680 260 720 0 760 260 800 262

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221 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 801 462 841 0 881 75 921 470 802 629 842 0 882 0 922 639 803 737 843 0 883 0 923 749 804 774 844 0 884 0 924 786 805 737 845 0 885 0 925 749 806 629 846 0 886 0 926 639 807 462 847 75 887 0 927 470 808 262 848 264 888 0 928 266 809 75 849 465 889 0 929 76 810 0 850 633 890 0 930 0 811 0 851 742 891 0 931 0 812 0 852 779 892 0 932 0 813 0 853 742 893 0 933 0 814 0 854 633 894 0 934 0 815 0 855 465 895 76 935 0 816 0 856 264 896 265 936 0 817 0 857 75 897 468 937 0 818 0 858 0 898 637 938 0 819 0 859 0 899 746 939 0 820 0 860 0 900 784 940 0 821 0 861 0 901 746 941 0 822 0 862 0 902 637 942 0 823 75 863 0 903 468 943 76 824 263 864 0 904 265 944 267 825 464 865 0 905 76 945 471 826 631 866 0 906 0 946 641 827 739 867 0 907 0 947 751 828 777 868 0 908 0 948 789 829 739 869 0 909 0 949 751 830 631 870 0 910 0 950 641 831 464 871 75 911 0 951 471 832 263 872 264 912 0 952 267 833 75 873 467 913 0 953 76 834 0 874 635 914 0 954 0 835 0 875 744 915 0 955 0 836 0 876 782 916 0 956 0 837 0 877 744 917 0 957 0 838 0 878 635 918 0 958 0 839 0 879 467 919 76 959 0 840 0 880 264 920 266 960 0

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222 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 961 0 1001 76 1041 478 1081 0 962 0 1002 0 1042 649 1082 0 963 0 1003 0 1043 760 1083 0 964 0 1004 0 1044 799 1084 0 965 0 1005 0 1045 760 1085 0 966 0 1006 0 1046 649 1086 0 967 76 1007 0 1047 478 1087 76 968 268 1008 0 1048 270 1088 272 969 473 1009 0 1049 76 1089 481 970 643 1010 0 1050 0 1090 653 971 753 1011 0 1051 0 1091 765 972 791 1012 0 1052 0 1092 804 973 753 1013 0 1053 0 1093 765 974 643 1014 0 1054 0 1094 653 975 473 1015 76 1055 0 1095 481 976 268 1016 269 1056 0 1096 272 977 76 1017 476 1057 0 1097 76 978 0 1018 647 1058 0 1098 0 979 0 1019 758 1059 0 1099 0 980 0 1020 796 1060 0 1100 0 981 0 1021 758 1061 0 1101 0 982 0 1022 647 1062 0 1102 0 983 0 1023 476 1063 76 1103 0 984 0 1024 269 1064 271 1104 0 985 0 1025 76 1065 479 1105 0 986 0 1026 0 1066 651 1106 0 987 0 1027 0 1067 763 1107 0 988 0 1028 0 1068 801 1108 0 989 0 1029 0 1069 763 1109 0 990 0 1030 0 1070 651 1110 0 991 76 1031 0 1071 479 1111 76 992 269 1032 0 1072 271 1112 273 993 474 1033 0 1073 76 1113 482 994 645 1034 0 1074 0 1114 655 995 756 1035 0 1075 0 1115 768 996 794 1036 0 1076 0 1116 806 997 756 1037 0 1077 0 1117 768 998 645 1038 0 1078 0 1118 655 999 474 1039 76 1079 0 1119 482 1000 269 1040 270 1080 0 1120 273

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223 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 1121 76 1161 485 1201 0 1241 76 1122 0 1162 659 1202 0 1242 0 1123 0 1163 772 1203 0 1243 0 1124 0 1164 811 1204 0 1244 0 1125 0 1165 772 1205 0 1245 0 1126 0 1166 659 1206 0 1246 0 1127 0 1167 485 1207 76 1247 0 1128 0 1168 274 1208 276 1248 0 1129 0 1169 76 1209 488 1249 0 1130 0 1170 0 1210 664 1250 0 1131 0 1171 0 1211 777 1251 0 1132 0 1172 0 1212 816 1252 0 1133 0 1173 0 1213 777 1253 0 1134 0 1174 0 1214 664 1254 0 1135 76 1175 0 1215 488 1255 76 1136 274 1176 0 1216 276 1256 278 1137 484 1177 0 1217 76 1257 491 1138 657 1178 0 1218 0 1258 668 1139 770 1179 0 1219 0 1259 782 1140 809 1180 0 1220 0 1260 821 1141 770 1181 0 1221 0 1261 782 1142 657 1182 0 1222 0 1262 668 1143 484 1183 76 1223 0 1263 491 1144 274 1184 275 1224 0 1264 278 1145 76 1185 487 1225 0 1265 76 1146 0 1186 661 1226 0 1266 0 1147 0 1187 775 1227 0 1267 0 1148 0 1188 814 1228 0 1268 0 1149 0 1189 775 1229 0 1269 0 1150 0 1190 661 1230 0 1270 0 1151 0 1191 487 1231 76 1271 0 1152 0 1192 275 1232 277 1272 0 1153 0 1193 76 1233 490 1273 0 1154 0 1194 0 1234 666 1274 0 1155 0 1195 0 1235 779 1275 0 1156 0 1196 0 1236 819 1276 0 1157 0 1197 0 1237 779 1277 0 1158 0 1198 0 1238 666 1278 0 1159 76 1199 0 1239 490 1279 76 1160 274 1200 0 1240 277 1280 278

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224 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 1281 493 1321 0 1361 76 1401 500 1282 670 1322 0 1362 0 1402 679 1283 784 1323 0 1363 0 1403 795 1284 824 1324 0 1364 0 1404 835 1285 784 1325 0 1365 0 1405 795 1286 670 1326 0 1366 0 1406 679 1287 493 1327 76 1367 0 1407 500 1288 278 1328 280 1368 0 1408 282 1289 76 1329 496 1369 0 1409 76 1290 0 1330 674 1370 0 1410 0 1291 0 1331 789 1371 0 1411 0 1292 0 1332 828 1372 0 1412 0 1293 0 1333 789 1373 0 1413 0 1294 0 1334 674 1374 0 1414 0 1295 0 1335 496 1375 76 1415 0 1296 0 1336 280 1376 281 1416 0 1297 0 1337 76 1377 498 1417 0 1298 0 1338 0 1378 677 1418 0 1299 0 1339 0 1379 793 1419 0 1300 0 1340 0 1380 833 1420 0 1301 0 1341 0 1381 793 1421 0 1302 0 1342 0 1382 677 1422 0 1303 76 1343 0 1383 498 1423 76 1304 279 1344 0 1384 281 1424 282 1305 494 1345 0 1385 76 1425 501 1306 672 1346 0 1386 0 1426 681 1307 786 1347 0 1387 0 1427 798 1308 826 1348 0 1388 0 1428 838 1309 786 1349 0 1389 0 1429 798 1310 672 1350 0 1390 0 1430 681 1311 494 1351 76 1391 0 1431 501 1312 279 1352 280 1392 0 1432 282 1313 76 1353 497 1393 0 1433 76 1314 0 1354 675 1394 0 1434 0 1315 0 1355 791 1395 0 1435 0 1316 0 1356 831 1396 0 1436 0 1317 0 1357 791 1397 0 1437 0 1318 0 1358 675 1398 0 1438 0 1319 0 1359 497 1399 76 1439 0 1320 0 1360 280 1400 282 1440 0

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225 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 1441 0 1481 75 1521 516 1561 0 1442 0 1482 0 1522 699 1562 0 1443 0 1483 0 1523 817 1563 0 1444 0 1484 0 1524 858 1564 0 1445 0 1485 0 1525 817 1565 0 1446 0 1486 0 1526 699 1566 0 1447 75 1487 0 1527 516 1567 79 1448 283 1488 0 1528 292 1568 294 1449 503 1489 0 1529 79 1569 519 1450 683 1490 0 1530 0 1570 702 1451 800 1491 0 1531 0 1571 821 1452 840 1492 0 1532 0 1572 862 1453 800 1493 0 1533 0 1573 821 1454 683 1494 0 1534 0 1574 702 1455 503 1495 79 1535 0 1575 519 1456 283 1496 292 1536 0 1576 294 1457 75 1497 515 1537 0 1577 79 1458 0 1498 697 1538 0 1578 0 1459 0 1499 815 1539 0 1579 0 1460 0 1500 855 1540 0 1580 0 1461 0 1501 815 1541 0 1581 0 1462 0 1502 697 1542 0 1582 0 1463 0 1503 515 1543 79 1583 0 1464 0 1504 292 1544 293 1584 0 1465 0 1505 79 1545 517 1585 0 1466 0 1506 0 1546 701 1586 0 1467 0 1507 0 1547 819 1587 0 1468 0 1508 0 1548 860 1588 0 1469 0 1509 0 1549 819 1589 0 1470 0 1510 0 1550 701 1590 0 1471 75 1511 0 1551 517 1591 78 1472 284 1512 0 1552 293 1592 294 1473 504 1513 0 1553 79 1593 520 1474 685 1514 0 1554 0 1594 704 1475 802 1515 0 1555 0 1595 823 1476 842 1516 0 1556 0 1596 864 1477 802 1517 0 1557 0 1597 823 1478 685 1518 0 1558 0 1598 704 1479 504 1519 79 1559 0 1599 520 1480 284 1520 292 1560 0 1600 294

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226 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 1601 78 1641 522 1681 0 1721 77 1602 0 1642 708 1682 0 1722 0 1603 0 1643 827 1683 0 1723 0 1604 0 1644 868 1684 0 1724 0 1605 0 1645 827 1685 0 1725 0 1606 0 1646 708 1686 0 1726 0 1607 0 1647 522 1687 77 1727 0 1608 0 1648 295 1688 296 1728 0 1609 0 1649 78 1689 525 1729 0 1610 0 1650 0 1690 711 1730 0 1611 0 1651 0 1691 831 1731 0 1612 0 1652 0 1692 872 1732 0 1613 0 1653 0 1693 831 1733 0 1614 0 1654 0 1694 711 1734 0 1615 78 1655 0 1695 525 1735 77 1616 295 1656 0 1696 296 1736 297 1617 521 1657 0 1697 77 1737 527 1618 706 1658 0 1698 0 1738 714 1619 825 1659 0 1699 0 1739 834 1620 866 1660 0 1700 0 1740 876 1621 825 1661 0 1701 0 1741 834 1622 706 1662 0 1702 0 1742 714 1623 521 1663 78 1703 0 1743 527 1624 295 1664 296 1704 0 1744 297 1625 78 1665 523 1705 0 1745 77 1626 0 1666 709 1706 0 1746 0 1627 0 1667 829 1707 0 1747 0 1628 0 1668 870 1708 0 1748 0 1629 0 1669 829 1709 0 1749 0 1630 0 1670 709 1710 0 1750 0 1631 0 1671 523 1711 77 1751 0 1632 0 1672 296 1712 297 1752 0 1633 0 1673 78 1713 526 1753 0 1634 0 1674 0 1714 712 1754 0 1635 0 1675 0 1715 833 1755 0 1636 0 1676 0 1716 874 1756 0 1637 0 1677 0 1717 833 1757 0 1638 0 1678 0 1718 712 1758 0 1639 78 1679 0 1719 526 1759 77 1640 295 1680 0 1720 297 1760 298

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227 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 1761 528 1801 0 1841 75 1881 532 1762 715 1802 0 1842 0 1882 722 1763 836 1803 0 1843 0 1883 844 1764 878 1804 0 1844 0 1884 886 1765 836 1805 0 1845 0 1885 844 1766 715 1806 0 1846 0 1886 722 1767 528 1807 76 1847 0 1887 532 1768 298 1808 298 1848 0 1888 299 1769 77 1809 530 1849 0 1889 75 1770 0 1810 718 1850 0 1890 0 1771 0 1811 839 1851 0 1891 0 1772 0 1812 881 1852 0 1892 0 1773 0 1813 839 1853 0 1893 0 1774 0 1814 718 1854 0 1894 0 1775 0 1815 530 1855 75 1895 0 1776 0 1816 298 1856 299 1896 0 1777 0 1817 76 1857 531 1897 0 1778 0 1818 0 1858 721 1898 0 1779 0 1819 0 1859 842 1899 0 1780 0 1820 0 1860 884 1900 0 1781 0 1821 0 1861 842 1901 0 1782 0 1822 0 1862 721 1902 0 1783 76 1823 0 1863 531 1903 74 1784 298 1824 0 1864 299 1904 299 1785 529 1825 0 1865 75 1905 533 1786 717 1826 0 1866 0 1906 723 1787 838 1827 0 1867 0 1907 845 1788 879 1828 0 1868 0 1908 887 1789 838 1829 0 1869 0 1909 845 1790 717 1830 0 1870 0 1910 723 1791 529 1831 75 1871 0 1911 533 1792 298 1832 298 1872 0 1912 299 1793 76 1833 531 1873 0 1913 74 1794 0 1834 719 1874 0 1914 0 1795 0 1835 841 1875 0 1915 0 1796 0 1836 883 1876 0 1916 0 1797 0 1837 841 1877 0 1917 0 1798 0 1838 719 1878 0 1918 0 1799 0 1839 531 1879 75 1919 0 1800 0 1840 298 1880 299 1920 0

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228 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 1921 0 1961 73 2001 536 2041 0 1922 0 1962 0 2002 727 2042 0 1923 0 1963 0 2003 850 2043 0 1924 0 1964 0 2004 892 2044 0 1925 0 1965 0 2005 850 2045 0 1926 0 1966 0 2006 727 2046 0 1927 74 1967 0 2007 536 2047 71 1928 299 1968 0 2008 299 2048 299 1929 534 1969 0 2009 72 2049 536 1930 724 1970 0 2010 0 2050 729 1931 846 1971 0 2011 0 2051 852 1932 888 1972 0 2012 0 2052 894 1933 846 1973 0 2013 0 2053 852 1934 724 1974 0 2014 0 2054 729 1935 534 1975 73 2015 0 2055 536 1936 299 1976 299 2016 0 2056 299 1937 74 1977 535 2017 0 2057 71 1938 0 1978 726 2018 0 2058 0 1939 0 1979 849 2019 0 2059 0 1940 0 1980 891 2020 0 2060 0 1941 0 1981 849 2021 0 2061 0 1942 0 1982 726 2022 0 2062 0 1943 0 1983 535 2023 72 2063 0 1944 0 1984 299 2024 300 2064 0 1945 0 1985 73 2025 536 2065 0 1946 0 1986 0 2026 728 2066 0 1947 0 1987 0 2027 851 2067 0 1948 0 1988 0 2028 893 2068 0 1949 0 1989 0 2029 851 2069 0 1950 0 1990 0 2030 728 2070 0 1951 73 1991 0 2031 536 2071 70 1952 299 1992 0 2032 300 2072 299 1953 534 1993 0 2033 72 2073 537 1954 725 1994 0 2034 0 2074 729 1955 848 1995 0 2035 0 2075 853 1956 890 1996 0 2036 0 2076 895 1957 848 1997 0 2037 0 2077 853 1958 725 1998 0 2038 0 2078 729 1959 534 1999 72 2039 0 2079 537 1960 299 2000 299 2040 0 2080 299

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229 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 2081 70 2121 538 2161 0 2201 67 2082 0 2122 731 2162 0 2202 0 2083 0 2123 855 2163 0 2203 0 2084 0 2124 897 2164 0 2204 0 2085 0 2125 855 2165 0 2205 0 2086 0 2126 731 2166 0 2206 0 2087 0 2127 538 2167 68 2207 0 2088 0 2128 299 2168 299 2208 0 2089 0 2129 69 2169 538 2209 0 2090 0 2130 0 2170 732 2210 0 2091 0 2131 0 2171 856 2211 0 2092 0 2132 0 2172 899 2212 0 2093 0 2133 0 2173 856 2213 0 2094 0 2134 0 2174 732 2214 0 2095 70 2135 0 2175 538 2215 53 2096 299 2136 0 2176 299 2216 265 2097 537 2137 0 2177 68 2217 495 2098 730 2138 0 2178 0 2218 684 2099 854 2139 0 2179 0 2219 806 2100 896 2140 0 2180 0 2220 848 2101 854 2141 0 2181 0 2221 806 2102 730 2142 0 2182 0 2222 684 2103 537 2143 68 2183 0 2223 495 2104 299 2144 299 2184 0 2224 265 2105 70 2145 538 2185 0 2225 53 2106 0 2146 731 2186 0 2226 0 2107 0 2147 855 2187 0 2227 0 2108 0 2148 898 2188 0 2228 0 2109 0 2149 855 2189 0 2229 0 2110 0 2150 731 2190 0 2230 0 2111 0 2151 538 2191 67 2231 0 2112 0 2152 299 2192 298 2232 0 2113 0 2153 68 2193 538 2233 0 2114 0 2154 0 2194 732 2234 0 2115 0 2155 0 2195 857 2235 0 2116 0 2156 0 2196 899 2236 0 2117 0 2157 0 2197 857 2237 0 2118 0 2158 0 2198 732 2238 0 2119 69 2159 0 2199 538 2239 52 120 299 2160 0 2200 298 2240 265

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230 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 2241 496 2281 0 2321 50 2361 495 2242 685 2282 0 2322 0 2362 685 2243 807 2283 0 2323 0 2363 808 2244 849 2284 0 2324 0 2364 850 2245 807 2285 0 2325 0 2365 808 2246 685 2286 0 2326 0 2366 685 2247 496 2287 51 2327 0 2367 495 2248 265 2288 264 2328 0 2368 262 2249 52 2289 495 2329 0 2369 49 2250 0 2290 685 2330 0 2370 0 2251 0 2291 807 2331 0 2371 0 2252 0 2292 849 2332 0 2372 0 2253 0 2293 807 2333 0 2373 0 2254 0 2294 685 2334 0 2374 0 2255 0 2295 495 2335 50 2375 0 2256 0 2296 264 2336 263 2376 0 2257 0 2297 51 2337 495 2377 0 2258 0 2298 0 2338 685 2378 0 2259 0 2299 0 2339 808 2379 0 2260 0 2300 0 2340 850 2380 0 2261 0 2301 0 2341 808 2381 0 2262 0 2302 0 2342 685 2382 0 2263 52 2303 0 2343 495 2383 48 2264 264 2304 0 2344 263 2384 262 2265 495 2305 0 2345 50 2385 494 2266 685 2306 0 2346 0 2386 685 2267 807 2307 0 2347 0 2387 808 2268 849 2308 0 2348 0 2388 850 2269 807 2309 0 2349 0 2389 808 2270 685 2310 0 2350 0 2390 685 2271 495 2311 50 2351 0 2391 494 2272 264 2312 263 2352 0 2392 262 2273 52 2313 495 2353 0 2393 48 2274 0 2314 685 2354 0 2394 0 2275 0 2315 807 2355 0 2395 0 2276 0 2316 850 2356 0 2396 0 2277 0 2317 807 2357 0 2397 0 2278 0 2318 685 2358 0 2398 0 2279 0 2319 495 2359 49 2399 0 2280 0 2320 263 2360 262 2400 0

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231 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 2401 0 2441 47 2481 493 2521 0 2402 0 2442 0 2482 684 2522 0 2403 0 2443 0 2483 807 2523 0 2404 0 2444 0 2484 849 2524 0 2405 0 2445 0 2485 807 2525 0 2406 0 2446 0 2486 684 2526 0 2407 48 2447 0 2487 493 2527 44 2408 261 2448 0 2488 259 2528 258 2409 494 2449 0 2489 45 2529 492 2410 685 2450 0 2490 0 2530 683 2411 808 2451 0 2491 0 2531 806 2412 850 2452 0 2492 0 2532 849 2413 808 2453 0 2493 0 2533 806 2414 685 2454 0 2494 0 2534 683 2415 494 2455 46 2495 0 2535 492 2416 261 2456 260 2496 0 2536 258 2417 48 2457 493 2497 0 2537 44 2418 0 2458 684 2498 0 2538 0 2419 0 2459 807 2499 0 2539 0 2420 0 2460 850 2500 0 2540 0 2421 0 2461 807 2501 0 2541 0 2422 0 2462 684 2502 0 2542 0 2423 0 2463 493 2503 45 2543 0 2424 0 2464 260 2504 258 2544 0 2425 0 2465 46 2505 492 2545 0 2426 0 2466 0 2506 684 2546 0 2427 0 2467 0 2507 807 2547 0 2428 0 2468 0 2508 849 2548 0 2429 0 2469 0 2509 807 2549 0 2430 0 2470 0 2510 684 2550 0 2431 47 2471 0 2511 492 2551 43 2432 261 2472 0 2512 258 2552 257 2433 494 2473 0 2513 45 2553 491 2434 685 2474 0 2514 0 2554 683 2435 807 2475 0 2515 0 2555 806 2436 850 2476 0 2516 0 2556 848 2437 807 2477 0 2517 0 2557 806 2438 685 2478 0 2518 0 2558 683 2439 494 2479 45 2519 0 2559 491 2440 261 2480 259 2520 0 2560 257

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232 A ppendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 2561 43 2601 490 2641 0 2681 39 2562 0 2602 682 2642 0 2682 0 2563 0 2603 805 2643 0 2683 0 2564 0 2604 847 2644 0 2684 0 2565 0 2605 805 2645 0 2685 0 2566 0 2606 682 2646 0 2686 0 2567 0 2607 490 2647 40 2687 0 2568 0 2608 255 2648 253 2688 0 2569 0 2609 42 2649 489 2689 0 2570 0 2610 0 2650 681 2690 0 2571 0 2611 0 2651 804 2691 0 2572 0 2612 0 2652 846 2692 0 2573 0 2613 0 2653 804 2693 0 2574 0 2614 0 2654 681 2694 0 2575 42 2615 0 2655 489 2695 38 2576 256 2616 0 2656 253 2696 252 2577 491 2617 0 2657 40 2697 487 2578 682 2618 0 2658 0 2698 679 2579 806 2619 0 2659 0 2699 803 2580 848 2620 0 2660 0 2700 845 2581 806 2621 0 2661 0 2701 803 2582 682 2622 0 2662 0 2702 679 2583 491 2623 41 2663 0 2703 487 2584 256 2624 254 2664 0 2704 252 2585 42 2625 489 2665 0 2705 38 2586 0 2626 681 2666 0 2706 0 2587 0 2627 805 2667 0 2707 0 2588 0 2628 847 2668 0 2708 0 2589 0 2629 805 2669 0 2709 0 2590 0 2630 681 2670 0 2710 0 2591 0 2631 489 2671 39 2711 0 2592 0 2632 254 2672 252 2712 0 2593 0 2633 41 2673 488 2713 0 2594 0 2634 0 2674 680 2714 0 2595 0 2635 0 2675 803 2715 0 2596 0 2636 0 2676 846 2716 0 2597 0 2637 0 2677 803 2717 0 2598 0 2638 0 2678 680 2718 0 2599 42 2639 0 2679 488 2719 38 2600 255 2640 0 2680 252 2720 251

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233 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c Hour Solar_flux/I c 2721 486 2761 0 2801 35 2841 482 2722 678 2762 0 2802 0 2842 674 2723 802 2763 0 2803 0 2843 798 2724 844 2764 0 2804 0 2844 840 2725 802 2765 0 2805 0 2845 798 2726 678 2766 0 2806 0 2846 674 2727 486 2767 36 2807 0 2847 482 2728 251 2768 249 2808 0 2848 245 2729 38 2769 484 2809 0 2849 34 2730 0 2770 677 2810 0 2850 0 2731 0 2771 800 2811 0 2851 0 2732 0 2772 843 2812 0 2852 0 2733 0 2773 800 2813 0 2853 0 2734 0 2774 677 2814 0 2854 0 2735 0 2775 484 2815 35 2855 0 2736 0 2776 249 2816 247 2856 0 2737 0 2777 36 2817 482 2857 0 2738 0 2778 0 2818 675 2858 0 2739 0 2779 0 2819 798 2859 0 2740 0 2780 0 2820 841 2860 0 2741 0 2781 0 2821 798 2861 0 2742 0 2782 0 2822 675 2862 0 2743 37 2783 0 2823 482 2863 33 2744 250 2784 0 2824 247 2864 244 2745 485 2785 0 2825 35 2865 480 2746 678 2786 0 2826 0 2866 673 2747 801 2787 0 2827 0 2867 796 2748 844 2788 0 2828 0 2868 839 2749 801 2789 0 2829 0 2869 796 2750 678 2790 0 2830 0 2870 673 2751 485 2791 35 2831 0 2871 480 2752 250 2792 248 2832 0 2872 244 2753 37 2793 483 2833 0 2873 33 2754 0 2794 676 2834 0 2874 0 2755 0 2795 799 2835 0 2875 0 2756 0 2796 842 2836 0 2876 0 2757 0 2797 799 2837 0 2877 0 2758 0 2798 676 2838 0 2878 0 2759 0 2799 483 2839 34 2879 0 2760 0 2800 248 2840 245 2880 0

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234 Appendix C (Continued) Table C 1 (continued) Hour Solar_flux/I c Hour Solar_flux/I c 2881 0 2921 6 2882 0 2922 0 2883 0 2923 0 2884 0 2924 0 2885 0 2925 0 2886 0 2926 0 2887 32 2927 0 2888 243 2928 0 2889 479 2929 0 2890 672 2930 0 2891 795 2931 0 2892 838 2932 0 2893 795 2933 0 2894 672 2934 0 2895 479 2935 6 2896 243 2936 95 2897 32 2937 230 2898 0 2938 351 2899 0 2939 431 2900 0 2940 459 2901 0 2941 431 2902 0 2942 351 2903 0 2943 230 2904 0 2944 95 2905 0 2945 6 2906 0 2946 0 2907 0 2947 0 2908 0 2948 0 2909 0 2949 0 2910 0 2950 0 2911 6 2951 0 2912 98 2952 0 2913 233 2914 354 2915 435 2916 464 2917 435 2918 354 2919 233 2920 98

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ABOUT THE AUTHOR Monica Annmarie Gray was born in Montego Bay, Jamaica. She graduated with a Bachelors of Science ( Summa Cum Laude/ First Class Honors) from the University of the West Indies, St. Augustine Campus, Trinidad in Agricultural Engineering and a minor in Bio systems Engineering. She then went on to complete a Master o f Science in Biological Engineering at the University of Georgia, Athens. While at the University of South Florida, Tampa, Monica undertook a PhD in Civil and Environmental Engineering in Water Resources Engineering and a Master of Public Health in Environmental and Occupational Health. Two of her lifes most awesome dreams are to fly an F 16 (Fighting Falcon) Fighter Jet and to be Jamaicas first woman Prime Minister.


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Sustainable control of Ascaris lumbricoides (worms) in a rural, disease endemic and developing community :
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by Monica Annmarie Gray.
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[Tampa, Fla] :
University of South Florida,
2008.
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Dissertation (Ph.D.)--University of South Florida, 2008.
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Text (Electronic dissertation) in PDF format.
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ABSTRACT: Parasitic infections, inadequate sanitation, and poor nutrition represent major etiologies that operate in synergy to cause some of the world's most disabling diseases. Citizens of developing nations, especially children living in rural areas, are the most affected. Current research and subsequent interventions have attempted to solve these issues using vertical interventions aimed at minimizing specific health outcomes. This approach does not consider the interaction among causes and the interrelationship between human beings and their environment. Challenges solved in this manner often fail to produce sustainable results or worse, create new problems. This project proposed the systems approach framework to address these challenges.The systems thinking dynamical modeling software, STELLA, was used to model the conditions that promoted and/or hindered Ascaris lumbricoides and other gastrointestinal parasitic diseases in the rural developing community of Paquila, Guatemala. The interventions chosen were: administration of anti helminthic drugs, supplying protein nutrition, and an excreta management system that allowed for effluent recycling to crop production. A new design for a Solar Latrine was proposed and the solar heating and microbial deactivation processes were modeled using the commerically available, Finite Element Method software COMSOL. From the simulations, disease eradication was most likely to occur when at least 50% of the host population were treated every 3 months for 2 years or more with an anti helminthic drug of 94% efficacy or better, latrine coverage and usage were at least 70%, and nutrition was provided at about 1.1 g protein per kg (human mass) per day.Given the climatic conditions in Paquila and the proposed latrine design, sustained treatement temperatures of up to 65C were possible in the fecal materail and with a minimum of 1 month (4 months maximum) retention time, it was concluded that the resulting humanure would meet US EPA Class A Biosolids microbial requirements.
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Advisor: Noreen Poor, Ph.D.
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Chemotherapy
Excreta reuse
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