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Emergency department capacity planning for a pandemic scenario

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Title:
Emergency department capacity planning for a pandemic scenario nurse allocation
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English
Creator:
Rico, Florentino Antonio
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University of South Florida
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Tampa, Fla
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Subjects / Keywords:
Time-series
Forecasting
Regression
Neural networks
Computer simulation
Dissertations, Academic -- Industrial and Management Systems Engineering -- Masters -- USF   ( lcsh )
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non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: The problem considered in this research is the efficient allocation of resources in an emergency department during a large flow of patient consequent to a pandemic influenza breakout. Predicting the impact of a Pandemic Influenza is very complex due to the many unknown variables that may play a role to how severe a pandemic can be. Scenario planning is considered in this research to forecast different potential outcomes and help decision makers better understand the role of uncertainties and become prepared to make important decisions. The goal is to first create a forecast model to estimate the patient demand during the breakout period accessing an emergency department and employ it as input of a simulation model to replicate the dynamics of the system under a set of pandemic influenza scenarios.The results yielded by this approach will be used as decision tool for hospital managers to better utilize and allocate medical staff considering the fluctuant demand of the system on the zones of the emergency department: triage, red, yellow, green, and black. Emergency departments are already overwhelmed during everyday operations; thus, it is expected in a case of pandemic influenza, their operations will be challenged beyond their limits. Hospitals are the first responders in a case of pandemic influenza since they will admit and treat the first cases, also they will be the first to identify the new virus. It is critical for hospitals to plan and create strategies to more effectively face the large number of patients arriving, and the best use of the available resources. Once the simulation model has been run and verified, and optimization procedure will be put in place to minimize the number of patients waiting in queue to be treated while maximizing flow of patients.The model is built using ARENA simulation software and OptQuest heuristic optimization to propose various combinations for the number of nurses needed for healthcare delivery. The proposed method significantly improves system efficiency by reducing the number of patients waiting in queue for health treatment and care, and also increases the total number of patients treated.
Thesis:
Thesis (M.S.I.E.)--University of South Florida, 2009.
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 Florentino Antonio Rico.
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Title from PDF of title page.
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Document formatted into pages; contains 111 pages.

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aleph - 002069430
oclc - 608476883
usfldc doi - E14-SFE0003245
usfldc handle - e14.3245
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Emergency Department Capacity Planning for a Pandemic Scenario: Nurse Allocation by Florentino Antonio Rico A thesis submitted in partial fulfillment of the requirements for the degree of Masters of Science in Industrial Engineering Department of Industrial and Management Systems Engineering College of Engineering University of South Florida Major Professor: Grisselle Centeno, Ph.D. Ali Yalcin, Ph.D. Kingsley Reeves, Ph.D. Date of Approval: November 3 2009 Keywords: time series, forecasting, regression, neural networks, computer simulation Copyright 2009, Florentino Antonio Rico

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DEDICATION To my loving parents Florentino Antonio and Martha Cecilia, my brother Jorge and his lovely wife Ximena, my dear sister Heid y, and my nephews Camilo and Alejandro Last but not least, to Michael.

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ACKNOWLEDGEMENTS I would like to thank Dr. Centeno for her guidance and support during all these years. Thanks for being an incredible advisor and friend. Nothing of this would have happened without your encouragement and advice. I am very grateful for the help and advice from my thesis committee Dr. R eeves and Dr. Yalcin. I want to thank my family that has been the major motivation in my life, and example to follow Also, many thanks for all the love and support from my all friends, especially to Michael and the Marker Family. Thank you for adopting me as a family member in this country.

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i TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES iv ABSTRACT vi CHAPTER 1 INTRODUCTION 1 Pandemic Influenza Overview 1 Pandemic Influenza Impact 3 Current Situation 6 Nursing Capacity Planning 7 General Problem Description and Approach 8 Thesis Organization 10 CHAPTER 2 PROBLEM STATEMENT 11 Introduction and Motivation 11 Research Objectives 14 Methodology 15 CHAPTER 3 FORECASTING MODELING FOR VISITS TO ED UNITS FROM PATIENTS WITH INFLUENZA 17 Abstract 17 Introduction 17 Literature Review on Forecasting 19 Research Methodology 21 Problem Formulation 22 Time Series Forecasting Models 24 Seasonal Decomposition Using Moving Averages 26 Winterss Method 27 Causal Models 28 Regression Analysis 28 Neural Networks Overview 30 Results 34 Performance Metrics 38 Comparison of Techniques 4 0 Discussion 4 4

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ii CHAPTER 4 PANDEMIC INFLUENZA SCENARIOS 4 6 Abstract 4 6 Introduction 4 6 Motivation 4 8 Background 49 Problem Formulation 5 2 Methodology 5 3 Pandemic Influenza Model 5 4 Model Selection 5 5 Pandemic Influenza Severity Index Demand Models 5 8 Discussion 6 3 CHAPTER 5 EMERGENCY DEPARTMENT SIMULATION MODEL DURING A PANDEMIC INFLUENZA OUTBREAK 6 4 Abstract 6 4 Introduction 6 4 Literature Review 6 6 Problem Formulation 6 8 Methodology 70 Model Description 7 1 Conceptual Model 7 2 Assumptions 7 4 Verification 7 6 Validation 7 7 Results 7 8 Optimization 8 1 Allocation of Resources 84 Conclusions 87 Future R esearch 88 REFERENCES 89 APPENDICES 9 4 Appendix A: World Health Organization Pandemic Phases 9 5 Appendix B: Percentage of Visits for Influenzalike Illness Reported 9 6 Appendix C: Neural Networks code 9 8 Appendix D: Mechanisms of Pandemic Virus Origination 99 Appendix E: Statistical Test of MAD 100 Appendix F: Assumptions for Pandemic Influenza impact 102 Appendix G: Number of beds per hospital in Tampa 103 Appendix H: W eekly demand of patients for five scenarios 104 Appendix I: Time estimates for the processes held in the ED. 105 Appendix J: Snapshot of simulation animation 106 Appendix K: SIMAN simulation summary report 107 Appendix L: Queue length and waiting times for the current system 111

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iii LIST OF TABLES Table 1: Fourier coefficients 3 6 Table 2: Compa rison of Forecasting Techniques 4 1 Table 3: Pandemic Severity Index 5 5 Table 4: Forecasting Method Selection Criteria 5 6 Table 5: Total Demand for the PSI 6 1 Table 6: Pandemic Proportional Constants 6 2 Table 7: Estimates for Rate o f Illness, Outpatient Visits, Resources Utilization, and Deaths f or Pandemic Assumptions 7 5 Table 8: Estimates for t he Resources Available According to t he VA Respiratory Infectious Diseases Emergency Plan 7 6 Table 9: Resource Utilization Estimates for t he Nurses in t he Various Zones with t he Current Allocation Policy 79 Table 10 : List of Responses for t he Optimiza tion Procedure i n Optquest 8 2 Table 11: Resource Allocation as a Percentage of T otal Number of Nurses f or Objective 1 8 4 Table 12: Resource Allocation as a Percentage of Total Number of Nurses f or Objective 2 8 4 Table 13: Resource Allocation as a Per centage of Total Number o f Nurses f or Objective 3 8 6 Table 14: Percentage of Visits for Influenzalike Illness 96 Table 15: Number of beds per Hospital in Tampa 103 Table 16: Demand of Patients by Week 104 Table 17: Processing Times 105 Table 18: Queue length and Waiting Times Results 111

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iv LIST OF FI GURES Figure 1: General Problem and Approach 10 Figure 2: Trends in Emergency Department Visits, Number of Hospitals, and Number of Emergency Departments in the United States, 19942004 1 3 Figure 3: Thesis Methodology 1 6 Figure 4: Forecasting Methods 1 7 Figure 5: Methodology 2 2 Figure 6: Examples of Trend and Seasonal Patterns in Healthcare. 2 5 Figure 7: Se asonal Patient Demand over 137 W eeks 2 6 Figure 8: Fourier S eries F itting and Residuals P lot 30 Figure 9: Neural Network Model 3 2 Figure 10: Moving Average R esults 3 5 Figure 11: Winter's Method Results 3 5 Figure 12: Reg ression Analysis using Fourier Series 3 7 Figure 13: Neural Network Forecasting R esults 3 8 Figure 14: Tracking Signal for Forecasted R esults 4 2 Figure 15: Current seas on 20082009 ILI Vi sits versus F orecasts. 4 3 Figure 16: Three Pandemic Waves: Weekly Combined Influenza and Pneumonia Mortality 50 F igure 17: "U and "W shaped Combined Influenza and Pneumonia M ortality 5 1 Figure 18: Thesis Flow for Chapter 4 5 4

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v Figure 19: Integrals as th e Area under a Function Curve 60 Figure 20: Five pandemic Influenza Demand Scenarios 6 2 Fig ure 21: Thesis Flow for Chapter 5 65 Figure 22: Steps in Simulation Study 70 Figure 23: Process Flow for the EDs during a Pandemic Influenza 73 Figure 24: Nurse Utilization in the Various Zones for the Five Severity Scenarios with the C urrent System Allocation Policy 7 9 Figure 25: Number of Patients Waiting in each Zone of the ED 80 Figure 26: Queue Waiting Times (Hrs) for the Current System 8 0 Figure 27: Resource Utilization after Optimization 85 Figure 28: Number of Patients Waiting in the Various Zones of the ED in the Optimized System 87 Figure 29: WHO Pandemic Phases 95 Figure 30: Mechanisms of Pandemic Origination 99 Figure 31: Assumptions for the Pandemi c Influenza Impact 102 Figure 32: Snapshot of Simulation Animation 106

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vi EMERGENCY DEPARTMENT CAPACITY PLANNING DURING A PANDEMIC INFLUENZA BREAKOUT Florentino Antonio Rico ABSTRACT The problem considered in this research is the efficient allocation of resources in an emergency department during a large flow of patient consequent to a pandemic influenza breakout. Predicting the impact of a Pandemic Influenza is very complex due to the many unknown variables that may play a role to how severe a pandemic can be. Scenario planning is considered in this research to forecast different potential outcomes and help decision makers better understand the role of uncertainties and become prepar ed to make important decisions. The goal is to first create a forecast model to estimate the patient demand during the breakout period accessing an emergency department and employ it as input of a simulation model to replicate the dynamics of the system under a set of pandemic influenza scenarios. The results yielded by this approach will be used as decision tool for hospital managers to better utilize and allocate medical staff considering the fluctuant demand of the system on the zones of the emergenc y department: triage, red, yellow, green, and black. Emergency departments are already overwhelmed during everyday operations; thus, it is expected in a case of pandemic influenza, their operations

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vii will be challenged beyond their limits. Hospitals are t he first responders in a case of pandemic influenza since they will admit and treat the first cases, also they will be the first to identify the new virus. It is critical for hospitals to plan and create strategies to more effectively face the large number of patients arriving, and the best use of the available resources. Once the simulation model has been run and verified, and optimization procedure will be put in place to minimize the number of patients waiting in queue to be treated while maximizing f low of patients. The model is built using ARENA simulation software and OptQuest heuristic optimization to propose various combinations for the number of nurses needed for healthcare delivery. The proposed method significantly improves system efficiency by reducing the number of patients waiting in queue for health treatment and care, and also increases the total number of patients treated.

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1 CHAPTER 1 INTRODUCTION Pandemic Influenza Overview Pandemic Influenza outbreak appears when a novel influenza virus emerges, it is able to cause illness in humans, and it can transmit from human to human easily. What makes these novel viruses a potential threat to the worldwide population is that human would have little o no immunity, and it is expected to be very deadly (CDC, 2009). To be better understand the intentions of this research, and what Pandemic Influenza also known as Pandemic Flu implies, it is important to define the terms that will be used throughout this paper: Seasonal Influenza is a respiratory illness caused by both human influenza A and B viruses that can be transmitted person to person. Most people have some immunity and a vaccine is available. Pandemic Influenza (or pandemic flu) is virulent human influenza A virus that causes a global outbreak, or pandemic, of serious illness in humans. Because there is little natural immunity, the disease spreads easily and sustainably from person to person. H1N1 Influenza is a respiratory disease of pigs caused by type A influenza viruses that causes regular outbreaks in pigs. People do not normally get swine flu, but human infections can and do happen.

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2 Avian (or bird) Influenza is caused by influenza A viruses that occur naturally among wild birds. Low pathogenic avian influenza is common in birds and causes few problems. Highly pathogenic avian influenza A (H5N1), or HPAI H5N1, is deadly to domestic fowl and can be transmitted f rom birds to humans. There is no human immunity and at this point in time only one Food and Drug Administration (FDA) approved human vaccine has been approved. The FDA has approved this vaccine for individuals who may be at increased risk of exposure to t he HPAI H5N1 virus, but it is not commercially available. This vaccine has been included within the Strategic National Stockpile (SNS). According to the National Strategy and Emergency Management Systems (EMS) Pandemic Management Systems Pandemic Influenza guidelines created in 2007, a nimals are the most likely reservoir for an emerging influenza virus. Avian influenza viruses played a role in the development of the human influenza viruses associated with the last three influenza pandemics. Two of these viruses remain in circulation among humans today and are responsible for the majority of seasonal influenza cases each year. There will be very little discussion of specifics regarding avian influenza epidemiology in this research as it is impossibl e to predict what kind of virus will in fact be the cause of a future pandemic. Currently, there is c oncern with the current circulating H5N1 virus due to its high mortality among reported human cases and its broad geographic distribution. Most cases o f H5N1 virus infection in humans have resulted from

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3 direct or close contact with infected poultry (e.g., domesticated chicken, ducks, and turkeys) or surfaces possibly contaminated from feces and/or respiratory secretions from infected birds. While there have been a few cases of probable personto person spread of H5N1, it has been limited, and inefficient as of this point in time. Planners should be able to distinguish among the following: Endemic Levels is the constant presence of a disease or infectious agent in a certain geographic area or population group. Epidemic is the rapid spread of a disease in a specific area or among a certain population group. Pandemic is a worldwide epidemic an epidemic occurring over a wide geographic area and affecting a large number of people. For example, the Severe Acute Respiratory Syndrome (SARS) epidemic from 2002 2003 never progressed to a pandemic even though SARS moved to Canada from its origins in Asia. Although SARS covered a wide geographic area, the number of people affected by the disease was limited (EMS, and US Department of Transportation, 2007) Pandemic Influenza Impact The global impact of pandemic influenza could be severe in terms of lives lost and individual and community suffering, as well as sev ere negative impact upon social and economic systems. The following are potential impacts of pandemic influenza:

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4 Rapid Worldwide Spread: When a pandemic influenza virus emerges, its global spread is likely inevitable. Preparedness activities should assume that the entire world population will be affected by the virus. Countries might, through measures such as border closures and travel restrictions, delay arrival of the virus, but would not be able to stop it. Health Care Systems Overloaded: Most people have little or no immunity to a pandemic virus. Infection and illness rates will be very high. Medical Supplies Inadequate: The need for vaccine and antiviral medications is likely to outstrip supply early in a pandemic period. In addition, a pandemic may c reate a shortage of hospital beds, ventilators and other supplies. Surge capacity at nontraditional sites such as schools may be created to cope with demand. Shortages may result in the need for difficult decisions regarding who should get antiviral drugs and vaccines. Economic and Social Disruption: Travel bans, closings of schools and businesses and cancellations of events could have major impact on communities and citizens. Care for sick family members and fear of exposure can result in significant work er absenteeism. T he characteristics for todays society are not the same as it was during the pandemics in the last 100 years. The population has grown, and transportation systems are easier to get access to This might affect how fast and virus can spre ad, and how severe it can be. Society entities responding to this type of disasters are hospitals, transportation systems, and law enforcement agencies.

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5 Public Health plays an important role in any case of kind of disaster that involves human causaliti es. Disaster have been defined as disruptions, or emergencies, of a severity and magnitude that results in deaths, injuries, illness, and/or property damage that cannot be effectively managed by the application of routine procedures or resources and that result in a call of outside assistance ( Landesman, L., et al., 2000). The life cycle of a disaster event is typically known as the disaster continuum, or emergency management cycle. This cycle consists on the Preimpact, during or Impact, and the after or Post impact phase. The Basic phases of disaster management include mitigation or prevention, warning and preparedness, and response and recovery. The U.S. Department of Health and Human Services has been working actively on preparedness and response in a case of a Pandemic Influenza outbreak. Planning is being carried out in different levels of society; that is, preparation in the Federal, State and Local, Workplace, Health care and Individual level. On the federal level The National Strategy for Pandemic Influenza, issued by President of the United States on November 1st 2005 guides our nation's preparedness and response for an influenza pandemic, with the intent of stopping, slowing or otherwise limiting the spread of a pandemic to the United States. By limiting the domestic spread of a pandemic, and mitigating disease, suffering and death, and sustaining infrastructure and mitigating impact to the economy and the functioning of society (Homeland Security Council 2005).

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6 State and Local Planning is very important also since a pandemic occurs in many localities. According to the U.S Department of Health and Human Services, much of the planning for a pandemic must be the responsibility of state and local governments. Community strategies that delay or reduce the impact of a pandemic (also called nonpharmaceutical interventions) may help reduce the spread of disease until a vaccine is available (CDC 2006). The Florida Department of Health has developed an emergency operation plan for an Influenza pandemic: t his document contains detailed information on the risk assessment of the situation, assumptions, operations for notification, activation, and deactivation of the protocols, and finally it contains essential information about preparedness, response, recovery, and mitigation strategies. Current Situation June 11th 2009 : "The world is now at the start of the 2009 influenza pandemic, WHO press conference. O n the basis of available evidence and expert assessments of the evidence, the scientific criteria for an influenza pandemic have been met. The Director General of WHO has therefore decided to raise the level of influenza pandemic alert from phase 5 to 6. A description for WHO the pandemic phases can be seen in Appendix A: World Health Organization Pandemic Phases At this time, W orld Health Organization (WH O ) considers the overall severity of the influenza pandemic to be moderate. This assessment is based on scientific evidence available to WHO, as well as input from its Member States on

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7 the pandemic's impact on their health systems, and their social and economic functioning. The moderate assessment reflects that: Most people recov er from infection without the need for hospitalization or medical care. Overall, national levels of severe illness from influenza A(H1N1) appear similar to levels seen during local seasonal influenza periods, although high levels of disease have occurred i n some local areas and institutions. Overall, hospitals and health care systems in most countries have been able to cope with the numbers of people seeking care, although some facilities and systems have been stressed in some localities. WHO is concerned about current patterns of serious cases and deaths that are occurring primarily among young persons, including the previously healthy and those with preexisting medical conditions or pregnancy. Large outbreaks of disease have not yet been reported in many countries, and the full clinical spectrum of disease is not yet known. Nursing Capacity Planning Currently, there is being an increasing concern and appreciation of how important nurses are in healthcare systems. In a time where healthcare resources ar e becoming more overwhelmed, limited, and more expensive, concentrating efforts on increasing productivity and capacity planning is crucial. Therefore, one of the important operational issues in healthcare involves capacity planning such that the goals of high resource utilization and providing high quality

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8 service are met (Cote and Bretthauer, 1998). According to [Adenso et al. 2002], to design a model that permits the determination of the number of nurses required to cover minimum levels of quality, it is necessary to define several prior steps including : Patients must be classified (not all patients require the same nursing care), so as to subsequently identify the different tasks that nurses carry out in their work. Discover a way of determining the time taken to carry out each nursing task. Identify the desired levels of quality in the hospital. Establish the relationships between the theoretical staff and quality levels. Establish the procedure for calculating staff. General Problem Description and Approach Forecasting a Pandemic Influenza: According to experts, Pandemic Influenza does not follow any periodicity, or epidemiological profile. It is not possible to know what the real impact of a novel influenza virus will have on the infrastructur e of a country. But, it is necessary to plan for this event, and this research proposes a series of scenarios that will help decision makers create the capabilities in emergency department to improve care given to patient, and better allocate resources. Healthcare systems: During a Pandemic Influenza a substantial percentage of the worlds population will require some form of medical care. Nations are unlikely to have the staff, facilities, equipment and

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9 hospital beds needed to cope with large numbers of people who suddenly fall ill. Death rates may be high, depending on four factors: the number of people who become infected, the virulence of the virus, the underlying characteristics and vulnerability of affected populations and the effectiveness of preventive measures. Nursing Capacity Planning: Determining nursing staff levels in healthcare provider sites is a complex task because of the characteristics of staff management in any activity in the service sector and the social economic importance of the work that nurses do. An urgent need exists to match patient needs with the health resources available. In recent years, demand for both medical and nursing staff has grown notably without these resources increasing to match demand (Cote and Bretthauer, 1998). Figure 1 gives a global approach for the problem that is being analyzed in this thesis. The global objective is to study the nursing capacity planning under a hi gh demand and overwhelming case of a Pandemic Influenza outbreak. To get this point, a forecast of potential demand and simulation model will be proposed. Making use of available academic tools as it can be seen in the figure, different models and scenari os will be tested and find which better fits the needs of this thesis objectives.

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10 Nursing Capacity Planning under Pandemic Influenza Scenario Simulation Modeling Forecasting Techniques Time-series Causal Models Scenario Building Arena simulation software OptQuest optimization software MatLab Microsoft Office Tools: Excel, Visio, Word Seasonal Decomposition Winterss Method Optimization Neural Networks Regression Analysis Pandemic Severity Index Pandemic Proportional Constants Global Objective Partial Objective Theoretical Support Computational Tools Figure 1 : General Problem and Approach Thesis Organization This thesis is organized as follows: four more chapters follow after this point. Each chapter is organized in partial independent form, and at same time, they are cohesive, and necessary to reach the final objective (as it can be seen in Figure 3 ). The format used in the following chapters follow s a scholarly journal format : each chapter contains an introduction, literature review, problem statement, resea rch questions, methodology, results, and a discussion.

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11 CHAPTER 2 PROBLEM STATEMENT Introduction and Motivation The problem considered in this research is originated due to the need for efficient methods to allocate resources in an emergency department during a large demand of patient following a pandemic influenza breakout. D ue t o the recent outbreaks of swine flu in 2009, it has become imminent for healthcare agencies managers to plan for this type of disaster. T he first goal of this work is to develop a forecasting model that accurately estimates the patient demand for EDs during the breakout period. Results from the forecast will be used as input to a simulation model in charge of replicat ing the dynamics of healthcare providers under various pandemic influenza scenarios. The results yielded by the se models will assist hospital managers in the decision making process to better utilize and allocate medical staff considering the fluctuant demand for the system and for the individual zones of the emergency department. According to pandemic protocols from CDC and World Health Organization, once an outbreak occurs, hospitals must dedicate an exclusive area for patients with the pandemic virus. This area should b e divided into five zones: triage, green, yellow, red and black [Davey et. al. 2006]. The model proposed aims to optimize the system by modifying the resource levels in the various zones of the ED to minimize the waiting time for the patients, and number

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12 of patients waiting to be treated while maximizing the flow of patients throughout the system. Special attention is given to those resources such as nurses and respiratory therapists who are essential for the delivery of care, and with the highest expecte d demand. According to [ Toner 2006], h ospital preparedness for these types of events is not clearly defined, and should be revise d to define specific, nationally sanctioned preparedness goals, priorities, and metrics Emergency Departments are an essent ial element of healthcare systems because they provide immediate care for patients. However, they are also the most overwhelming component. According to the Institute of Medicine, EDs overcrowd represents an obstacle to the safe and timely delivery of health care. [Kellermann, 2008] exposes the worrying situation of EDs in the Unites States. Figure 2 illustrates how the number of emergencies departments have decreased from approximate 5000 to 4600 (about 8%) while the number of total emergency visits have increased from 90 to 110 million (about 18%) from 1994 to 2004.

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13 Figure 2 : Trends in Emergency Department Visits Number of Hospitals, and Number of Emergency Departments in the United States, 19942004 EDs are already overwhelmed during everyday operations; thus, it is expected that in a case of pandemic influenza, their operations will be challenged beyond their limits. Moreover, it is anticipated that these units will a dmit and treat the first cases, and also they will be the first to identify the presenc e of a new virus. For that reason, it is critical for hospitals to plan and create a robust plan to effectively process large number of patients arriving, and efficiently use of the limited available resources. According to the Health and Human Service s (HHS) planning assumptions and using the Center for Disease Control and Preventi on (CDC) FluSurge 2.0 software assumptions the availability of the hospital resources that would be needed for influenza patients alone are: 191% of actual non ICU beds, 461% of actual ICU beds, and 198% of actual ventilators. Moreover [ Toner 2006] shows

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14 that there are shortages of healthcare workers of all kinds; for instance, 100,000 additional registered nurses (8% of current work force) are needed under normal circums tances alone. Also, they reported that about 48% of emergency departments in the US are currently at or over capacity, which it is a problem that obstructs for the promptness and quality of care delivery. Research Objectives The specific objectives of this research are as follows: To create and validated a forecast ing tool for the demand of patients assessing the ED during a pandemic influenza breakout. To explore and compare time series methods and causal models using nontraditional forecasting models to patient surge to the ED such as neural networks. To develop a simulation model that mimics the dynamics of the ED during the breakout. To analyze the system by changing the level of resources in the various zones and allocate resources in a way where w aiting time and number of patients in queue are minimized. To determine the maximum capacity for an ED system. Specifically, t he following questions will be answered in this thesis: Is seasonal influenza data useful to predict pandemic influenza visits behavior? Which forecasting technique works better for seasonal influenza hospital demand?

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15 Does allocation of resources impact the efficiency in an ED? If so, which zones are more critical or need more resources? Is forecasting by scenario building a good option to predict the potential impact? What is the maximum ca pacity that a hospital can work? Methodology The final goal for this research is to design a nurse allocation policy, determine the maximum capacity, and give recommendations to improve the sys tem studied. At this point, Chapter 1 and 2 have stated the why, what, and how: what the motivation to do this study is, what problem is being analyzed, and how is it going to be done. The way this thesis work s is that each chapter is designed and studied in an independent way following a journal structure, but each chapter harmonizes with the rest because its output is the input of the next chapter as it is seen in Figure 3 Chapter 3 makes use of various forecasting techniques both times series and causal models for the demand of patient visits with influenzalike illness. These forecasting techniques are c ompared and evaluated using popular performance measures. Chapter 4 makes use of scenario building forecasting for a pandemic influenza using the forecasting model found in the previous chapter, and it proposes a Pandemic Proportional Constant to describe five levels of severity. Chapter five uses the five demand scenarios as input of a simulation model. This simulation model allows analysts to study what if scenarios, and an optimized allocation of resources is proposed.

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16 Chapter 3: Forecasting Modeling of Visits for Patients with Influenza Chapter 4: Pandemic Influenza Scenarios Chapter 5: Simulation Modeling and Optmization Chapter 1 and 2 Input CDC Surveillance Data Time-series and Causal Forecasting methods Forecasting Performance Metrics Problem Statement Motivation Research Methodology Problem Formalization Research Objectives Forecast estimates for influenza patient demand using: Seasonal Decomposition Winterss Method Regression analysis Neural Networks Previous Pandemic Influenza data Set of potential scenarios for a pandemic influenza patient surge to a hospital Data collection of the emergency department activities. System analysis, description and modeling Assumptions Nurse Allocation Maximum Capacity Determination Recommendations Limitations Figure 3 : Thesis Methodology

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17 CHAPTER 3 FORECASTING MODELING FOR VISITS TO ED UNITS FROM PATIENTS WITH INFLUENZA Abstract The challenge studied in this section is the determination of a forecasting model for the demand of patient that access hospital suffering from influenza. Current surveillance programs provide valuable information to help estimate the burden the disease has on the surge of patient s assessing the emergency department. F our methods are implemented in this work with greater emphasis on Neural Network s and Fourier series regression. Results are compared using performance metrics such as MAD, MAPE, RMSE, TS, and ME. Performance results for the forecasting methods were compared using a t test, and it was found that no method was statistically better than any other. Other criterion beyond accuracy needs to be considered. Introduction Forecasting is applied in a vast variety of fields, and its complexity level can range from very simple methods to very complicated algorithms (Nahmias, 2001). Forecasting and prediction is often performed by healthcare decision makers, practitioners, and researchers. Forecasting is often confused wit h planning. Planners can use forecasting methods to predict the outcomes for alternative plans predict the number of patients that would access the system,

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18 how much medication should be kept in inventory, and so on For ecasting serves many needs: It can help people and organization to plan better for the future and to make rational decisions. It can help in deliberations about policy variables (Armstrong, 2001). For example, how many resources will be used in the proces s? What work force do we need? Are there enough vaccines to fulfill the demand? Forecasts can be either subjective or objective. Subjective forecasts are motivated by human judgment (i.e. Surveys, Delphi method, and expert opinions among others). Objecti ve forecasting are those derived from analysis of data. They can be t imes series which uses only past values of the situation analyzed or Causal models that assume that there may be other variables related in some way to what is being forecasted. Figure 4 gives a list of some objective forecasting methods used in time Series analysis and Causal methods, as well as subjective methods. In the next secti ons, the forecasting method used to predict the seasonal influenza patient demand will be explained and expanded, and finally compared on how well they performed.

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19 Forecasting Methods Objective Subjective Time Series Methods Causal Methods Moving Average Exponential Smoothing Simple ES Holts Method Winters Method Simple Regression Analysis Seasonal Decomposition MA Simulation Econometric Models Neural Networks Regression Analysis Sales Composite Forecasts Delphi Method Forecast by Analogy Surveys Scenario Building Figure 4 : Forecasting Methods Literature Review on Forecasting This research will make use of different forecasting techniques to analyze the seasonal time series of the number of patients arriving to a Hospital with influenzalike symptoms. Data of seasonal influenza from national s urveillance have been used in models to better understand the burden of the disease and its impact on all cause deaths in the United States, and these data have contributed towards the development of statistical models to estimate the burden of epidemic di seases. Influenza Mortality rates have been studied by different authors. [Serfling, 1963], and [Simonsen et al., 1997] used data from 108 US cities, and NCHS

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20 (National Center for Health Statistics) weekly death data to implement linear regression models to estimate pneumonia and influenza related deaths trends. [Izurieta et al., 2000] used NCHS weekly death data to create baseline rate model for the summer and per season to estimate hospitalizations, death rates, and outpatient visits. [Simonsen e t al., 2005 ] used the data available to create a cyclical regression model to estimate excesses in pneumonia and influenza and allcause mortality for each influenza season since 1972. Death rates also show a cyclical pattern. It is important to note that the regression models applied to death, can in similar ways apply to patient demand. The studies mentioned above have used regression analysis to reach their goals, and they have been important to understand the impact of seasonal influenza on deaths, but they have not gone on analyzing on patient demand is impacted every year. Regression models such as Fourier series with the help of modern computer tools are able to capture the seasonality, trend, cycle, and residual error effect (Lim et al., 2000; Proietti, 2000). Neural Networks is a causal forecasting model that is also able to forecast under the presence of seasonal effects. [Sharda et al. 1992] examined 88 seasonal time series and found that Neural Networks can model seasonality effectively and without seasonal decomposing the data, which can translate in time savings. [Gorr, 1994] found that Neural Networks are able to detect nonlinear trend and seasonality. Besides seasonality, other studies have found that Neural Networks are able to recognize patterns change in the data (Nam et al 1995; Franses et al 1997). Neural Networks are increasing in popularity

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21 since they provide a very good function approximation to model the trend and seasonality of the data (Zhang, 2005). For ecasting is a tool used in this research to study emergency deparments Other h ealthcare systems applications include : forecast the outcome for cancer treatment (OhnoMachado L. et al. 1998), simulate physician behavior of Elastic Tissue (Radetzky et. al 1998), Medical Image Analysis (Lasch et. al, 2000), and decision support in prescription and outcome prediction in drug therapy (Byrne et al. 2000). Others fields include: economy analysis and prediction (Grudnitski et al. ,1993; Wong et al. 1995; Hann et al. 1996), ecosystems and meteorology forecasting (Atiya et al. 1999), power systems, manufacturing, optimization, signal processing, and social/psychological sciences (Kalogirou, 2000). Research Methodology The research procedure that is carried out through this research is depicted in Figure 5 After reviewing the literature available, it proceeds with problem statement formalization. Then, it is explain ed where the data used in this work comes from, and give s an overview of the forecasting models, and implementation F inally the results are compared and analyzed. This research aims to provide some em pirical evidence on the effectiveness of time series forecasting methods and causal model such as Neural Network s on modeling and forecasting seasonal influenza and trend time series.

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22 Formulate Problem Obtain Information Select Methods Implement Methods Evaluate Methods Use Forecasts CDC Surveillance data Information for two years Time Series Methods: Seasonal Decompostion Winters Method Causal Methods: Regression Analysis Neural Networks MAD MSE MAPE RMSE ME TS Figure 5 : Forecasting Methodology Problem Formulation The problem considered in this chapter is the forecasting of the patient demand with influenza like symptoms to EDs in a hospital. The objective is to find a model that represents the data seasonality and gives the best fit and generalization of its demand behavior. Determining the burden of seasonal influenza is complicated. Influenza diagnosis is generally not laboratory confirmed and are attributed to pneumonia and other seco ndary complications (Simonsen et al. 1997). These secondary complications are referred as influenzalike illnesses, and the data used in this investigation is using this information on patient visits to health care providers for influenzalike illness. Data is collected through the US Outpatient Influenzalike Illness Surveillance Network (ILINet).

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23 Through the analysis provided in this chapter, it will be answered whether seasonal influenza surveillance data can be used to mimic the beh avior of a pandemic influenza with a different severity level. Based on weekly historical data, various forecasting methods will be compared for accuracy of representation using a set performance metrics. Data T he U.S. influenza surveillance system is a collaborative effort between CDC and its many partners in state and local health departments, public health and clinical laboratories, vital statistics offices, healthcare providers, clinics and emergency departments. Information in five categories is collected from nine different data sources that allow CDC to f ind out when and where influenza activity is occurring; track influenzarelated illness, d etermine what influenza viruses are circulating ; d etect changes in influenza viruses and m easure the impact influenza is having on deaths in the United States The outpatient Influenza L ike Illness Surveillance Network (ILINet) consists of about 2,400 healthcare providers in the 50 s tates reporting approximately 16 million patient visits each year. Each week, approximately 1,300 outpatient care sites around the country report data to CDC on the total number of patients seen and the number of those patients with influenzalike illness (ILI) by age group. This information is available in the Centers for Disease Control and P reventions website and on Appendix B: Percentage of Visits for Influenzalike Illness Reported by Sentinel Providers, National Summary 200708 and Previous 2 Seasons

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24 Time Series Forecasting Models The use at time t of available observations of the weekly number of emergency department patient visits from a time series to forecast its value at some future time t + l can provide a basis for a variety of applications such as: customer demand, medications inventory control, economic and business planning, and general control of healthcare systems (Box et al., 2008). We suppose that observations are available at discrete, equally spaced intervals of time (that is, the demand for patients dt is the current demand in week t and the demand Dt 1, Dt 2, Dt 3, in previous weeks might be used to forecast demand for l number of periods in the future l:1,2,3,.,n weeks ahead. Let zt(l) be the forecast made at origin t of the demand zt+l at some future time t + l. The function zt(l), which provides the forecasts at origin t for all future periods in the future, based on the available information from the current and previous values Dt 1, Dt 2, Dt 3, through time t will be called the forecast function at origin t Our objective is to obtain a forecast function such that the average of the sum of the deviations zt+l zt(l) Trend: It refers to the tendency for a decrease or increase in the data values over time. (i.e. the budgeted amount of money dedicated to the between the actual and forecasted values is as small as possible for each lead time l Time series forecasting methods assume that historical data is a good indicator of future demand. Before proceeding to the theory of the models, it is important to define the following terminology:

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25 production of a vaccine for a pandemic influenza has increasing trend, and it ca n been seen in Figure 6 a) Seasonality : It is a repeating pattern in the data values over time: day of the week, hour of the day, month of the year, et c. (i.e. Pneumonia and influenza mort ality rate shows a seasonal patter as seen in Figure 6 .b) Cycles: It refers to a cyclic variation similar to seas onality, except that the length and the magnitude of the cycle may vary. Randomness: it refers to a series in which there is no recognizable pattern to the data. Figure 6 : Examples of Trend and Seasonal Patterns in Healthcare Seasonal Influenza visits showed a seasonal patterns as it can be graphically perceived in Figure 7 with period N = 52 weeks which is equivalent to a year The time series methods used in this studied were selected due to the capacity they have to recognize trend and seasonal patterns in the data. Millions of dollars

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26 Seasonal Decomposition Using Moving Averages Moving average is the arithmetic average of the most recent N observations in a times series. Then zt To describe the seasonal pattern in a time serie s, it is assumed that there exists a set of multipliers c the forecast made in period t 1 for period t, is given by: t for with the property that The multiplier c t represents the average proportion amount that the demand in the tthFigure 7 period of the season is above or below the overall average. N is referred to the number of periods before the pattern begins to repeat as the length of the season (as it is shown in ) Figure 7 : Seasonal Patient Demand Over 137 Weeks

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27 Winter ss Method Winter s seasonal exponential smoothing method assumes that a time series is considered to consist of three components: level, trend and seasonality, and they change over time. In the additive version, a prediction is calculated by adding the components (Archibald, 2003). Winterss method is a type of triple exponential smoothing, and this has the important advantage of being easy to update as new data become available. The model has the following form: Where is the base signal or intercept at time t = 0 excluding seasonality, G is the trend or slope component, ct This model also assumes that the season is exactly N periods and that the seasonal factors are the same each season and have the property that Three exponential smoothing equations are used each period to update estimates o f seasonal decomposed series, the seasonal factors, and the trend. These equations may have different smoothing constants, which we will label is the multiplicative seasonal component in period t, and as the error term. = Smoothing constant for the level ( ) = Smoothing constant for the trend = Smoothing constant for the seasonal factor

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28 The Series: The Trend: The Seasonal Factors : Finally, the forecast made in period t for any future period t + is given by: Ca u s al Model s Causal models assume that forecasted data generating process can be explained by interaction of causal (cause andeffect) independent variables in the environment. Determining how t hese variabl e s are related to the output of a model or system can be a challenging problem, but the understanding of how variables are correlated can be very helpful. The causal models that are used for the seasonal patient demand in this research are Regression Anal ysis and Neural Networks. Regression Analysis A popular class of singleequation models to apply multivariate time series data is the multiple regression models. This class of model is probably the most widely used in practice and feature prominently in many texts on forecasting for management science and business students (Chatfield, 2001). Let (x1,y1), (x2,y2), (xn,yn) be n pair data points for the two variables X(weeks) and

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29 Y(demand) Assume that yi is the observed value of Y when xi Where and represent the amplitudes, and represents the periods. In order to find the Fourier series that fits the data well, it is necessary to determine how many cycles exist. MatLab 7.6.0 R2008a and the General Equations pane of the Create Custom Equation GUI (Graphic User Interface) was used to find the parameters that best described the seasonality of the data. For the first attempt, a c is the observed value of X. Refer to Y as the dependent variable and X as the independent va riable. Data is a seasonal time series, which suggests that the relationship exists between X and Y that can be represented by a Fourier series The Fourier series is a sum of sine and cosine functions that is used to describe a periodic signal. In this case, the Fourier series is used to find a function that is able to fit and describe the trend (if any) and seasonality patter n, and it is of the form : 1 = 522 week cycle is assumed and fit the da ta using one sin term and one cosine term. The goodness of the fit is evaluated using R square, and r esiduals plot analysis. R square statistical measure of how well a regression function approximates real data points. If the fit does not describe the data well, additional sine and cosine terms are added with unique period coefficients until a good fit is obtained.

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30 Demand Residuals The fit is an improvement over the previous fit, and appears to account for most of the cycles present in the seasonal influenza data set. The residuals appear random for most of the data as it appears is in Figure 8 Figure 8 : Fourier series Fitting a nd Residuals Plot Neural Networks Overview A Neural Network is a nonlinear model whose structure is thought to mimic the design of the human brain. Neural Network s have been applied successfully to a wide variety of scientific problems, and increasingly to statistical applications, notably pattern recognition (C hatfield, 2001). A Neural Network is a parallel, distributed information processing structure consisting of processing elements (which can possess a local memory and can carry out localized information processing operations) interconnected together with u nidirectional signal channels called connections. Each processing element has a single output connection which branches into as many collateral 0 20 40 60 80 100 120 -10 -5 0 5 10 15 Residuals 0 20 40 60 80 100 120 10 20 30 40 50 60 70 Data and Fits p vs. x (smooth) fit 2 fit 2 Weeks

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31 connections as desired (each carrying the same signal: the processing element output signal). The processing element output signal can be of any mathematical type desired. All of the processing that goes on within each processing element must be completely local: i.e., it must depend only upon the current values of the input signals arriving at the processing el ement via impinging connections and upon values stored in the processing element's local memory (Hecht Nielsen, 1989). Neural Network s consist of an input layer, an output layer and one or more hidden layer as seen in Figure 9 The nodes or neurons of the n etwork are arranged in consecutive layers (hidden layers) and the arcs are directed from one layer to the next from left to right. This type of Neural Network s is called feedforward networks or perceptrons. Basically, Neural Network s are built from simple units (neurons). These neurons are interlinked by a set of weighted connections ( w ). Each node or neuron is a processing unit that contains a weight and a s ummation function. A weight returns a mathematical value for the relative strength of connections to transfer data from one layer to the next. On the other hand, a summation function y computes the weighted sum of all input elements entering a neuron. In Figure 9 each neuron in the hidden layer computes the summation using the following formula:

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32 Input Layer Hidden Layer Output Layer Input 2 Input 1 Input j x1x2xj X0=-1 y0=-1xi,wijyj,wkjk Y1 Figure 9 : Neural Network Model Furthermore, a sigmoid function is used to transform the output so that it falls into an acceptable range (between 0 and 1). The objective is to prevent the output f rom being too large. The sigmoid function is of the following form: As previously described, Neural Network s consist of neurons or nodes organized in different layers: input, hidden, and output. The input layer corresponds to the factors that would be feed into the Network The information is propagated through the weighted connections to the hidden layers where it is analyzed. Then, the result of this processing is propagated to the next layer and eventually, to the output layer. The output is obtained by the following function:

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33 Once the network weights and biases are initialized, the network is ready for training. The network can be trained for function approximation (nonlinear regression), pattern association, or pattern classification. The training process requires a set of exampl es of proper network behavior: network inputs p and target outputs t. The back propagation algorithm objective is to minimize the mean square error function: This error functions tells us how good an approximation to the real function F is. The idea of the back propagation algorithm is to minimize this error (threshold) by adding for each training period, small changes in the directions that minimize the error function. This minimization method is called the steepest descent method. T he general learning process is described in the following steps: Random numbers are assigned to the weights For all data points in the data set, calculate the output using the summation functions of each neuron. Compare estimated output with actual values If the results from 3 do not meet a threshold value, repeat steps 2 and 3. A common problem that may occur when fitting the Neural Network to training data is over fitting. Over fitting occurs when the error of the training set is minimized to a very small value. As a result, when new data is introduced into the network the error becomes very large. In this situation the network has memorized the data set, and it is not able to generalize when new data is

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34 introduced into the network. Generalization r efers to the ability of the model to perform well on data that has not been used to train the network. There are two strategies that can be used to avoid over fitting: regularization and early stopping. Regularization involves modifying the performance function. Early stopping involves dividing the data set into two subsets. The first subset is the training set and the second subset is the validation set. At the beginning of the training process the error for the validation and testing sets tends to decrease; however, when the network starts to over fit the data both errors will increase. When the error for the validation set continues to increase for a specific number of iterations, then training is stopped. This research applies Neural Network as a tool to forecast patient demand to EDs unit when suffering of seasonal influenza. The traditional back propagation algorithm is used as the learning method for our network and early stopping criteria is used to avoid over fitting. Results Seasonal Decom position using Moving Averages: by comparing different estimates for N, the one with the smallest average error (Forecasted estimate in time t minus actual demand in time t) was chosen. Thi s method was implemented using N = 10. The forecasted estimates for the 137 weeks versus the actual demand are shown in Figure 10.

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35 Figure 10 : Moving Average Results Winterss method: after experimenting with various values of the parameters that would give the best fit of previous forecasts t o the observed history of the series. The estimates were found to implement winters method. According to [Nahmias, 2001], large values of the smoothing constant will result in more responsive but less stable forecasts The forecasted demand for the time series and real demand can be visualized for 137 weeks in Figure 11. Figure 11 : Winter's Met hod Results Regression Analysis using Fourier series : the function chosen to describe the time series for seasonal influenza visits to a hospital is a Fourier series 0 10 20 30 40 50 60 70 80 0 50 100 150DemandWeeks Demand MA(10) 0 10 20 30 40 50 60 70 80 0 50 100 150DemandWeeks Forecast Demand

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36 since the data clearly behave in a periodic form. Using MatLab curve fitting tool (cvtool ) the function of the form shown bellow is f o und: With: SSE: 1716, R square: 0.8775, adjusted R square: 0.8717, and RMSE : 3.705 And parameters: Table 1 : Fourier coefficients Coefficients (with 95% confidence bounds): a 0 = 19.15 (18.5, 19.8) a1 = 6.734 ( 8.336, 5.132) a 2b = 0.5396 ( 2.385, 1.305) 1 = 11.72 (10.54, 12.9) b 2c = 4.011 ( 4.973, 3.048) 1 = 52 (51.29, 52.72) c 2 = 26.19 (25.54, 26.84) The function suggests that two cycles exist in the data, one ( c1) equal to 52 weeks which is year ly and another ( c2Figure 12 ) of 26 weeks or bi annually The fitted function versus the historical data can be seen in

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37 Figure 12 : Regression Analysis Using Fourier Series Neural Network s: The architecture for the Neural Network used to predict the behavior of the time series is of the form: W b b W + + Butt on Input Layer Layer Output Butt on MatLab 7.6.0 was used for the calculation of this Neural Network the code used for this can be found in Appendix C: Neural Networks code. T he data obtained were studied using the layered Neural Network with a back propagation least mean square error learning algorithm. To predict patient demand, a Neural Network with 3 input nodes (year, month, and week), a single output node (number of patient that would asses a hospital suffering from influenzalike symptoms), and a onelayer back propagation network has been used. There is no standard formula to calculate the number of nodes needed in the hidden layer (Wang 1996). Basically, the number of hidden layers may be tested by trial and 0 10 20 30 40 50 60 70 80 0 50 100 150DemandWeeks Demand f(x)

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38 error. Figure 13 show the Neural Network forecasted values and historical data during 137 weeks. Figure 13 : Neural Network Forecasting Results Performance Me trics The forecasting methods used in this research are evaluated by the calculation of different performance measures. That is, Mean Absolute Percentage Error (MAPE), Absolute Deviation (MAD), Mean Square Error (MSE), Root Mean Square Error (RMSE), Tracking Si gnal (TS), and the Mean Error. In the following sections, each one of these performance measures is described. Mean Absolute Deviation (MAD) : The mean absolute deviation (MAD) is the average of the absolute deviation over all periods. MAD measures the average distance of the sam ple errors from the error mean If the value of MAD is large, it is reasonably to say that the errors in the data set are spread out (variable). In contrast to MSE, the MAD is very good at detecting overall performance of the mod el. It does not concentrate largely on the error of individual observations. The MAD is given by 0 10 20 30 40 50 60 70 80 0 50 100 150DemandWeeks Demand forecast

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39 MAD is appropriate to use when the numerical difference between the forecast value and the actual value is important. Mean Square Error (MSE): The Mean Square Error (MSE) can be related to the variance of the forecast error. This is extremely useful since it can be used to measure the variability or dispersion of the error. The forecast error for a particular period t is given by: MSE penalizes large errors for a single observation, and it is very good at detecting if a few observations have large errors. The smaller the value of the MSE the closer the fit is to the data. Mean Absolute Percentage Error (MAPE) : The mean absolute percentage error (MAPE) is the average absolute error as a percentage of demand and is given by: In practice a MAPE between 10% and 15% is excellent while a MAPE between 20% and 30% is average. Root Mean Squar e Error (RMSE): The RMSE is the distance on average of a data point from the fitted line, measured along a vertical line. The RMSE is given by :

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40 This statistic is easier to interpret since it has the same units as the values plotted in the vertical axis. Mean Error : The mean error is an estimate of the forecast bias. The mean bias should converge to zero as N increases if the forecasting is not biased one way or the other. The mean squared error is defined as follows : Tracking Signal (TS) : The tracking signal (TS) is used to monitor forecast bias. If the TS exceeds a predetermined bound, this indicates an alert that the forecast is being bias one way or the other. In general, the bound of the TS is between 6 units from the mean. If the TS is below 6 then the model is under forecasting. On the other hand, if the TS is above +6 then the model is over forecasting. This would indicate an alert for analysts who may have to decide on using another model. The TS is defined as follows Comparison of Techniques The forecasting techniques used in this research: seasonal decomposition using moving averages (N=10), Winter ss method ( ), regression analysis using a Fourier series, and Neural Network analysis ( 3 input nodes, one single output node: number of patient that would asses a hospital

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41 suffering from influenza like symptoms) The performance metrics described in the last section are applied to the forecasting methods and the results are shown in Table 2 : Table 2 : Comparison of Forecasting Techniques (note: all values are in generic units). MA(10) Winters Fourier Neural Net Mean Absolute Deviation (MAD) 2.88 5.18 3.66 3.56 Mean Square Error (MSE) 23.93 47.70 44.95 37.77 Mean Absolute Percentage Error (MAPE) 11.26% 24.70% 15.51% 15.43% Root Mean Square Error (RMSE) 4.89 6.91 6.70 6.15 Mean Error 0.03 4.39 1.07 0.17 Tracking Signal (TS) 0.10 0.99 0.05 0.14 Based on the results and its graphic representations Seasonal Decomposition using Moving A verage and Neural Networks yielded the smallest error when compared to the influenza demand data for the seasons 20042005, 20052006, and 20072008. The reason why the fist method works relatively better than the other s can be attributed to the small N = 10, which makes the model more sensitive to changes in levels but also more sensitive to noise that can be undesirable for future forecasts. Neural Networks and Fourier series also yielded similar errors estimates (being Neural Networks smaller) and both models give a smoother fitting and generalization of the data. RMSE indicates on average what the distance of the forecasted value with respect to the actual values is. The RMSE is an excellent performance measure for the forecast since it provides information easy to interpret that can be used for managers that can take this error into account for planning purposes (Rojas, 2006). For the methods used in this work, it was shown that the RMSE vales vary from 4.89 and 6.91.

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42 The mean error is an estimate of the forecast bias. If the forecasting model is not biased, the mean bias should converge to zero as N increases. Based on the results, Winterss method showed a tendency to under forecast while Neural Networks method and Moving Average are close to zero, which leads to believe that they are unbiased. Another metric to evaluate whether a method is under or over forecasting is the TS. If the TS at any period is outside the range 6, this indicates a signal that the forecast is over forecasting or under forecasting. Figure 14 shows that none of the methods falls outside allowable limits in any period, but it can b e seen a slight under forecasting under the demand picks for Neural Networks and Regression analysis forecasts. Figure 14 : Tracking Signal f or Forecasted Results 6.00 4.00 2.00 0.00 2.00 4.00 6.00 0 20 40 60 80 100 120Signal Value Neural Net Regr Winters MA(10)

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43 The forecasts were finally compared with the most current data available for ILI patients for the 2008 2209 seasons, the forecasts (red) and the current demand (blue) are shown in Figure 15. Seasonal Decomposition still demonstrated to be the most accurate representation. The forecasting methods estimates for the MAD are: Winters Fourier MA(10) NN 5.83 7.59 5.46 5.75 Figure 15 : Current Season 20082009 ILI Visits versus Forecasts. (Vertical axes represent demand and horizontal axes represent weeks) It was found that no method performed better than any other. Seasonal Decomposition using Moving Average appeared to be the most accurate representation based on the data. However, a paired t test was conducted on

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44 the Mean Absolute Deviation (MAD) to det ermine if the performance difference between the utilized models was statistically considerable ( Appendix E: Statistical Test of MAD ). The test statis tics revealed that the difference in performance between the Seasonal Decomposition model and the other models is not statically significant (large p value) for this case. Discussion The time series methods were more sensitive to the data and demand changes (i.e. according to the CDC, during the weeks between Christmas holidays and New Years, the demand of patients going to a hospital decreases) but they fell short in providing a generalized behavior of the data which in some cases is mor e desirable. [Yokum, 1995] studied the criteria used to select a forecasting technique, and it was determined that other than accuracy, other factors including: ease of implementation, use and interpretation, theoretical relevance, and flexibility should be considered. This selection criterion is expanded in the next chapter Neural Networks does not require developing algorithms specific to problems and they can easily handle nonlinear functions. An advantage over other traditional methods : to analyze a nonlinear relationship using linear regression analysis, it is necessary to first analyze the nonlinearity of the system and determine whether some input need to be squared or two input variables need to be combined. This analysis is overcom e by the neural networks capabilities.

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45 Another aspect that this comparison yielded is that there is no significant statistical difference on performance between regression analysis with Fourier series and Neural N etworks and there is no statistical evidence to suspect that one method performed better than the other as it is demonstrated with a paired t test where the two methods were compared ( Appendix E: Statistical Test of MAD ).

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46 CHAPTER 4 PANDEMIC INFLUENZA SCENARIOS Abstract Predicting the impact of a Pandemic Influenza is very complex due to the many unknown variables that may play a role to how severe a pandemic can be. Scenario planning is considered a type of forecasting that consider a set a different potential outcomes and help decision makers better understand the role of uncertainties and become prepared to make important decisions This research considers five scenarios for the demand of patients to a hospital based on the severity levels, and proposes a Pandemic Proportion Constant (KPPCIntroduction ) that helps determine how severe a Pandemic Influenza can be as a function of seasonal influenza forecasted demand. The Centers for Disease Control and Prevention has developed a surveillance system that collects and reports data concerning influenza activity with special focus on the months of October through May which represent th e season where influenzarelated cases are more frequent (Thompson, 20 06). In the last years, this information has become more comprehensive and complex, and together with data on national hospitalization mortality rates, statistical models have been created to estimate the burden of the disease associated with influenza in the United States.

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47 The previous chapter studied the most recent data for the influenza seasons (20042005, 20052006, 20062007, and 20082009), and made use of different forecasting methods both timeseries and causal models. It was found that Seasonal Decomposition using Moving Averages yielded the best results or smallest estimates for every performance metric used (MAD, MAPE, MSE, RMSE,ME, and TS), and it was also very accurate w hen it was compared to the most recent data available (20082009) for influenz a visits Neural Networks and Regression Analysis came after Seasonal Decomposition (very close to each other) with still small forecasting error s and good description of the data. One very important application of the implementation of surveillance is the estimation of the possible impact of future pandemic. According to the Centers for Disease Control and Prevention, examining demographic trends among the United States population and patters in influenzaassociated mortality provides useful information concerning the future effects of seasonal and pandemic influenza. In this research, we use seasonal influenza data estimates to estimate the potential burden of a pandemic influenza to the flow and operations of EDs Five different scenarios are evaluated depending on five different severity levels; thus, it ranges from the mildest severity levels that refers to the seasonal or inter pandemic influenza behavior, to the most severe w hich it compares to the 1918 Spanish influenza that left an estimated of 548,000 deaths in the US. These scenarios and the demand model for the pandemic scenarios will be expanded in the subsequent sections of this chapter.

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48 Motivation There exists a widespread concern among policy makers and public health experts about the worldwide epidemic of influenza. Novel influenza A (H1N1) is a new flu virus of swine origin that was first detected in April, 2009. The virus, also referred as swine flu, is a type of influenza virus that causes respiratory disease. The virus is currently infecting people and is spreading from personto person, sparking a growing outbreak of illness in the United States. An increasing number of H1N1 cases are being reported internationally as well (CDC, 2009). The s pread of the disease is thought to be in the same way that regular seasonal influenza viruses spread (coughs and sneezes). According to experts, it is uncertain at this time how severe this novel H1N1 outbreak will be in terms of illness and death compared with other influenza viruses. Because this is a new virus, most people will not have immunity to it, and illness may be more severe and widespread as a result. In addition, currently there is no vaccine to protect against this novel H1N1 virus. CDC anticipates that there will be more cases, more hospitalizations and more deaths associated with this new virus in the coming days and weeks. The challenge of creating the public health infrastructure in the US that would be adequate to face a situation of this nature is of imminent need. The US Government has committed $3.8 billion toward planning and preparing for the next Pandemic Influenza, and Australia has also put AUD$555 million toward this initiative (Murray et al., 2006). These considerable efforts are in part due to the

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49 potential mortality and overall chaos. Mortality estimates that start from 2 to 360 million and even up to 1 billion have been proposed (WHO, 2005). Background Three mayor Pandemic Influenza outbreaks have emerged during the 20th Century: The 1918 Spanish Influenza, the 1957 Asian Influenza, and the 1968 Hong Kong Influenza. [Belshe, 2005] stated that pandemic influenza virus may originate through at least two mechanisms: the reassortm ent between an animal influenza virus and a human influenza virus that yields a new virus, and direct spread and adaptation of a virus from an animal to a human. In 1918, an H1N1 virus closely related to avian viruses adapted to replicate efficiently in h umans. In 1957 and in 1968, reassortment events led to new viruses that resulted in pandemic influenza. The 1957 influenza virus acquired three genetic segments from an avian species, and the 1968 influenza virus (Hong Kong influenza, an H3N2 virus) acqui red two genetic segments from an avian species. Future pandemic strains could arise through either mechanism (Belshe, 2005). In Appendix D: Mechanisms of Pandemic Virus Origination analysis of virus origination is further explained. The 191820 Spanish Flu Pandemic is considered the most mortal Pandemic Flu in History. Experts have estimated casualties of about 20 to 100 million deaths worldwi de. These estimates are based on various historical documents, including national commission, eyewitness accounts, and local government reports (Murray et al. 2006). [Taubenberger, 2006] explains that the Spanish influenza caused approximately 50 million deaths worldwide out of

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50 almost 500 millions infected persons. The Spanish influenza appeared in three waves, being the second one the most lethal. In Figure 16 the three waves and the death rates for the United Kingdom case are shown. Figure 16 : Three Pandemic Waves: Weekly Combined Influenza and Pneumonia Mortality, Unit ed Kingdom 1918 1919. Another interesting characteristic of this pandemic compared to historical data of previous influenza for the last 150 years, which show the highest mortality rates in the infants and very old, is that it also had a high mortality r ate for the young adults (Taubenberger 2006). Figure 17 shows U and W shaped combined influenza and pneumonia mortality by age at death, per 100, 000 persons in each age group, United States, 1911 1918. Influenzaand pneumoniaspecific death rates are plotted for the inter pandemic years 1911 1917 (dashed)

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51 Figure 17 : "U And W Shaped Combined Influenza and Pneumonia M ortality CDC expresses that even with the current method, planning, and preparations; the return of a pandemic virus equivalent in pathogenicity to the virus of 1918 would likely cause more than 100 million deaths worldwide. A pandemic virus with the pa thogenic potential of some recent H5N1 outbreaks could cause substantially even more deaths. The Influenza Virus is naturally carried by birds worldwide, and is very contagious among them. There are di fferent types of influenza virus and all known virus e s can be found in birds. There are only three known A subtypes of influenza virus (HIN1, H1N2, and H3N2) that are currently circulating among humans, and for which we have immunity. The main problem is that avian influenza viruses are constantly emerging and mutating; thus, they might become capable to spread among humans, leaving us exposed to a new deadly disease for which we might not have immunity (CDC 2007) Among the virus that have been able to cross the barrier from animal to human, H5N1 has been the most lethal with the largest number of detected

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52 cases. As of June 2009, the current situation for the novel swine flu H1N1 in the United States reports a total of 7927 confirmed or probable cases and 11 deaths (CDC, 2009). Problem Formulation A pandemic is caused by influenza A virus for which there is no preexisting immunity, facilitating the viruss rapid spread throughout the world. During the past 120 years, 4 pandemics have occurred. Although some mortality surveillance h as been in place in selected areas since the 1889 pandemic, new surveillance techniques have increased our understanding of features based on the past 3 pandemics (Monto et al. 2006). Pandemics do not follow a pattern, and data review of previous pandemic data suggests that no epidemiological profile, periodicity, origin, and timing between waves exist (Taubenberger, 2006). The problem considered in this chapter is the estimation of the potential patient demand that an emergency department will have under a set of five levels of severity ( scenarios ) for a pandemic influenza breakout The concept of severity levels has been adopted by information available from the CDC and WHO, and how they defined five Pandemic Severity Index es (PSI) The objectives are as it follows: To develop a demand model that replicates a generalized behavior of the seasonal influenza. By a generalized behavior we mean one that shows the periodic, bell shaped or sinuous behavior of the seasonal influenza

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53 visits to a hospital, and without the i mpa ct of undesired noise (i.e. d ecrease on demand due to New Years holidays). To prove that there is a severity level such that a severe influenza season can be modeled as a proportion of another less severe. To explore and determine which seasonal influenz a demand forecasting models is the most appropriate to represent the behavior of the data. To define a set of scenarios for the demand from a mild influenza season to a severe pandemic (1918 Spanish Influenzalike). Specifically, the following questions w ill be answered in through this work : Can a seasonal influenza season patient demand be modeled by the product of a proportional estimate and another less or more severe season? Can a seasonal influenza based model be used to replicate a more severe pandemic influenza? What demand is calculated for each influenza demand scenario for every week? What is considered a s an influenza season and what length of time should be used? Methodology Figure 18 depicts how this chapter interacts with the rest of this thesis. Based on the forecasting estimates from previous chapters, the model that best represents the seasonal influenza patient demand is chosen. Based on information available from the pandemic influenza that has appeared in the last

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54 hundred years, and the seasonal influenza forecasting model, a patient demand surge model is created to replicate five scenarios with different severity levels. Chapter 3: Forecasting Modeling of Visits for Patients with Influenza Chapter 4: Pandemic Influenza Scenarios Chapter 5: Simulation Modeling and Optmization Chapter 1 and 2 CDC Surveillance Data Time-series and Causal Forecasting methods Forecasting Performance Metrics Problem Statement Literature review Research Methodology Problem Formalization Research Objectives Forecast estimates for influenza patient demand using: Seasonal Decomposition Winterss Method Regression analysis Neural Networks Previous Pandemic Influenza data Set of potential scenarios for a pandemic influenza patient surge to a hospital Data collection of the emergency department activities. System analysis, description and modeling Assumptions Nurse Allocation Maximum Capacity Determination Recommendations Limitations Figure 18 : Thesis Flow for Chapter 4 Pandemic Influenza Model In February 2007, the Unites States government released guidelines to help cities and states prepare for an Influenza Pandemic The guidelines included a Pandemic Severity I ndex (PSI) designed to help officials predict the severity of an outbreak and put appropriate mitigation strategies in place. The PSI was developed by the Centers for Disease Control and Prevention, and the characteristics fo r every category in terms of case fatality (proportion of death among the critically ill), excess death rate (the rate of death per 10,000 persons

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55 compared to the normal seasonal baseline, and the equivalent influenza event in the United States experience are listed in Table 3 Table 3 : Pandemic Severity Index PSI Case fatality (%) Excess death rate (%) Potential no. of deaths (2006 population) US Experience 1 < 0.1 < 30 < 90,000 Seasonal Influenza 2 [0.1, 0.5) [30, 150) [90,000, 450,000) 1957 and 1968 pandemics 3 [0.5, 1.0) [150, 300) [450,000, 900,000) none 4 [1.0, 2.0) [300, 600) [900,000, 1.8 mil) none 5 > 2.0 > 600 > 1.8 mil 1918 pandemic From this point on, seasonal influenza is going to be considered as a Pandemic Influenza with and PSI equal to one. The objective is to determine which forecasting method implemented in Chapter 3 is more adequate to represent the demand during seasonal influenza. Model Selection Four forecasting methods were used to predict t he demand of patient visits to hospitals and a series of performance metrics were applied to measure accuracy (results can be obtained from Table 2 ). Seasonal Decomposition yielded the smallest errors at forecasting, but after comparing its performance using a paired t it was found that the re was no significant difference on their performance. The selection criteria procedure used in this paper for the forecasting method (chapter 3) that would be more appropriate to describe the patient demand during a Pandemic Influenza with PSI equal to one is based on the study made by Thomas Yokum and Scott Armstrong: Beyond Accuracy: Comparison of Criteria Used to Select Forecasting Methods. According to

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56 Yocum, research in forecasting has assumed that accuracy i s the primary criterion in selecting among forecasting techniques in the past. It has been used as the only criterion in many studies. Moreover, in the 1992 International Journal of Forecasting papers that compared the results of different techniques and series, only one used criteria other than accuracy. In this paper we expanded the selection criteria based on sole accuracy to other important forecasting characteristics such as: ease of interpretation, use, implementation, and adaptation to conditions. The procedure to select the appropriate method consist s on rating each forecasting method in every criteria type. A scale ranging from 1 to 4 is used: 1 referring to the lowest ranking and 4 as the highest. Table 4 lists the forecasting criteria facets and the weight for each one. The weights are the average ranking (out of 7 points) of importance given by 322 experts from a total of 738 questi onnaires sent to International Institute of Forecasting (IIF) members and nonmembers. For every forecasting method, the weighted total ranking is calculated as the sum of the product of the method rating and weight for every criteria facet. Table 4 : Forecasting Method Selection Criteria. ( Note: All values are in generic units) Criteria Weight (out of 7) Seasonal Decomposition Neural Networks Regression Analysis Winters Accuracy 6.2 4 3 3 2 Ease of interpretation 5.69 3 3 4 3 Adaptive to conditions 5.58 2 4 4 2 Ease of use 5.54 3 4 4 3 Ease of implementation 5.41 3 4 4 3 85.88 101.79 107.48 73.48

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57 It was found in chapter 3 that Seasonal Decomposition had the smallest performance error (MAD, MAPE, MSE, TS, ME), but it did not have a significant difference in performance when compared with the other methods. Therefore, accuracy cannot be the only se lection parameter in this case. T he introduction of other parameters i s very important. The model to be used as the representation for the influenza patient demand is r egression modeling with a Fourier series because it had the highest rating due to good interpretation capabilities, and it is a mathematical function that can be adapted to different conditions by varying the par ameters (amplitude, period, level) T he Fourier function with independent variable x = weeks and y =patient demand: With: SSE: 1716, R square: 0.8775, adjusted R square: 0.8717 RMSE : 3.705 a nd parameters: Coefficients (with 95% confidence bounds ) ) a0 a = 19.15 (18.5, 19.8) 1 a = 6.734 ( 8.336, 5.132) 2 b = 0.5396 ( 2.385, 1.305) 1 b = 11.72 (10.54, 12.9) 2 c = 4.011 ( 4.973, 3.048) 1 c = 52 (51.29, 52.72) 2 = 26.19 (25.54, 26.84)

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58 Pandemic Influenza Severity Index Demand Models Studies have been done to identify the length of an epidemic period, and it has been defined as those weeks when the observed number of deaths exceed the epidemic threshold defined by the CDC as the upper 95% confidence limit to the baseline (Simonsen, 1997). It has been found that the model for the pandemic season last for 12.5 weeks in average (range from 6 to 18 weeks), and this also coincides with the assumptions made by the CDC, and also the Influenza Pandemic Plans for the Veterans Hospitals assumptions (VA, 2006) and FluSurge: a pandemic patient demand estimator software available (Zhang, 2005). The model that thi s study will implement will assume outbreak duration of 12 weeks ( ) in which the demand ( ) will vary following the Fourier functi on found in the last section. It is intended to find the demand function of the expected Pandemic Influenza patient demand for fi ve different severity scenarios: The most critical PSI proposed by the CDC is comparable to the Spanish Flu pandemic that occurred in 1918. Having already determined the demand function for the PSI 1, it is aimed to find the demand function for a PSI 5 scenario. The procedure to do so is explained as it follows: Define assumptions: a ccording to the CDC propose pandemic planning assumptions, he clinical disease attack rate will likely be 30% or higher in the overall population during the pandemic. Illness rates will be highest among school aged children (about 40%) and decline with age. Among working adults (ages from 1865) an average of 20% will become ill

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59 during a community outbreak. Of those who become ill with influenza, 50% will seek outpatient medical care. Other assumptions made for the parameters used in CDC planning models model can be seen in Appendix F: Assumptions for Pa ndemic Influenza impact This model takes into cons ideration the age distribution for the population that is being studied. The Hillsboroug h county population data used belongs to the 2007 census bureau: Persons under 18 years old, percent, 2007 292,834.43 Persons between 18 and 65 years old, percent, 2007 749,797.84 Persons 65 years old and over, percent, 2007 138,151.73 Total 1,180,784.00 Choose site for the model application: This study is intended to be applied to individual emergency departments. For practical purposes, a Hospital in the city of Tampa FL is chosen The proportion of t he total patient arrival s for a particular hospital is based on its capacity. For the city of Tampa, the list of emergency departments and capacity (expressed as number of beds) are shown in Appendix G : Number of beds per hospital in Tampa James A. Haley Veterans' Hospital is use d as example, and it is expected that 13.43% of the total patient cases will be seeking treatment in this facility Estimate total demand: a ccording to the CDC assumptions it is expected that a total of 354,235 persons in the Hillsborough county will become ill, out which 177,117 (50%) will be seeking treatment in a hospital during the

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60 12 week outbreak 23,786 ( 13.43% ) of those persons are ex pected to access to the James A. Haley Veterans' Hospital Establish total demand function: Choosing a function that is continuous through the interval posses a geometric motivation: the total demand over the time range (112) can be r epresented as the ar ea of the region bounded by and Figure 19 gives the graphical representation of the area by integrating : Where is such that and indicates an increment larger than 0. Figure 19 : Integrals as the Area under a Function Curve The results for the total demand (considered as where is the function for the P andemic S everity I ndex ). By integrating the Fourier series for the PSI 1 patient demand model is given by:

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61 Estimation of a Pandemic Proportional Constant ( ): This research aims to propose that the demand function for PSI 2,3,4,and 5 can be expressed a the demand function for PSI 1 multiplied by a constant named Pandemic Proportional Constant ( : The total demand is used to calculate and the estimates are shown in Table 5 The total demand for the severity levels between the mildest and the most severe was calculated by interpol ating between the PSI 1 and PSI 5, using the same proportions implemented by the CDC guidelines as shown in Table 5 : Total Demand for the PSI Table 3 Table 5 : Total Demand for the PSI Pandemic Severity Index Demand (12 weeks) 1 438 2 2,973 3 5,947 4 11,893 5 23,786 Let Then the fundamental theorem of calculus says that the derivate exists at each point in the open interval [a, b] where is continuous and for each we have Also, it has been proven that:

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62 A list of the KppcTable 6 constants found in this study for the five PSIs is show in Finally, the demand functions for every scenario were found, and they are graphically represented in Figure 20 Table 6 : Pandemic Proportional Constants Figure 20 : Five Pandemic Influenza Demand Scenarios Pandemic Severity Index 1 1 2 6.8 3 13.6 4 27.2 5 54.3 Number of visits

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63 Discussion Due to the uncertainty of how an Influenza Pandemic would impact society systems such as transportation, economy, healthcare systems, schools, and other social disruptions, this research considers that contemplating different scenarios from the most optimist to the w orst case scenario. According to [Edmonston and Fost 1998], an increasing number of analysts are using this technique, and that for some businesses have reacted faster and better than their rivals when the changes happened, because scenario planning exercises had prepared them to respond well to change s. Scenario building is another way of analyzing, and it is way of avoiding predicting the future wrong in fundamental and critical ways. According to author John Petersen, president of the A rlington Inst itute it is not possible to plan for all possible scenarios. It is preferable to consider some of them, and question what common elements exist across all of them?, What are the major threats?, and start building the system capability necessary to face t he potential impact. These scenarios will be consider ed in chapter five, and they will be used as input to a simulation model that replicates the dynamics in a emergency department.

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64 CHAPTER 5 EMERGENCY DEPARTMENT SIMULATION MODEL DURING A PANDEMIC INFLUENZA OUTBREAK Abstract This research proposes a nurse allocation policy to manage patient overflow by simulating five scenarios of different severity levels for a pandemic influenza outbreak. The objective is to minimize the number of pa tients waiting in queue to be treated by a nurse while maximizing patient flow. The model is built using ARENA simulation software and OptQuest heuristic optimization to propose various combinations for the number of nurses needed for healthcare delivery. Results are compared with a basic setting that closely emulates the resources and components in a Veterans Hospital. The proposed method reduced patient average waiting of various activities held in the emergency department: baseline assessment, registration, and treatment by 90%, 93%, and 96% respectively. The average number of patients waiting for baseline assessment, registration, and treatment was reduced between 85% and 89 also Introduction This chapter studies an emergency department system dur ing a pandemic influenza outbreak. The results obtained from the previous chapters; specifically, the patient demand scenarios obtained from chapter 4 are used as input to a

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65 simulation model. T o visualize how this chapter follows in this work, see Figure 22. Chapter 4: Pandemic Influenza Scenarios Chapter 5: Simulation Modeling and Optmization Previous Pandemic Influenza data Set of potential scenarios for a pandemic influenza patient surge to a hospital Data collection of the emergency department activities. System analysis, description and modeling Assumptions Nurse Allocation Maximum Capacity Determination Recommendations Limitations Figure 21 : Thesis Flow for Chapter 5 According to many scientists and epidemiologists, a new Influenza Pandemic outbreak was unavoidable. Moreover, on June 11, 2009 the first pandemic outbreak of swine flu of this century has been confirmed by the WHO with a moderate severity Experts agreed that it was not a matter of whether or not it would occur, but when (Roche, 2007). The word pandemic has been defined as a disease that emerges when a new virus appears, and then spreads easily from person to person worldwide. Pandemic occurs after thre e conditions are met: first, the emergence of a new flu strain; then, the ability of the strain to infect humans and cause serious illness; and finally, the easily human to human spread (DHHS 2007). Due to drastic increase in the number of patients ass essing hospitals services during a severe pandemic influenza outbreak it is vital for hospital management to develop a reliable plan to face events of this magnitude. Also,

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66 e mergency department environments possess a limited number of resources (i.e., nu rses, physicians, pharmacists) for the everyday routinely requirements. During and after an Influenza Pandemic incidence, the impact on patients demand and the complexity of the cases could become overwhelming enough to result in a chaotic system impossi ble to operate. In this research, a simulation modeling approach is developed to enhance understanding of emergency departments intricacies, as well as nurse allocation and utilization. In general, simulation modeling is an adaptable and informative tool, and it can be used in assisting decision makers to better strategize when allocating limited staff personnel to critical tasks. Literature Review Simulation in Healthcare has grown in popularity because it can be used for dynamic as opposed to static analysis (Eldabi and Paul 2001). Simulation has been used in emergency department for maximizing capacity (Baesler et al. 2003), assisting expansion plans (Wiinamaki and Dronzek 2003), reducing length of stay (Samaha et al. 2003), and to assess indoor ai rborne infection risks (Liao et al. 2003). To capture how emergency departments systems behave during normal conditions and how they react to unexpected situations, a variety of methods ranging from simulation to optimization techniques have been utilized in the literature. For example, ED systems analyzers have studied queuing systems complexities (Panayiotopoulos 1984); other analysts have used metamodels (a model of a set of related models) a technique widely used in artificial neural

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67 networks. Metamodeling is a good technique to explore when dealing with the stochastic n ature and complex dynamics of the Hospital EDs (Kilmer 1995); to reduce overcrowding and reduce the number of patients leaving without being t reated (Hung et al. 2007); [Kolker, 2008] utilized principles of Operation Research to mimic different scenarios and propose solutions to reduce patient length of stay; to reduce overcrowding prediction in emergency departments (Hoot et al. 2008). We present a computer simulation model that captures the dynamics on an ED during a drastic increase of patient deman d over a short period of time (12 weeks). This research focuses on modeling the allocation of nurses. Because there is no way of know what the real impact of a new Pandemic Influenza outbreak would be, various scenarios are explored and a set of alternati ves are generated to determine the maximum capacity and best combination of resources that increases patient flow and decreases the number of patients waiting. Although simulation modeling has been widely used in various health care environments, it has n ot been used very extensively in the area of biological disease outbreaks or chemical attacks. A few of the models found in the literature include: a probabilistic transmission dynamic model created to assess indoor airborne infection risks considering v arious scenarios of exposure in a susceptible population for a range of R0 (basic reproductive number) (Liao et al. 2005); a software called SEARUMS (Studying the Epidemiology of Avian influenza Rapidly Using Modeling and Simulation) which enables rapid scenario

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68 analysis to identify epicenters and timelines of outbreaks using existing stat istical data (Rao et al., 2008); a simulation based type of methodology developed to analyze the spread of H5N1 using stochastic interactions between waterfowl, poultry, and humans (Rao et al. 2008). Problem Formulation A large flow of patients is expected to access EDs during an out break. Thus, a pre pandemic planning or a course of action is crucial to provide quality service, effective care to ill persons, and intelligent strategies that help prevent further spread of the infection. According to pandemic protocols, once the outbre ak occurs, hospitals must dedicate an exclusive area for patients with the pandemic virus. This area will be divided into five zones: triage, green, yellow, red and black (Davey, et. al. 2006). Given the limited availability of nurses (even during normal daily operations), this study explores how to efficiently allocate nurses to the different zones for improved ED performance. Nursing personnel are essential for an effective response to high patient demand, including patient care, patient tracking and information management, and logistical support This study concentrates on this critical resource, by finding an optimal combination on levels of resources in the five zones with capacity and resource utilization objectives such as: Maximize patient throughput in the system: It is aimed to prove that by improving the efficiency of the system, more patients will be able to be treated during the breakout.

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69 Minimize number of patients transferred to other facilities: when the system reaches its maximum ca pacity, patients arriving will be sent to other facilities to be treated Minimize average number of patients waiting to be treated: quality of service is measure by how many and how long patients are waiting for treatments. Resource utilization: the goal is to find the service levels in every area and find the combination that utilizes the resources in proportional levels; that is, resource utilization in any zone should not be significantly higher than in another zone. Specifically, the following questions will be answered in through this work: How does the allocation of resources impact the efficiency of the system, in terms of queue length and waiting times? What are the most critical zones in the ED during the five Pandemic Influenza scenarios? What bottlenecks can be identified in the current system? What is the optimum nurse allocation during each of the five patient demand scenarios? How does the optimal proposed system impact resource utilization for the nurses in the different areas? Can assumptions made for this model be validated with current moderate Swine Flu pandemic outbreak?

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70 Methodology In this chapter a simul ation model is created, and us es the arrival rates obtain in c hapter five for five patient demand scenarios ( the dema nd function curves can be seen in Figure 20 in Chapter 4 ) Besides the forecasting results from previous chapter, data collection from emergencies departments and other assumptions for the impact of a pandemic influenza outbreak are also implemented in the model. The first step towards the creation of the simulation model for this study is, as depicted in Figure 22 a problem form ulation and defining the objectives and research questions. Problem Formulation Setting of Objectives and overall project plan Model Building Data Collection Coding Verified> Validated? NO NO NO YES Experimental Design Production Runs Documenting and reporting Figure 22 : Steps in Simulation Study

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71 A simulation model is created and is run for 5 replications to better capture the behavior of the system and obtain better estimates. The verification process is iterative; the simulation model is verified to determine whether the computer implementation of the conceptual model is correct The simulation model is also animated to visually verify the system is behaving properly ; that is, it can be detect ed actions that might seem illogical R esults are analyzed, and by using OptQuest optimization tool of ARENA, a new allocation of resources is proposed in accordanc e with the chosen objective functions and performance measures. The final output of this is a new allocation model for nurses levels in the different zones of the ED, limitations of the model are explained, and recommendations are given to face the situat ion under study. Model Description This simulation model is developed using Arena 10.0 simulation software. The initial objective is to evaluate th e system performance during different levels of demand. Then, OptQuest for Arena is used to find the optimal allocation of resources in the different areas of the hospital. The simulation model is divided in to five zones These five zones include: Triage Process Green Zone Yellow Zone Red Zone Black Zone

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72 Every patient is c onsidered an entity entering the model. A patient accesses the triage zone where he/she is processed by a nurse. In the next section, a more detailed description of the processes that occur in the system is given. Conceptual Model Potential infected pati ents arrive to triage process. Triage is a sorting process where nurses determine how critical a patients illness is. The patient is tagged with a color that represent one of the different zones where he or she can receive a proper treatment (these categ ories are red, yellow, green, and black). The criterion of sorting a patient to the different areas depends on the severity of the symptoms that the patient exhibits, and the complexity or number of medical procedures that might be required (Vance and Spr ivulis, 2005). A patient accesses the triage zone where he is processed by a nurse. The estimated time for the triage process is based on a triangular distribution with parameters 1.42, 2.75, and 4.5 minutes (Hupert et al., 2003). Patients with the mildest symptoms are considered an outpatient visit, and these patients go the green zone, where they will be registered, receive a health condition assessment and medical tests, and finally treatment. Patients with the most severe sympt oms go to the yellow and red zone. In the red zone, patient with the most severe symptoms are present, and they need ICU treatment. Patients in less advanced stage of the illness go to the yellow area and use ventilator and recurrent treatment. Patients that are beyond any medical help are taken to the black zone. Figure 23 gives a graphic representation of the process that is being described here.

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73 Figure 23 : Process Flow for the EDs during a Pandemic Influenza After the triage process the processes performed by nurses for the red and yellow zones are similar: the registration is performed, and baseline assessment while the patient waits to be treated. The patient seizes a bed and waits to be seen by a nurse. The nurse decides if a c onsultant should be called to conduct a more detailed examination of the patient. The physician might order more tests for the patient if needed (this process is represented in the simulation as delay) The consultant could also discharge the patient base d on his expertise. If the consultant orders tests, the patient will continue through the process of testing. The consultant or an authorized member of the staff can decide which type of treatment should be provided. If there is no need for a consultant, the patient is treated by the nurse who performs the first examination. Once the tests have

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74 been completed, there is a delay until a clinical decision can be made by the attending physician. The clinical decision determines illness level of severity and t he treatment to be used. The patient will stay in the systems while receiving treatment. After a period of time, the pati ent should improve and go home. Time estimates for the processes can be retrieved from Appendix I: Time estimates for the processes held in the ED. Assumptions The number of hospitalizations and deaths will depend on the virulence of the pandemic virus. The number The clinical disease attack rate will likely be 30% or higher in the overall population during the pandemic (CDC Pandem ic Planning Assumptions, 2009). of N umber of episodes of illness, healthcare utilization, and death associated with moderate and severe pandemic Influ enza scenarios. (CDC Pandemic Planning Assumptions, 2009). Estimates on impact of virulence of a pandemic on healthcare can be seen Table 7 in and are based on extrapolation from past pandemics in the United States. Average length of nonICU hospital stay (yellow zone) for influenzarelated illness is 5 6 days (CDC FluSurge, 2005). Rates of absenteeism will depend on the severity of the pandemic. The simulation model in this study assumes that the number of nurses will decrease 5% weekly for the first 5 weeks of the outbreak.

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75 Average length of ICU stay and ventilator usage (red zone) for influenzarelated illness is 10 days (CDC FluSurge, 2005). Patient s in the yellow zone will require receiving treatment every 6 hours from the nurses during the length of stay. For the red zone, the frequency of treatments is every 3 hours. Table 7 : Estimates for Rate of Illness, Outpatient Visits, Resources Utilization, and Deaths for Pandemic Assumptions. Estimates Are Based On 2006 Population Characteristic Moderate 1958/68like (number of persons) Severe 1918like (number of persons) Illness 90, 000, 000 90, 000, 000 Outpatient medical care 45, 000, 000 45, 000, 000 Hospitalization 865,000 9,900,000 ICU care 128,750 1,485,000 Mechanical ventilation 64,875 742,500 Deaths 209,000 1,903,000 This simulation models uses the CDC pandemic planning assumptions on the virulence of the virus. The triage sorting process that takes place in the ED determines what proportion of visits goes to the green, red, yellow, and black zone. Based on the estim ates from Table 7 this study assumes that out all visits to the ED, 22% of visits will be needing hospitalization, re current treatment, and they go to the yellow zone, 5% percent of visits requires more intensive treatment (ICU and ventilators) and goes to the red zone, 68% of visits will not require to be hospitalized but will go through the process once to receive treatment, and the other 4.2 percent

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76 of visits will be those who are beyond medical help, and are sent to the black zone. If an influenza pandemic progresses to the point where thousands of people are ill at the same time, most cases will be clinically diagnosed and treated empirically without laboratory confirmation (Association of State and Terri torial Health Officials, 2002). The Hospital chosen as prototype for the implementation of the simulation is the James A. Haley Veterans Hospital, and estimates for the resources a vailable according to the VA Respiratory Infectious Diseases Emergency Plan (Farley 2006) is depicted in Table 8 Table 8 : Estimates for the resources available according to the VA Respiratory Infectious Diseases Emergency Plan Resources available Nurses 30 Non ICU Beds 111 ICU Beds 40 Number of Ventilators 84 Verification The checking process is iterative. In the process of building the simulation model, when discrepancies among the conceptual and operational model appeared, the model was checked for errors. The verification process in this study included the examination of the simulation program SIMAN to insure that the operational model accurately reflects the conceptual model.

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77 The verification procedure also included checking that the input data (arrival times, processing time, and decision modules) were being used appropriately (i.e. Make sure that times units concord throughout the model and results were reasonable). Finally, the simulation model was animated to detect actions that were behaving wrongly or resource utilization levels during the run of the simulation A snapshot of the simulation model for week 7 of the outbreak animation can be seen in Appendix J: Snapshot of simulation animation. Validation Validation refers to the variety of subjective and objective techniques used to validate the conceptual model. A c onceptual model of a real world system must appear reasonable to those that are knowledgeable about the real system. To achieve this, t he conceptual model was designed together with the emergency management program coordinator from the James Haley VA hospi tal. Also, we were able to be part of the 2007 pandemic influenza drill where many the tasks that nurses perform and protocols used could be documented and implemented in the conceptual model. Other than opinions of expert personnel in the area, the simulation assumptions validity is enhanced by the use of assumption from institutions specialized in the area of study; that is, the Center for Disease Control and Prevention (CDC), the World Health Organization, and UD Homeland Security assumptions.

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78 Results The model was run for 5 replications of 2016 hours (~12 weeks). A SIMAN summary of results can be seen in Appendix K: SIMAN simulation summary report The current system allocation model assumes distribute the number available of nurses (30) as it follows: Green Zone 7 Yellow Zone 7 Red Zone 7 Triage Zone 7 Black Zone 2 Resource utilization: It is observed that the utilization for the nurses in the yellow zone is considerable higher than in the other zones. Even though the yellow zone receives 22% of patients visits compared to the green zone which receive 68% of patient demand, patient s in the yellow and red do need recurrent treatment from the nurses. A 3D surface comparing resource utilization for nurses in the various zones for the five severity levels is depicted in Figure 24, and estimates used for this graph can be obtained from

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79 Figure 24 : Nurse Utilization of the Various Zones for the Five Severity Scenarios with the C urrent System Allocation Policy Table 9 : Resource Utilization Estimates for the Nurses in the Various Zones with the Current Allocation Policy Triage Nurse Green Zone Nurse Yellow Zone Nurse Red Zone Nurse Black Zone Nurse PSI 1 0.17% 1.85% 18.82% 3.44% 0.08% PSI 2 0.71% 7.32% 80.91% 13.72% 0.07% PSI 3 1.24% 12.73% 96.85% 24.99% 0.10% PSI 4 2.44% 25.18% 98.49% 40.34% 0.17% PSI 5 5.27% 54.05% 99.16% 59.43% 0.20% Figure 24 clearly shows that the current system workload is not balanced; while some resources are under utilized (i.e. triage nurse utilization ranges from 0.17% to 5.2%), other resources are over uti lized (yellow zone nurse utilization). This translates is a poor quality of healthcare and working conditions for the Medical personnel. In the next section, three optimization criteria is evaluated to PSI 1 Utilization PSI 2 Utilization PSI 3 Utilization PSI 4 Utilization PSI 5 Utilization 0.00% 20.00% 40.00% 60.00% 80.00% 100.00%Triage Nurse Green Zone Nurse Yellow Zone Nurse Red Zone Nurse Black Zone NurseResource Utilization for the Current System 80.00% 100.00% 60.00% 80.00% 40.00% 60.00% 20.00% 40.00% 0.00% 20.00%

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80 find a new allocation policy that addresses the issues regarding resource utilization and queue length. Queue length and waiting times: as the utilization peaked for the nurses in the yellow zone, the same happened for the queue waiting times and length in the yellow zone. Waiting time also peaked to an aver age of 2030 patients waiting for a bed in average in the red zone for the scenario with PSI 5 A graphical representation for the average number of patients and time waiting in the difference phases of the process for each zone is given in Figure 25 and Figure 26. The estimates for the queue length and waiting times can be obtained in appendix L. Figure 25 : Number of Patients Waiting in each Zone of the ED

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81 Figure 26 : Queue Waiting Times (Hrs) f or the Current System Optimization The design follow to apply this optimization procedure is divided into the following elements: Controls: these are the variables or resources in the model that you can manipulate, such as the number of nurses of each zone. After you define the controls in your simulation model, you can select which controls to optimize in OptQuest. OptQuest will change the v alues of these controls with each simulation until OptQuest finds values that yield the best objective. The controls are defi ned in the following way:

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82 Responses: these are the outputs of the simulation you are interested on measuring. For this simulation model, the responses used in the analysis are: p atient f low in the green, red, and yellow zones number of patients transferred to other facilities bec ause of system too full and q ueue length for the various zones, and per process type. The list of response s as used in the OptQuest is listed o n t able 10. Constraints: these define a relationship among controls and/or responses, and set the limits on which variables can vary. For the system, the capacity used is of 30 nurses, thus the total number of nurses in the ED (for all the zones) should be equal to this amount. Table 10: List Of Responses For The Optimization Procedure In Optquest yellow_patient_out red_patient_out green_patient_out Transferred patients G_assessment.Queue.NumberInQueue G_registration.Queue.NumberInQueue G_Treatment_Seize.Queue.NumberInQueue R_assessment.Queue.NumberInQueue R_Bed_Seize.Queue.NumberInQueue R_registration.Queue.NumberInQueue R_Treatment_Seize.Queue.NumberInQueue Triage Process.Queue.NumberInQueue Y_assessment.Queue.NumberInQueue Y_Bed_Seize.Queue.NumberInQueue Y_registration.Queue.NumberInQueue Y_Treatment_Seize.Queue.NumberInQueue

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83 Objective: This function defines the goal of the optimization. OptQuest for Arena allows you to define more than one objective, but only one objective can be used for an optimization. Three objectives were defined for this model: Objective 1 = Maximize pa tient throughput in the system: Objective 2 = Minimize number of patients transferred to other facilities: Objective 3 = Minimize average number of patients waiting to be treated:

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84 Run : The optimization model was run for every scenario, and the results for the allocation of nurses is expressed in percentages of total available nurses to give a more general representation on how workforce levels in each zone should be allocated As it wa s observed in the results sections, the response values (Queue length and waiting times) in the PSI1 and PSI 2 were equal to zero. For this reason, no optimization was applied to these scenarios; results for the optimization are summarized in the next sect ion. Allocation of Resources Objective 1 = Maximize patient throughput in the system: Table 11: Resource Allocation as a Percentage of Total Number of Nurses for Objective 1 PSI 3 PSI 4 PSI 5 Black 3.33% 3.33% 6.67% Green 16.67% 16.67% 23.33% Red 10.00% 10.00% 10.00% Triage 13.33% 13.33% 6.67% Yellow 56.67% 56.67% 53.33% Objective 2 = Minimize number of patients transferred to other facilities: Table 12: Resource Allocation as a Percentage of Total Number of Nurses for Objective 2 PSI 3 PSI 4 PSI 5 Black 3.33% 3.33% 3.33% Green 13.33% 13.33% 23.33% Red 10.00% 10.00% 10.00% Triage 6.67% 6.67% 3.33% Yellow 66.67% 66.67% 60.00% Objective 1 and 2 suggest that approximately from 53% to 66% of the workforce should be concentrated on the yellow zone, and it becomes in the

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85 most critical zone in the ED. In the optimization model it was found that the system was able to process more patients: 10% more patients under the PSI 5, 80% more under the PSI 4, and 100% more patients during the PSI 3. The number of patient that had to be transferred to other facilities also decreased 90% ( from 1704 to 165) under the PSI 5, and100% for the other severity scenarios. The optimized allocation policy also had a positive impact on the utilization of nurses throughout the ED in the sense that it made the utilization more balanced as it can be seen in Figure 27 compared with resource utilization in current system shown in Figure 24 Figure 27 : Resource Utilization after Optimization

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86 Objective 3 = Minimize average number of patients waiting to be treated: Table 13: Resource Allocation as a Percentage of Total Number of Nurses for Objective 3 PSI 3 PSI 4 PSI 5 Black 3.33% 3.33% 13.33% Green 13.33% 13.33% 33.33% Red 13.33% 13.33% 16.67% Triage 3.33% 3.33% 6.67% Yellow 66.67% 66.67% 30.00% Table 13 presents the allocation policy obtained after optimizing the system with the objective of minimizing the number of patients waiting the various queues for beds, baseline assessment, registration, and treatment. Results were obtained for the queue waiting times and length, and it was f o u n d good improvement for the number of patients waiting for nurses yellow zone. The average waiting to times baseline assessment, registration, and treatment was reduced by 90%, 93%, and 96% respectively. The average number of patients waiting for baseline assessment, registration, and treatment was reduced by 85%, 89%, 86% respectively. Figure 28 depicts the resource utilization fo r the nurses i n the various zones for the processes that nurses are involved and beds utilization. It can be seen in Figure 28 that after optimizing and finding a better allocation of nurses where queue and waiting times have improved, and patient flow increased, beds have become the new bottleneck in the system.

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87 Figure 28 : Number of Patients Waiting i n the Various Zones of the ED i n t he Optimized System Conclusions A simulation model that replicates the dynamic s in the ED during a pandemic influenza outbreak was created. The main goal for this model was to assess the system capacity and capabilities to respond to this type of disaster. It was found that the most critical zone was not the green zone which had t he highest demand, or the red zone that treated the most ill patients, but it was the yellow zone that showed larger resource utilization for the nurses and queue length and waiting times. After the system was optimized, a new allocation was determined by assigning a percentage of total available nurses to each zone in the ED. The results were favorable; moreover, number of patients waiting in

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88 queue, and waiting times were reduced about 90% in the yellow zone. Also, the resource utilization for the nurses in the various zones was more balance throughout the system. This study corroborates the argument of how important nurses are in the healthcare delivery, and by concentrating on this resource, the quality and efficiency of the system improves. This study is intended to help policy makers in the process of making decisions on how to allocate resources and improve efficiency of the system. Future R esearch Research on the area of allocation of resources can be expanded to other critical areas of the hospit al such as physicians, vaccines, antiviral medications beds, and ventilators. These resources are also very critical for the operation of the hospital during pick patient demand scenarios. Hospital managers make very complex decisions. But in cases of mas s casualty events where there does not exit enough experience, the process of decisionmaking turns come complex; thus, it is essential to use computer support systems to evaluate policies, and the potential impact on the hospital performance. These polici es include: when to discharge a patient? How often treatment should be delivered? The scope can also be expanded to other institutions that are affected by the emergence of pandemic influenza virus such as transportation systems, schools and airports so s trategies can be planned ahead by simulating theses systems.

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89 REFERENCES Adenso, B., et al (2002). Capacity planning in hospital nursing: a model for minimum staff calculation. Nursing Economics. 06 Jun, 2009. Armstrong (2001). Principles of Forec asting. Boston, MA Kluwer Academic. Association of State and Territorial Health Officials (2002). Pandemic Influenza: Preparedness Planning for State Health Officials. . Atiya et al (1999). A Comparison between Neural Network Forecasting Techniques Case Study: River Flow Forecasting. IEEE Transactions on Neural Networks 10:2. Baesler, F. F., Jahnsen, H., DaCosta, M. (2003). the use of simulation and design of experiments for estimating maximum capacity in an emergency room. Proceedings of the 2003 Winter Simulation Conference. . Belshe, R. (2005). The Origins of Pandemic Influenza Lessons from the 1918 Virus. The Nwe England Journal of Medicine, 21: 220911 Bretthauer, Kurt M (1998). A model for planning resource requirements in health care organizations. Decision Sciences. . Box, G., Jenkins, G., et al. (200 8). Time Series Analysis. New Jersey: John Woley & Sons, 4th Ed. Byrne et al. (2000). Using Neural Nets for pecision Support in Prescription and Outcome Prediction in Anticoagulation Drug Therapy. Artificial Intelligence in Medicine. Chatfield, C. (2001) Time Series Forecasting. New York: Chapman & Hall/CRC, 1st Ed. Centers for Disease Control and Prevention (2009). Pandemic Planning Assumptions. < http://www.pandemicflu.gov/plan/pandplan.html>.

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90 Centers for Disease Control and Prevention (2007). In a M oments Notice: Surge Capacity for Terrorists Bombings. . Davey, V., Raab, C., and Knighton, T. (2006). VA Pandemic Influenza Plan. Department of Veteran Affairs. Washington, DC Department o f Health & Human Services (2007). General Information: pandemic Flu. . Department of Transportation (2007). Preparing for Pandemic Influenza. Emergency Management Systems (EMS) Edmonsen, B., and Fost, D (1998). How to think about the future scenario forecasting. American Demographics. . Eldabi, T., & Paul, R. J. (2001). A proposed approach for modeling healthcare systems for understan ding. Proceedings of the 2001 Winter Simulation Conference. . Farley, F. (2006). Respiratory Infectious Diseases Emergency Plan. James A. Haley Veterans Hospital. Hospital Policy Memorandum No 1133. Tampa, FL. Franses, P.H. (1996). Recent advances in modeling seasonality. Journal of Economic Survey 10: 299 345. Gorr, W.L. (1994). Research prospective on Neural Networks forecasting. International Journal of Forecasting 10:1 4. Grudnitski, G., Osburn, L., 1993. Forecasting S and P and gold futures prices: An application of neural networks. The Journal of Futures Markets, 13: 631 643. Hann, T.H., Steurer, E., 1996. Much ado about nothing? Exchange rate forecasting: Neural networks vs. linear models using monthly and weekly data. Neurocomputing 10: 323 339. Hecht Nielsen, R. (1989). Theory of the Back propagation Neural Network. Harcourt Brace & Co.2:6593. Homeland Security Council (2005). National Strategy for Pandemic Influenza. Homeland Security Counci l.

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91 Hupert, N., Cuomo, J., and Neukermans, C. (2003). The Weill/Cornell Bioterrorism and Epidemic Outbreak Response (BERM). The Agency for Healthcare Research and Quality. Well Medical College of Cornell University. Izurieta et al (2000). Influenza and the rates of hospitalization for respiratory disease among infants and young children. New England Journal of Medicine 342: 232 9. Kalogirou (2000). Applications of artificial Neural Networks for energy systems. Applied Energy 67:1735. Kang, S. (1991) An investigation of the use of feed forward Neural Networks for forecasting. Ph.D. Dissertation, Kent State University, Kent, OH. Kellermann, A. (2008). Crisis in the Emergency Department. The New England Journal of Medicine, 13: 13001303. Landesman, L. et al. (2000). Roles and Responsabilities of Public Health in Disaster Preparedness and Respone. Piblic Health Administration. Sudbury, Mass.: Jones and Bartlett. Lasch P. et al (2000). Image Reconstruction of FT IR Microspectrometric Data. The Robert K och Institute . Liao, Chung Min, Chao Fang Chang, & Huang Min Liang (2003). A probabilistic transmission dynamic model to assess indoor airborne infection risks. Journal of Risk Analysis 25: 1097. Lim C. and Randall, R.M. (2000). A Seasonal Analysis of Asian tourist Arrivals to Australia. Applied Economics 32:99510. Murray et al. (20060. Estimation of potential global pandemic infl uenza mortality on the basis of vital registry data from the 1918 20 pandemic: a quantitative analysis. Lancet, 368: 2211 18. Monto, A., et al. (2006). Epidemiology of Pandemic Influenza: Use of Surveillance and Modeling for Pandemic Preparedness. Journal of Infectious Diseases, 104:s9297. Nahmias, S. (2001). Production a nd Operations Analysis. McGrawHill, 4th Ed. Nam, K., et al. (1995). Forecasting international airline passenger traffic using neural networks. Logistics and Transportation, 31 :239 251.

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92 OhnoMachado L. et al (1998). Diagnosing Breast Cancer from FNAs: Var iable Relevance in Neural Networks and Logistic Regression Models. Harvard publication. Overby, J, et al. (2005). Looming Cognition for Global Competition: The Approaching Avian Influenza Pandemic. Asia Pacific Journal of Marketing and Logistics 17 Pat vivatsiri, L. (2006). A Simulation Model for Bioterrorism Preparedness in an Emergency Room. Proceedings of the 2006 Winter Simulation Conference. Monterey, CA. 1 Mar 2007. Proietti, T. (2000). Comparing Seasonal Components for Structural Time Series Mod els. International Journal of Forecasting 16: 247260. Roche Pharmaceuticals (2007). Pandemic Planning Tool kit: Flu Pandemic Background. . Rojas,D. (2006). Revenue Management Techniques Applied to the Parking Industry. Master Thesis manuscript. University of South Florida. Rockwell Automation. (2004). OptQuest for Arena: User Guide. Rockwell Software Inc. and OptTek Systems Inc., USA. Radetzky A. et al (1998). The Simulation of Elastic Tissue in Virtual Medicine Using Neuro Fuzzy Systems. Computational Intelligence group . Samaha, S., Armel, W. S., & Starks, D. W. (2003). The Use of Simulation to Reduce the Length of Stay in an Emergency Department. Proceedings of the 2003 Winter Simulation Conference. . Sargent, R. (2005). Verification and Validation of Simulation Model. Proceedings of the 2005 Winter Simulation Conference. Sharda, R., Patil, R.B. (1992). Connectionist approach to time series prediction: An empirical test. Journal of Intelligent Manufacturing 3: 317 323. Serfling (1963). Methods for current statistical analysis of excess pneumoniainfluenza deaths. Public Health Rep 78:494 505. Sharda, R.et al (1992). Connectionist approach to time series prediction: An empirical test. Journal of Intelligent Manufacturing 3:317 323.

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93 Simonsen et al (1997). The impact of i nfluenza epidemics on mortality: introducing a severity index. American Journal of Public Health 87:1944 50. Simonsen et al (2005). Impact of influenza vaccination on seasonal mortality in the US elderly population. Arch Intern Med 2005; 165:265 72. Thomps on, W., et al. (2006). Epidemiology of Seasonal Influenza: Use of Surveillance Data and Statistical Models to Estimate the Burden of Disease. The Journal of Infectious Diseases, 194:S82 91. Toner et al. (2006). Hospital Preparedness for Pandemic Influenza. Bio security and Bioterrorism: Bio defense, Practice, and Science 4:207217. Tang, Z. et al (1993). Feed forward Neural nets as models for time series forecasting. ORSA Journal of Computing 5:374 385. Taubenberger, Jeffery K., and David M. (2006). 1918 Influenza: The Mother of all Pandemics. Emerging Infectious Disease 12:1, 15. . Vance, J., and P. Sprivulis. (2005). Triage Nurses Validly and Reliably Estimate Emergency Department Patient Complexity Emergency Medicine Australasia 17: 382. Wiinamaki, A., & Dronzek, R. (2003). Using simulation in the architectural concept phase of an emergency department design. Proceedings of the 2003 Winter Simulation Conference. . Wong, B.K., Bodnovich, T.A., Selvi, Y. (1995). A bibliography of neural networks business application research: 1988 September 1994. Expert Systems, 12: 253 262. Yocum J., and Armstrong, J. (1995). Beyond Accuracy: Comparison of Criteria Used to Select Forecasting Methods. International Journal of Forecasting, 11: 591597. Zhang (2005). Neural Networks forecasting for seasonal and trend time series. European Journal of Operational Research 160:501 514. Zhang X, Meltzer MI, Wortl ey P. (2005). FluSurge2.0: a manual to assist state and local public health officials and hospital administrators in estimating the impact of an influenza pandemic on hospital surge capacity.

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94 APPENDICES

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95 Appendix A: World Health Organization Pandemic Phases Figure 29 : WHO Pandemic Phases

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96 Appendix B: Percentage of Visits for Influenza like Illness Reported by Sentinel Providers, National Summary 200708 and Previous 2 Seasons Table 14: Percentage of Visits for Influenza like Illness CDC Week (YYYY WW) %ILI from Sentinel Providers %ARI from DOD/ VA Sentinel Provider Baseline DoD/ VA Base line CDC Week (YYYY WW) %ILI from Sentinel Providers %ARI from DOD/ VA Sentinel Provider Baseline DoD/ VA Baseli ne 2005 40 1.2 2.16 2.2 3.2 2007 04 2.777 2.73 2.2 3.2 2005 41 1.218 2.13 2.2 3.2 2007 05 3.031 3.12 2.2 3.2 2005 42 1.298 2.18 2.2 3.2 2007 06 3.533 3.33 2.2 3.2 2005 43 1.345 2.3 2.2 3.2 2007 07 3.55 3.32 2.2 3.2 2005 44 1.592 2.37 2.2 3.2 2007 08 3.28 3.38 2.2 3.2 2005 45 1.47 2.52 2.2 3.2 2007 09 2.891 3 2.2 3.2 2005 46 1.608 2.43 2.2 3.2 2007 10 2.628 2.91 2.2 3.2 2005 47 1.84 2.83 2.2 3.2 2007 11 2.517 2.65 2.2 3.2 2005 48 1.76 2.81 2.2 3.2 2007 12 2.098 2.52 2.2 3.2 2005 49 1.942 2.94 2.2 3.2 2007 13 1.85 2.24 2.2 3.2 2005 50 2.357 3.17 2.2 3.2 2007 14 1.393 2.16 2.2 3.2 2005 51 2.962 3.59 2.2 3.2 2007 15 1.455 2.22 2.2 3.2 2005 52 3.262 4.36 2.2 3.2 2007 16 1.14 2.14 2.2 3.2 2006 01 2.607 3.59 2.2 3.2 2007 17 1.057 2.01 2.2 3.2 2006 02 2.248 2.82 2.2 3.2 2007 18 0.986 1.88 2.2 3.2 2006 03 2.357 2.89 2.2 3.2 2007 19 1.041 1.84 2.2 3.2 2006 04 2.407 2.84 2.2 3.2 2007 20 0.931 1.8 2.2 3.2 2006 05 2.52 3.03 2.2 3.2 2007 21 0.951 1.73 2.2 3.2 2006 06 2.656 3.19 2.2 3.2 2007 22 0.972 1.82 2.2 3.2 2006 07 3.125 3.26 2.2 3.2 2007 23 0.724 1.58 2.2 3.2 2006 08 3.103 3.47 2.2 3.2 2007 24 0.824 1.5 2.2 3.2 2006 09 3.165 3.15 2.2 3.2 2007 25 0.778 1.47 2.2 3.2 2006 10 3.096 3.08 2.2 3.2 2007 26 0.809 1.46 2.2 3.2 2006 11 2.654 2.86 2.2 3.2 2007 27 0.662 1.69 2.2 3.2 2006 12 2.42 2.82 2.2 3.2 2007 28 0.616 1.46 2.2 3.2 2006 13 2.364 2.76 2.2 3.2 2007 29 0.609 1.33 2.2 3.2 2006 14 1.868 2.5 2.2 3.2 2007 30 0.63 1.19 2.2 3.2 2006 15 1.46 2.27 2.2 3.2 2007 31 0.576 1.13 2.2 3.2 2006 16 1.317 2.2 2.2 3.2 2007 32 0.657 1.46 2.2 3.2 2006 17 1.151 2 2.2 3.2 2007 33 0.674 1.48 2.2 3.2 2006 18 1.074 2 2.2 3.2 2007 34 0.835 1.42 2.2 3.2 2006 19 1.048 1.97 2.2 3.2 2007 35 0.638 1.61 2.2 3.2 2006 20 1.025 1.96 2.2 3.2 2007 36 0.959 1.95 2.2 3.2 2006 21 0.913 1.86 2.2 3.2 2007 37 1.032 1.9 2.2 3.2 2006 22 0.958 1.89 2.2 3.2 2007 38 1.043 1.95 2.2 3.2 2006 23 0.869 1.67 2.2 3.2 2007 39 1.143 1.96 2.2 3.2 2006 24 0.79 1.61 2.2 3.2 2007 40 1.003 1.92 2.2 3.2 2006 25 0.776 1.6 2.2 3.2 2007 41 1.224 2.01 2.2 3.2 2006 26 0.725 1.53 2.2 3.2 2007 42 1.286 1.83 2.2 3.2

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97 Appendix B: (continued) 2006 30 0.635 1.44 2.2 3.2 2007 46 1.633 2.24 2.2 3.2 2006 31 0.609 1.42 2.2 3.2 2007 47 1.829 2.42 2.2 3.2 2006 32 0.687 1.46 2.2 3.2 2007 48 1.628 2.42 2.2 3.2 2006 33 0.616 1.59 2.2 3.2 2007 49 1.645 2.44 2.2 3.2 2006 34 0.599 1.73 2.2 3.2 2007 50 1.714 2.49 2.2 3.2 2006 35 0.621 1.8 2.2 3.2 2007 51 1.95 2.63 2.2 3.2 2006 36 0.801 2.08 2.2 3.2 2007 52 2.546 3.7 2.2 3.2 2006 37 0.773 1.99 2.2 3.2 2008 01 2.447 3.39 2.2 3.2 2006 38 0.806 2.14 2.2 3.2 2008 02 2.307 2.56 2.2 3.2 2006 39 0.787 2.1 2.2 3.2 2008 03 2.654 2.52 2.2 3.2 2006 40 1.146 2.08 2.2 3.2 2008 04 3.971 3.03 2.2 3.2 2006 41 1.148 2.02 2.2 3.2 2008 05 5.031 3.28 2.2 3.2 2006 42 1.225 2.05 2.2 3.2 2008 06 5.743 3.52 2.2 3.2 2006 43 1.208 2.07 2.2 3.2 2008 07 5.964 3.54 2.2 3.2 2006 44 1.312 2.13 2.2 3.2 2008 08 5.623 3.72 2.2 3.2 2006 45 1.453 2.37 2.2 3.2 2008 09 4.499 3.3 2.2 3.2 2006 46 1.523 2.26 2.2 3.2 2008 10 3.828 3.05 2.2 3.2 2006 47 1.884 2.59 2.2 3.2 2008 11 3.219 2.74 2.2 3.2 2006 48 1.795 2.6 2.2 3.2 2008 12 2.538 2.57 2.2 3.2 2006 49 1.959 2.69 2.2 3.2 2008 13 2.073 2.49 2.2 3.2 2006 50 2.378 2.84 2.2 3.2 2008 14 1.673 2.23 2.2 3.2 2006 51 2.836 2.96 2.2 3.2 2008 15 1.313 2.08 2.2 3.2 2006 52 2.982 3.84 2.2 3.2 2008 16 1.135 2.06 2.2 3.2 2007 01 2.372 3.3 2.2 3.2 2008 17 0.981 1.94 2.2 3.2 2007 02 2.081 2.65 2.2 3.2 2008 18 0.87 1.91 2.2 3.2 2007 03 2.275 2.68 2.2 3.2 2008 19 0.824 1.8 2.2 3.2 2008 20 0.802 1.78 2.2 3.2

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98 Appendix C : Neural Networks code %############################################################ %############### Neural Networks Forecasting ################### %######### Application: Patient Demand due to seasonal influenza ### %############################################################ % The data needs to be separated into two subsets: testing data and validation data % The testing data would be used to train the networ k and the validation data would %be used to test network % Data for y: years, w: weeks, d: demand is loaded... g=(unidrnd(2,13,1)); k=0; for i=1:13 for c=1:4 k=k+1; vec(k)=i; vec2(k)=g(i); end end data=[ y w d vec' vec2']; for i=1:1 %FOR EACH VALIDATION SET valid=data(find(data(:,5)==i),1:3); clear tdata z=0; for j=1:2%TRAINING DATA SET if i ~=j z=z+1; if z==1 tdata=data(find(data(:,5)==j),1:3); else tdata=[tdata;data(find(data(:,5)==j),1:3)]; end end end %*****************Neural Networks building************************** p=tdata(:,2)'; t=tdata(:,3)'; val.P=valid(:,2)'; val.T=valid(:,3)'; net=newff(minmax(p),[3,1],{'tansig','purelin'},'trainlm'); net.trainParam.show = 25; net.trainParam.epochs = 400; net = init(net); [net,tr]=train(net,p,t); %END NN#########################################

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99 Appendix D : Mechanisms of Pandemic Virus Origination Figure 30 : Mechanisms of Pandemic Origination

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100 Appendix E : Statistical Test of MAD Comparison for MAD metric performance between Seasonal Decomposition and the Fourier series: H0: 1 = 2 HA: 1 2 N Mean Std Dev. 95% CI Seasonal Decomposition 127 2.877 3.97 Fourier Series 137 3.664 5.63 t test 0.095752 sp 4.906095 v 249.2501 T Test of mean difference = 0 (vs not = 0): T Value = 0.0957 P Value = 0.18821 Based on this, there is no evidence to reject H0: 1 = 2. Where: 1 and 2 Comparison for MAD metric performance between Seasonal Decomposition and Neural Networks: represent the Mean Absolute D eviation (MAD) for Seasonal Decomposition and regression analysis methods (Fourier series). H0: 1 = 2 HA: 1 2 N Mean Std Dev. 95% CI Seasonal Decomposition 127 2.877 3.971 Neural Network 137 3.560 5.027 t test 0.077332 sp 4.550612 v 262.0108 T Test of mean difference = 0 (vs not = 0): T Value = 0.077 P Value = 0.2202 Based on this, there is no evidence to reject H0: 1 = 2. Where: 1 and 2 represent the Mean Absolute Deviation (MAD) for Seasonal Decomposition and Neural Networks.

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101 Appendix E : (continued) Comparison for MAD metric performance between Neural Networks and regression analysis: H0: 1 = 2 HA: 1 2 N Mean Std Dev. 95% CI Neural Networks 137 3.56 5.027 0.8494 Fourier Series 137 3.66 5.635 0.9520 t test 0.012628 Sp 5.339966 v 268.5372 95% CI for me an difference: ( 0.477, 0.686) T Test of mean difference = 0 (vs not = 0): T Value = 0.012 P Value = 0.87 Based on this, there is no evidence to reject H0: 1 = 2. Where 1 and 2 represent the MAD yielded by Neural Network and regression analysis method respectively.

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102 Appendix F : Assumptions for Pandemic Influenza I mpact Figure 31 : Assumptions for the Pandemic Influenza Impact

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103 Appendix G : Number of beds per hospital in Tampa Table 15: Number of beds per Hospital in Tampa Hospital Number of beds Capacity Tampa General Hospital 877 36.03% University Community Hospital 431 17.71% James A. Haley Veterans' Hospital 327 13.43% St Joseph's Hospital 309 12.70% Town & Country Hospital 201 8.26% Memorial Hospital Of Tampa 180 7.40% University Community Hospital At Carrollwood 109 4.48% Total Number of Beds Hillsborough County Tampa 2434

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104 Appendix H : W eekly demand of patients for five scenarios Table 16: Demand of Patients by Week week PSI1 PSI2 PSI3 PSI4 PSI5 KPPC 1 6.8 13.6 27.2 54.3 40 12.4 84.4 168.7 337.4 673.6 41 13.1 89.0 178.0 356.1 710.8 42 14.0 95.0 189.9 379.8 758.3 43 15.0 102.3 204.6 409.2 816.9 44 16.3 111.1 222.2 444.4 887.1 45 17.8 121.3 242.6 485.2 968.6 46 19.5 132.8 265.6 531.3 1060.6 47 21.4 145.4 290.9 581.7 1161.3 48 23.4 158.9 317.7 635.5 1268.6 49 25.4 172.8 345.5 691.1 1379.6 50 27.5 186.7 373.4 746.9 1491.1 51 29.5 200.3 400.6 801.1 1599.3 52 31.3 213.0 425.9 851.8 1700.5 1 33.0 224.3 448.6 897.2 1791.1 2 34.4 233.9 467.7 935.5 1867.6 3 35.5 241.3 482.6 965.1 1926.7 4 36.2 246.2 492.4 984.8 1965.9 5 36.5 248.4 496.8 993.6 1983.5 6 36.4 247.7 495.5 990.9 1978.2 7 35.9 244.2 488.4 976.7 1949.8 8 35.0 237.8 475.6 951.3 1899.0 9 33.7 228.8 457.7 915.3 1827.3 10 32.0 217.5 435.0 870.1 1736.9 11 30.0 204.2 408.5 816.9 1630.9 12 27.9 189.4 378.8 757.7 1512.6 13 25.5 173.6 347.1 694.3 1386.0 14 23.1 157.2 314.4 628.7 1255.1 15 20.7 140.8 281.6 563.1 1124.2 16 18.4 124.9 249.7 499.5 997.1 17 16.2 109.9 219.7 439.5 877.4 18 14.1 96.2 192.4 384.8 768.1 19 12.4 84.1 168.3 336.6 671.9 20 10.9 73.9 147.9 295.7 590.4 21 9.7 65.7 131.4 262.8 524.6 22 8.7 59.5 118.9 237.9 474.8 23 8.1 55.2 110.4 220.7 440.6 24 7.8 52.7 105.4 210.8 420.9 25 7.6 51.8 103.7 207.4 414.0

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105 Appendix I: Time estimates for the processes held in the ED. Processing times (minutes) using a triangular distribution (Patvivatsiri 2006) Table 17: Pro cessing Times Activity Red Area Yellow Area Green Area Bedside Registration (15,20,25) (15,20,25) (15,20,25) Baseline assessment (7,12,15) (7,12,15) (7,12,15) MD evaluation (delay) (15,25,40) (8,15,30) (5,15,25) Nursing Treatment (30,50,120) (30,50,90) (15,30,60)

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106 Appendix J: Snapshot of simulation animation Figure 32 : Snapshot of Simulation Animation

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107 Appendix K : SIMAN simulation summary report ARENA Simulation Results Summary for Replication 5 of 5 Project: Unnamed Project Run execution date : 6/29/2009 Analyst: Florentino Rico Model revision date: 6/29/2009 Replication ended at time : 2016.0 Hours Base Time Units: Hours TALLY VARIABLES Identifier Average Half Width Minimum Maximum Observations _____________________________________________________________________________ ____ __ Time in Red Zone 223.78 (Insuf) 195.99 256.03 126 Cycle time for Black People 18.761 (Insuf) 12.536 24.243 137 Cycle time for Red Patients 223. 83 (Insuf) 196.04 256.06 126 Time in Green Zone 1.9810 .04576 .76149 3.7033 1883 Time in Yellow Zone 148.31 .21076 144.29 153.90 696 Cyc le time for Green Patients 2.0290 .04585 .80718 3.7527 1883 Cycle time for Yellow Patients 148.35 .21075 144.34 153.95 696 Entity 1.VATime .04791 3.1376E 04 .02401 .07445 2842 Entity 1.NVATime .00000 .00000 .00000 .00000 2842 Entity 1.WaitTime 12.227 2.4081 .00000 108.25 2842 Entity 1.T ranTime .00000 .00000 .00000 .00000 2842 Entity 1.OtherTime 36.229 4.9355 .76149 256.03 2842 Entity 1.TotalTime 48.505 5.8177 .80718 256.06 2842 Entity 2.VATime ----0 Entity 2.NVATime ----0 Entity 2.WaitTime ----0 Entity 2.TranTime ----0 Entity 2.OtherTime ----0 Entity 2.TotalTime ----0 Seizing nurse and bed in Black zone.Queue. .00000 (Insuf) .00000 .00000 138 R_assessment.Queue.WaitingTime .00000 (Insuf) .00000 .00000 137 Y_assessment.Queue.WaitingTime 4.9622 .91262 .00000 48.620 734 Y_Bed_Seize.Queue.WaitingTime .00000 .00000 .00000 .00000 736 G_assessment.Queue.WaitingTime 7.1185E 04 .00147 .00000 .26842 1883 Triage Process.Queue.WaitingTime .00000 .00000 .00000 .00000 2894 R_Treatment_Seize.Queue.WaitingTime 4.8617E 06 1.0022E 05 .00000 .03501 7201 Patients transferring to zones.Queue.Waiti .00000 .00000 .00000 .00000 2894 R_Bed_Seize.Queue.WaitingTime .00000 (Insuf) .00000 .00000 137 Y_registrati on.Queue.WaitingTime 27.260 6.1539 .00000 87.930 736 R_registration.Queue.WaitingTime .00000 (Insuf) .00000 .00000 137 B_nurse_serize.Queue.WaitingTime .00000 (Insuf) 00000 .00000 138 G_Treatment_Seize.Queue.WaitingTime .00000 .00000 .00000 .00000 1883 Y_Treatment_Seize.Queue.WaitingTime 1.1406 .19503 .00000 5.0907 10767 G_registration.Queue.Wai tingTime 4.6187E 04 6.3822E 04 .00000 .20801 1883

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108 Appendix K : (Continued) DISCRETECHANGE VARIABLES Identifier Average Half Width Minimum Maximum Fi nal Value _____________________________________________________________________________ ______ Number of Patients in Black Zone 1.2725 (Insuf) .00000 6.0000 1.0000 Number of Patients in Yellow Zone 384.39 (Corr ) .00000 736.00 736.00 Number of Patients in Green Zone 969.09 (Corr) .00000 1883.0 1883.0 Number of Patients in Red Zone 69.138 (Insuf) .00000 137.00 137.00 Entity 1.WIP 70.798 (Corr) .00000 97.000 52.000 Entity 2.WIP 1.0000 (Insuf) .00000 1.0000 1.0000 Black zone_bed.NumberBusy 1.2725 (Insuf) .00000 6.0000 1.0000 Black zone_bed.NumberScheduled 6000.0 (Insuf) 6000.0 6000.0 6000.0 Black zone_bed.Utilization 2.1209E 04 (Insuf) .00000 .00100 1.6667E 04 Yellow zone_nurse.NumberBusy 15.474 (Corr) .00000 21.000 15.000 Yellow zone_nurse.NumberScheduled 16.000 (Insuf) 15.000 21.000 15.000 Yellow zone_nurse.Utilization .97487 (Corr) .00000 1.0 000 1.0000 Red zone_nurse.NumberBusy 4.0392 (Corr) .00000 15.000 2.0000 Red zone_nurse.NumberScheduled 17.000 (Insuf) 15.000 21.000 21.000 Red zone_nurse.Utilization .24663 (Corr) .00000 1.0000 .09524 Black zone_nurse.NumberBusy .02272 (Insuf) .00000 2.0000 .00000 Black zone_nurse.NumberScheduled 40.000 (Insuf) 40.000 40.000 40. 000 Black zone_nurse.Utilization 5.6812E 04 (Insuf) .00000 .05000 .00000 Red zone_bed.NumberBusy 14.539 (Insuf) .00000 28.000 11.000 Red zone_bed.NumberScheduled 40.000 (Insuf) 40.000 40.000 40.000 Red zone_bed.Utilization .36348 (Insuf) .00000 .70000 .27500 Yellow zone_bed.NumberBusy 53.067 (Corr) .00000 72.000 40.000 Ye llow zone_bed.NumberScheduled 111.00 (Insuf) 111.00 111.00 111.00 Yellow zone_bed.Utilization .47809 (Corr) .00000 .64865 .36036 Green zone_nurse.NumberBusy 2.0071 (Corr) .00000 17.000 .00000 Green zone_nurse.NumberScheduled 16.000 (Insuf) 15.000 21.000 21.000 Green zone_nurse.Utilization .12709 (Corr) .00000 1.0000 .00000 triage_nurse.N umberBusy .06875 (Corr) .00000 3.0000 .00000 triage_nurse.NumberScheduled 7.0000 (Insuf) 7.0000 7.0000 7.0000 triage_nurse.Utilization .00982 (Corr ) .00000 .42857 .00000 Seizing nurse and bed in Black zone.Queue. .00000 (Insuf) .00000 .00000 .00000 R_assessment.Queue.NumberInQueue .00000 (Insuf) .00000 .00000 .00000 Y_assessment.Queue.NumberInQueue 1.8076 .39363 .00000 30.000 2.0000 Y_Bed_Seize.Queue.NumberInQueue .00000 (Insuf) .00000 .00000 .00000 G_assessment.Queue.NumberInQueue 6.6489E 04 (Insuf) .00000 3.0000 .00000 Triage Process.Queue.NumberInQueue .00000 (Insuf) .00000 .00000 .00000 R_Treatment_Seize.Queue.NumberInQueue 1.7366E 05 (Insuf) .00000 1.0000 .00000 Patients transferring to zones.Queue.Numbe .00000 (Insuf) .00000 .00000 .00000 R_Bed_Seize.Queue.NumberInQueue .00000 (Insuf) .00000 .00000 .00000 Y_registration.Queue.NumberInQueue 9.9524 2.0751 .00000 32.000 .00000 R_registration.Queue.NumberInQueue .00000 (Insuf) .00000 .00000 .00000 B_nurse_serize.Queue.NumberInQueue .00000 (Insuf) .00000 .00000 .00000 G_Treatment_Seize.Queue.NumberInQueue .00000 (Insuf) .00000 .00000 .00000 Y_Treatment_Seize.Queue.NumberInQueue 6.0921 1.0385 .00000 29.000 2.0000

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109 Appendix K: (Continued) G_registration.Queue.NumberInQueue 4.3140E 04 (Insuf) .0000 0 3.0000 .00000 COUNTERS Identifier Count Limit _____________________________________________________________ Numbe system in 2894 Infinite transferred patients 0 Infinite yellow_patient_out 696 Infinite green_patient_in 1883 Infinite red_patient_out 126 Infinite green_patient_out 1883 Infinite yellow_patient_in 736 Infinite patients_admitted 2894 Infinite red_patient_in 137 Infi nite OUTPUTS Identifier Value _____________________________________________________________ Entity 1.NumberIn 2894.0 Entity 1.NumberOut 2842.0 Entity 2.NumberIn 1.0000 Entity 2.NumberOut .00000 Black zone_bed.NumberSeized 138.00 Black zone_bed.ScheduledUtilization 2.1209E 04 Yello w zone_nurse.NumberSeized 35243. Yellow zone_nurse.ScheduledUtilization .96714 Red zone_nurse.NumberSeized 7749.0 Red zone_nurse.ScheduledUtilization .23760 Black zone_nurse.NumberSeized 138.00 Black zone_nurse.ScheduledUtilization 5.6812E 04 Red zone_bed.NumberSeized 137.00 Red zone_bed.ScheduledUtilization .36348 Yellow zone_bed.NumberSeized 736.00 Yellow zone_bed.ScheduledUtilization .47809 Green zone_nurse.NumberSeized 13181. Green zone_nurse.ScheduledUtilization .12544 triage_nurse.NumberSeized 2894.0 triage_nurse.ScheduledUtilization .00982 System.NumberOut 2842.0

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110 Appendix K : (Continued) ARENA Simulation Results ITS Department Output Summary for 5 Replications Project: Unnamed Project Run execution date : 6/29/2009 Analyst: Florentino Rico Model revision date: 6/29/2009 OUTPUTS Identifier Av erage Half width Minimum Maximum # Replications _____________________________________________________________________________ ______ Entity 1.NumberIn 2901.0 54.220 2842.0 2965.0 5 Entity 1.NumberOut 2839.4 46.156 2779.0 2881.0 5 Entity 2.NumberIn 1.0000 .00000 1.0000 1.0000 5 Entity 2.NumberOut .00000 .00000 .00000 .00000 5 Black zone_bed.NumberSeized 140.60 11.959 130.00 153.00 5 Black zone_bed.ScheduledUtilization 2.1575E 04 1.4112E 05 2.0382E 04 2.3037E 04 5 Yellow zone_nurse.NumberSeized 34774. 553.19 34326. 35243. 5 Yellow zone_nurse.ScheduledUtilization .95910 .01278 .94450 .96977 5 Red zone_nurse.NumberSeized 7911.8 650.48 7434.0 8569.0 5 Red zone_nurse.ScheduledUtilization .24307 .01921 .22933 .26244 5 Black zone_nurse.NumberSeized 140.60 11.959 130.00 153.00 5 Black zone_nurse.ScheduledUtilization 5.7867E 04 5.0374E 05 5.3223E 04 6.3146E 04 5 Red zone_bed.NumberSeized 139.00 10.679 130.00 148.00 5 Red zone_bed.ScheduledUtilization .37148 .03039 .34949 .40249 5 Yellow zone_bed.NumberSeized 735.40 35.955 691.00 772.00 5 Yellow zone_bed.ScheduledUtilization .47563 .022 35 .44642 .49605 5 Green zone_nurse.NumberSeized 13193. 143.82 13097. 13391. 5 Green zone_nurse.ScheduledUtilization .12552 .00128 .12467 .12730 5 triage_nurse.NumberSeized 2901.0 54.220 2842.0 2965.0 5 triage_nurse.ScheduledUtilization .00992 2.4261E 04 .00965 .01016 5 System.NumberOut 2839.4 46.156 2779.0 2881.0 5 Simulation run time: 0.87 minutes. Sim ulation run complete.

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111 Appendix L: Queue length and waiting times for the current system Table 18: Queue length and Waiting Times Results Green Zone Yellow Zone Red Zone assessment registration treatment assessment bed seize registration treatment assessment bed seize registration treatment PSI 1 Avg. waiting time (hrs) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Avg. number waiting 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 PSI 2 Avg. waiting time (hrs) 0.0 0.0 0.0 0.6 0.0 1.6 0.2 0.0 0.0 0.0 0.0 Avg. number waiting 0.0 0.0 0.0 0.1 0.0 0.3 0.7 0.0 0.0 0.0 0.0 PSI 3 Avg. waiting time (hrs) 0.0 0.0 0.0 4.8 0.0 27.3 1.2 0.0 0.0 0.0 0.0 Avg. number waiting 0.0 0.0 0.0 1.8 0.0 10.0 6.2 0.0 0.0 0.0 0.0 PSI 4 Avg. waiting time (hrs) 0.0 0.0 0.0 1.0 0.6 49.8 3.1 0.0 0.0 0.0 0.0 Avg. number waiting 0.0 0.0 0.0 4.0 0.4 28.7 16.6 0.0 0.0 0.0 0.0 PSI 5 Avg. waiting time (hrs) 0.7 0.7 0.0 7.4 35.3 42.4 4.9 0.0 26.6 0.0 0.0 Avg. number waiting 2.7 2.6 0.0 6.7 33.2 39.7 25.8 0.0 5.0 0.0 0.0


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Emergency department capacity planning for a pandemic scenario :
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ABSTRACT: The problem considered in this research is the efficient allocation of resources in an emergency department during a large flow of patient consequent to a pandemic influenza breakout. Predicting the impact of a Pandemic Influenza is very complex due to the many unknown variables that may play a role to how severe a pandemic can be. Scenario planning is considered in this research to forecast different potential outcomes and help decision makers better understand the role of uncertainties and become prepared to make important decisions. The goal is to first create a forecast model to estimate the patient demand during the breakout period accessing an emergency department and employ it as input of a simulation model to replicate the dynamics of the system under a set of pandemic influenza scenarios.The results yielded by this approach will be used as decision tool for hospital managers to better utilize and allocate medical staff considering the fluctuant demand of the system on the zones of the emergency department: triage, red, yellow, green, and black. Emergency departments are already overwhelmed during everyday operations; thus, it is expected in a case of pandemic influenza, their operations will be challenged beyond their limits. Hospitals are the first responders in a case of pandemic influenza since they will admit and treat the first cases, also they will be the first to identify the new virus. It is critical for hospitals to plan and create strategies to more effectively face the large number of patients arriving, and the best use of the available resources. Once the simulation model has been run and verified, and optimization procedure will be put in place to minimize the number of patients waiting in queue to be treated while maximizing flow of patients.The model is built using ARENA simulation software and OptQuest heuristic optimization to propose various combinations for the number of nurses needed for healthcare delivery. The proposed method significantly improves system efficiency by reducing the number of patients waiting in queue for health treatment and care, and also increases the total number of patients treated.
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