Spatial expansions and travelling waves of rabies in vampire bats


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Spatial expansions and travelling waves of rabies in vampire bats

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Spatial expansions and travelling waves of rabies in vampire bats
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Biological Sciences
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Benavides, Julio A.
Valderrama, William
Streiker, Daniel G.
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Spatial Dynamics ( local )
Desmodus Rotundus ( local )
Zoonoses ( local )
Landscape Heterogeneity ( local )
Lyssavirus ( local )
Disease Control ( local )
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serial ( sobekcm )

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A major obstacle to anticipating the cross-species transmission of zoonotic diseases and developing novel strategies for their control is the scarcity of data informing how these pathogens circulate within natural reservoir populations. Vampire bats are the primary reservoir of rabies in Latin America, where the disease remains among the most important viral zoonoses affecting humans and livestock. Unpredictable spatiotemporal dynamics of rabies within bat populations have precluded anticipation of outbreaks and undermined widespread bat culling programs. By analysing 1146 vampire bat-transmitted rabies (VBR) outbreaks in livestock across 12 years in Peru, we demonstrate that viral expansions into historically uninfected zones have doubled the recent burden of VBR. Viral expansions are geographically widespread, but severely constrained by high elevation peaks in the Andes mountains. Within Andean valleys, invasions form wavefronts that are advancing towards large, unvaccinated livestock populations that are heavily bitten by bats, which together will fuel high transmission and mortality. Using spatial models, we forecast the pathways of ongoing VBR epizootics across heterogeneous landscapes. These results directly inform vaccination strategies to mitigate impending viral emergence, reveal VBR as an emerging rather than an enzootic disease and create opportunities to test novel interventions to manage viruses in bat reservoirs.
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Biological Sciences, Vol. 283, no. 1832 (2016-06-15).

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rspb.royalsocietypublishing.orgResearch Citethisarticle: BenavidesJA,Valderrama W,StreickerDG.2016Spatialexpansionsand travellingwavesofrabiesinvampirebats. Proc.R.Soc.B 283 :20160328. http://dx.doi.org/10.1098/rspb.2016.0328 Received:12February2016 Accepted:16May2016 SubjectAreas: healthanddiseaseandepidemiology,ecology Keywords: Desmodusrotundus ,diseasecontrol, zoonoses,spatialdynamics, Lyssavirus , landscapeheterogeneity Authorsforcorrespondence: JulioA.Benavides e-mail:julio.benavides@glasgow.ac.uk DanielG.Streicker e-mail:daniel.streicker@glasgow.ac.uk Electronicsupplementarymaterialisavailable athttp://dx.doi.org/10.1098/rspb.2016.0328or viahttp://rspb.royalsocietypublishing.org. Spatialexpansionsandtravellingwaves ofrabiesinvampirebatsJulioA.Benavides1,WilliamValderrama2andDanielG.Streicker1,31InstituteofBiodiversity,AnimalHealthandComparativeMedicine,UniversityofGlasgow, GlasgowG128QQ,UK2Asociacio ´ nparaelDesarrolloyConservacio ´ ndelosRecursosNaturales,Lima,Peru3MedicalResearchCouncil…UniversityofGlasgowCentreforVirusResearch,GlasgowG611QH,UK JAB,0000-0002-3920-9165 Amajorobstacletoanticipatingthecross-speciestransmissionofzoonoticdiseasesanddevelopingnovelstrategiesfortheircontrolisthescarcityofdata informinghowthesepathogenscirculatewithinnaturalreservoirpopulations. VampirebatsaretheprimaryreservoirofrabiesinLatinAmerica,wherethe diseaseremainsamongthemostimportantviralzoonosesaffectinghumans andlivestock.Unpredictablespatiotemporaldynamicsofrabieswithinbat populationshaveprecludedanticipationofoutbreaksandunderminedwidespreadbatcullingprograms.Byanalysing1146vampirebat-transmitted rabies(VBR)outbreaksinlivestockacross12yearsinPeru,wedemonstrate thatviralexpansionsintohistoricallyuninfectedzoneshavedoubledthe recentburdenofVBR.Viralexpansionsaregeographicallywidespread,but severelyconstrainedbyhighelevationpeaksintheAndesmountains. WithinAndeanvalleys,invasionsformwavefrontsthatareadvancingtowards large,unvaccinatedlivestockpopulationsthatareheavilybittenbybats, whichtogetherwillfuelhightransmissionandmortality.Usingspatial models,weforecastthepathwaysofongoingVBRepizooticsacrossheterogeneouslandscapes.Theseresultsdirectlyinformvaccinationstrategiesto mitigateimpendingviralemergence,revealVBRasanemergingratherthan anenzooticdiseaseandcreateopportunitiestotestnovelinterventionsto managevirusesinbatreservoirs.1.IntroductionBatsareassociatedwithnumerouszoonoticpathogens,includingSARSCoronavirusandEbolavirus,thathaveemergedunpredictablyintohumanand domesticanimalpopulationswithserioushealthandeconomicconsequences [1].Acentralimpedimenttoforecastingthecross-speciestransmissionofbat virusesanddevelopingstrategiesfortheircontrolisthescarcityofdatathat couldinformhowthesevirusesaremaintainedintheirbatreservoirs[2].In particular,datafrombatsareusuallycollectedfromsmallgeographicalareas overshorttimescales,whereasthehighmobilityofbatscanenablelong-term viralpersistenceacrosslargespatialscales[3].Bycontrast,cross-speciesinfections(‘spillovers’)canspanlargeareasandtimescales,butrarelyoccurat sufficientlyhighfrequencytoenablerobustinferenceintotransmission dynamicswithinbatsandareoftencomplicatedbythepossibilityofonward transmissionwithinspilloverhostspecies[2]. InLatinAmerica,commonvampirebats( Desmodusrotundus )arethemost importantsourceofhumanandanimalrabies,alethalencephalitistransmitted bythebitesofinfectedanimals[4].Thewidespreaddistributionofthevampire bat,fromMexicotoArgentina,coupledwithamechanismforcross-species transmission(obligatorybloodfeedingbehaviour)createshigheconomic, socialandpublichealthburdensofrabiesacrosstheregion[5].Although post-exposurevaccinationofhumansandpre-exposurevaccinationoflivestock &2016TheAuthors.PublishedbytheRoyalSocietyunderthetermsoftheCreativeCommonsAttribution Licensehttp://creativecommons.org/licenses/by/4.0/,whichpermitsunrestricteduse,providedtheoriginal authorandsourcearecredited.

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areavailableandefficacious,theyarenotpracticedatlarge scales[5,6].Instead,controlofvampirebat-transmitted rabies(VBR)usesbatpopulationcontrol,eitherbyindiscriminatekillingandroostdestructionorbygovernment-led campaignsthatuseapoisonouspaste,‘vampiricide’,tokill batsthatgroomtreatedconspecificsorfeedfromthe woundsoftreatedlivestock[7,8].Theefficacyoftheseprogrammeshasbeenquestionedbyfieldstudiesshowingthat ratesofVBRexposureinbatswereequivalentorhigherin culledcoloniesandindependentofnaturalvariationinbat colonysize[9].Furthermodellingworkshowedthatapparentlycounterproductiveeffectsofcullingcouldarise becauseVBRpersistsnotlocallywithinabatcolony,but byviraldispersalbetweencolonies[10]. Identifyingtheprecisenatureofspatialdynamics andhowthesecontributetolong-termviralpersistenceis criticaltoimprovingrabiescontrol.Detectionofepizootic expansionsorseasonallyvaryingtransmissioncouldhelp anticipatewhenandwherespillovercouldoccur,thereby enablingpreventativevaccinationofhumansandlivestock orinterventionswithinthebatpopulationaheadofoutbreaks [11,12].Becauserabiesisnottransmittedamonglivestockfollowinginfectionbybats,livestockprovideanidealsentinelto studythespatiotemporaldynamicswithinthenaturalbat reservoir.Todate,phylogeneticandtime-seriesanalyses ofVBRinlivestockhaverevealedcontrastingpatterns. EpizooticswerereportedinthenorthofArgentinainthe 1970s[13],butmorerecentanalysesshowcontinuous infectionoflivestock,indicativeofenzooticpersistence [5,9,12,14–16].However,incidencevarieswithinenzootic zonesandisspeculatedtobeaffectedbynaturalandanthropogenicprocesses.Ontheonehand,livestockvaccinationor batcullscouldconceivablydecreasetheburdenandtransmissionofVBR,respectively,ifpracticedintensively.Yet, landuseandclimatechangescouldoffsetthesegainsbyprovidinggreateravailabilityoflivestock(akeyfoodresource forbats)andincreasingminimalwintertemperatures, whichtogetherlimitthesizeandgeographicalrangeofvampirebats[17].IfVBRoutbreaksareincreasing,determining whetherincreasesarecausedbyspatialexpansionsintopreviouslyuninfectedareasorintensifiedtransmissionwithin enzooticzonesiscriticaltoappropriatelyallocatevaccines, surveillanceandeducationalcampaigns. ThenationalsurveillancesystemofPeruhasdocumentedthetimeandplaceofrabiesinfectionsinlargely unvaccinatedlivestockpopulationssince2004.Because rabiestransmittedbydogsisrestrictedtoasmall,isolated regionofPeru,virtuallyalllivestockcasesarespilloverinfectionsfromvampirebats[18,19].Thisuniquedatasetcreates aremarkableopportunitytoelucidatethespatiotemporal dynamicsunderlyingtheperpetuationofVBRinbatpopulationsandtherebyinformcontrolstrategiesacrossLatin America.Here,usinghigh-resolutiontime-seriesdataon VBRoutbreaks,we:(i)resolvethespatiotemporalpatterns underlyingpreviouslyundetectedincreasesintheburden ofVBRinPeru,(ii)testwhetherincreasesarecausedby spatialexpansionsorintensifiedtransmissionwithinhistoricallyenzooticzones,and(iii)assesspatternsofhowspatial expansionsoccurredacrossthelandscape.Next,inanarea ofintensiveVBRtransmissionintheAndes,wepairtimeseriesdatawithfielddataonbat–livestockcontacts, vaccinationandreportingpracticesto(iv)estimatethevelocityofadvancingepizooticsofVBRonaheterogeneous landscape,and(v)forecastimpendingspilloverrisksto humansandlivestock.2.Materialandmethods(a)Datasets(i)Nationalreportsofrabiesinfectionsinlivestockfrom2003 to2014Suspectedoutbreaksofrabieswerereportedbyfarmerstoone ofthe103satelliteofficesofNationalServiceofAgrarian HealthofPeru(SENASA)forsamplecollectionandlaboratory testingforrabiesinfection( n ¼ 2269,seeDataaccessibilitysection).Becausewefocusedonthespatiotemporaldynamicsof VBRratherthantheintensityofoutbreaks,weanalyseddata asoutbreaks(definedasoneormorelaboratory-confirmed rabiesinfectiononafarm)ratherthanasindividualcases; however,mostoutbreaks(83%)involvedonlyasinglesickor deadanimal.(ii)SpatialdistributionofbatbitesonlivestockInthesouthernAndes,weusedreportsofbatbitesonlivestock (aproxyforvampirebatpresence),combinedwithnational censusdata,toassessthepatchinessofbatsonthelandscape. Thespatialdistributionofbatbitesonlivestockwascollected bytheRegionalGovernmentofApurimacbyconducting visualinspectionoflivestockin169rabiesenzooticcommunities (1–4farmspercommunity)withintwovalleys(Chalhuancaand RioApurimac)fromJune2014untilJuly2015[20].Wehypothesizedthatpatchybatdistributionswouldrequirelongerbat flightsthatcouldleadtoacceleratedorpunctuatedspatial spreadofVBR,whereasthecontinuouspresenceofbatsmight enableslower,gradualspread.(iii)Questionnairedatafromvampirebat-transmittedrabies-free communitiesWeusedoralquestionnairestoevaluatethepresenceofvampire batsfeedingonlivestock,knowledgeofrabiesandvaccination practicesincommunitiesthatdidnotreportoutbreaksinthe nationalsurveillancedataset.Weinterviewed60farmersinsix districtsintheChalhuancavalleyand30farmersintwodistricts intheRioApurimacvalleyusingastandardizedquestionnaire (seetheelectronicsupplementarymaterialfordetailsandethical approvalinformation).(b)Spatiotemporalpatternsintheburdenand distributionofvampirebat-transmittedrabiesSpatialdynamicsofVBRwereexploredbycalculatingthe numberofoutbreaksperregionfrom2003to2014,theannual numberofdistrictsinfected,thecumulativenumberofdistricts thatreportedrabiesforthefirsttimeeachyearandthepercentageofdistrictsthathadaneighbouringdistrictreporting rabiespriortoitsfirstreport.Wetestedwhethertheaverage elevationofoutbreakschangedthroughtimeineachregionof Peruusinggeneralizedlinearmodels(GLM)withnormally distributederrors.TheAkaike’sinformationcriterion(AIC) wasusedformodelselection(chosenadifferenceofmorethan twoAICpoints),andthesignificanceofeachfactorwithinthe selectedmodelwastestedusingaWaldtest[21].Wealso testedtheoveralleffectofyearonoutbreakelevationusingageneralizedlinearmixedmodel(GLMM)withregionasarandom effectusingtheglmmADMBpackageofR.Districtandelevation mapswereobtainedfromtheGADMdatabase(gadm.org)and theCGIAR-CSI(http://www.cgiar-csi.org/)respectively,using rspb.royalsocietypublishing.org Proc.R.Soc.B 283 :20160328 2

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the raster packageofR.Temporalautocorrelationanalyseswere usedtoinvestigatetheseasonalityofVBRoutbreaksusingthe acf functionofR,whichallowssignificancetestingdifferent timelagsofautocorrelation.(c)Estimatingthevelocityofadvancingvampire bat-transmittedrabiesepizooticsThelargenumberofVBRoutbreaksintheneighbouringregions ofApurimac,AyacuchoandCusco(AAC,62%ofalloutbreaks inPeru)providedahigh-resolutiondatasettoresolvetheepidemiologicaldynamicsunderlyingspatialexpansionsdetected atthenationallevel.Changesintheinfectedareaovertime wereestimatedusingannualkerneldensitieswiththe bkde2D functionofthe KernSmooth packageofR(bandwidth ¼ 0.15 andgrid ¼ 200 200km)[22].Intwovalleyswheredata suggestedanepizooticadvance(ChalhuancaandRioApurimac, figure4 b ),wetestedwhetherspatialexpansionsfolloweda wave-likepatternusinglinearregressionsbetweenthetime andthedistanceofoutbreaksfromthepredictedindexcase. BecauseVBRpersistedlocallyafterinvadingnewareas,we dividedthelandscapeintoequidistanthexagonalbinsusing the hexbin function(xbinssetto6)ofthe hexbin packageinRand analysedthemonthofthefirstoutbreakineachcell.WeincorporatedeffectsofspatialheterogeneityonVBRspreadbycalculating distancestoindexcasesasleast-costdistancesbasedonalandscaperesistancemodel,definedastheminimumdistance alongelevations , 3600m,themaximumrecordedelevationof D.rotundus roostsinthearea(seetheelectronicsupplementary material).Asensitivityanalysisforthisassumptionusing200randomlyselectedelevationthresholdsfrom3500to4500mforeach ofthetwovalleysisprovidedintheelectronicsupplementary material.Theindexcasesofeachtravellingwavewereestimated bysimulating5000randomhypotheticaloriginsofeachwave andchoosingtheoriginthatmaximizedthe R2ofeachlinear regression[23].Wavefrontspeedswerecalculatedastheinverse oftheslopeofthelinearregressionwiththeinterceptsettozero. Weevaluatedthesensitivityofwavefrontspeedstotheinferred originbybootstrapresampling(withreplacement)thehexbins usedinthemainanalysis.Ineachof200bootstrapreplicatesin eachvalley,weevaluated5000randomhypotheticaloriginsand identifiedtheoriginlocationthatmaximizedthe R2ofthedistance/timeregression.Wethencomparedthedistributionsof bootstrappedwavefrontspeedsand R2tothemainanalysis. Weusedthebatbitedistributiondata(datasetii)toevaluate whetherthepatchinessofbatsonthelandscapecouldinfluence wavefrontspeeds.Wedividedeachvalleyintohexagonalcells withaspecific5kmradius(assumedasaconservativedistance forbatdispersal)[24].Withineachcell,wecalculatedthenumber oftownsfromthe2014census,thenumberofcommunitiesvisited forbiteinspectionandwhetherthecommunityreportedatleast onebatbite.Wetestedwhetherthevalleysdifferedonthe numberoftownspercellandthepercentageofcommunities reportingbitespercellusingaWilcoxontest.(d)Forecastingcross-speciestransmissionfrombatsto livestockInthetwovalleyswherewequantifiedwavefrontspeedsofVBR,we predictedthespatialspreadoffutureoutbreaksfrom2015to2017. Forecastsusedtheslopeofthelinearregressiontopredictthearrival ofrabiestoeachlocalityaccordingtotheleast-costdistanceofeach localitytotheinferredorigin.Asawithin-datavalidationofourpredictions,wedevelopedatrainingmodelbasedonthefirst75%of availabledataandappliedthistopredicttheremaining25%of rabiesarrivaldates.Detailsofthecross-validationanalysisare givenintheelectronicsupplementarymaterial.Allanalyseswere performedinR[25].3.Results(a)Spatialexpansionsunderliearecentdoubling ofrabiesspillovertolivestockIntotal,1146(51%)of2265suspectedoutbreaksbetween2003 and2014wereconfirmedrabiespositiveusingthefluorescent antibodytest,makingVBRthemostcommonnotifiabledisease inPeruvianlivestock(electronicsupplementarymaterial,figure S5 a ).Cattlewereinfectedin91%oftheconfirmedoutbreaks,followedbyhorses(4%),goats(2%),sheep(1%)andotherassorted species(2%,11pigs,fourbuffalosandonecamelid).Outbreaks werewidespreadacrosstheAndesandAmazon,with14of25 governmentalregionsreportingatleastonesuspectedoutbreak inlivestock,and12regionsreportingfrom7to470laboratoryconfirmedoutbreaks(figure1 a ).Temporalautocorrelation analysisrevealednoseasonalityinVBRspillovertolivestock ateitherthenationalortheregionallevel. Atthenationallevel,thenumberofVBRoutbreaksbegana consistentincreasein2011,withaneardoublingofoutbreaksby 2014(figure1 b ).Thisincreaseisunlikelytobecausedbychanges inreporting:the56otherlivestockdiseasestrackedbythesame surveillancesystemincreasedfromtheestablishmentofthe systemin2003until2008,butremainedstableinlateryears whenrabiesreportsintensified(electronicsupplementarymaterial,figureS5 b ).Furthermore,inalinearmodel includingtheeffectsofthenumberofotherdiseasesreported andyearontheannualnumberofrabiesoutbreaks,year ( F1,9¼ 11.1, p , 0.01),butnotoutbreaksofotherdiseases ( F1,9¼ 0.64, p . 0.1),wassignificant(fullmodel R2¼ 0.7). IncreasesinVBRoutbreakswerenotgeographicallyubiquitous. OutbreaksdeclinedorwerestableintheAmazon,butbecame morefrequentintheAndes,particularlyinthreeregionscharacterizedbyvalleyswithhighagriculturalproductionsurrounded byhighelevationpeaks:Apurimac(470outbreaks,41%ofthe nationaltotal),Ayacucho(197,17%)andSanMartin(128, 11%)(figure1 a ;electronicsupplementarymaterial,figureS6). Thenationalincreaseinrabiesoutbreaksoccurredconcurrentlywithspatialexpansionsintohistoricallyuninfected areas.Thecumulativenumberofdistrictswithconfirmed casesmorethantripledbetween2003and2014,suchthaton averageVBRspreadinto12(standarddeviation,s.d. ¼ 0.319) previouslyuninfecteddistrictsperyear(figure2,inset),apatternalsoobservedatthemonthlylevel(1districtmonth2 1, s.d. ¼ 0.007).Thenumberofinfecteddistrictsalsoincreasedin annual(non-cumulative)reports,withmostdramaticspatial expansionscoincidingwiththeincreaseinoutbreaksfollowing 2011(figures1 b ,2).Hotspotsofspatialexpansionoccurredinthe regionsofSanMartin,AmazonasandCajamarcainthenorthof Peru(5.2districtsyr2 1,s.d. ¼ 0.36)andinApurimac,Ayacucho andCuscointhesouth(4.1districtsyr2 1,s.d. ¼ 0.12).Bycontrast,fewnewdistrictswereinfectedintheAmazonian regionsofLoreto,UcayaliandMadredeDios(1.4districts yr2 1,s.d. ¼ 0.21),wherenonewdistrictswereinfectedinthe last3years.Consistentwithepizooticspatialexpansions fromenzooticzones,85%ofnewlyinfecteddistrictshada neighbouringdistrictinfectedinthesameorpreviousyear. SignificantincreasesintheelevationofVBRoutbreaks occurredinregionscontainingtransitionsfromtheAmazon rainforestintotheAndesmountains(i.e.Cusco,Cajamarca, SanMartinandUcayali).Bycontrast,themeanelevation ofrabiesoutbreakswasunchangedinregionswithonly high(i.e.ApurimacandAyacuchointheAndes)andlow rspb.royalsocietypublishing.org Proc.R.Soc.B 283 :20160328 3

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(i.e.MadredeDiosandLoretointheAmazon)elevations (figure3).Themodelwitharegionbyyearinteractionwas morestronglysupportedthanyear þ region( D AIC ¼ 91.2), yearalone( D AIC ¼ 1790.33)andregionalone( D AIC ¼ 96.05). OurGLMMshowedthat,controllingforregionasarandom effect,theelevationofoutbreaksgenerallyincreasedthrough time( z -value ¼ 2.93, p , 0.01).Howeverinseveralregions (e.g.Ayacucho,Cusco),theminimumelevationofoutbreaks decreasedthroughtimeconcurrentlywithincreasesinthemaximumelevationofoutbreaks,creatingafunnelpatternwhich indicatesthatdownhillinvasionsalsooccurred(figure3).(b)VelocitiesoftravellingwavesofvampirebattransmittedrabiesinheterogeneouslandscapesIntheAAC,kerneldensityestimatesshoweda74%increase inthespatialextentofVBRbetween2003and2014,equivalenttoanewlyinfectedareaofapproximately21000km2(figure4 c ).TwodifferentspatiotemporaldynamicsofVBR wereobserved.InthenorthoftheAAC(e.g.SanMiguel, Huanipaca,Huancaramadistricts),VBRpersistedenzooticallyviasporadicoutbreaksthroughthedurationofthe timeseries,consistentwithmetapopulationdynamicsproposedbyBlackwood etal .[10](figure4 a,b ).Bycontrast, VBRonlyrecentlyinvadeddistrictsinthesouthorsouthwest (e.g.Tintay,Mollepata,Circa). InthevalleysofChalhuancaandRioApurimac,strong linearrelationshipsbetweenthetemporalandtheleast-cost spatialdistancefromeachoutbreaktothepredictedindex casesrevealedwave-likeexpansionsofVBR(figure5).Bythe endof2014,thesewaveshadtravelled39kminChalhuanca (94outbreakssince2009)and54kminRioApurimac(45outbreakssince2012).Dispersalrateswerestrikinglyconsistent throughtime,asevidencedbyhigh R2valuesinlinear modelswithineachvalley( R2¼ 0.98and0.93forChalhuanca andRioApurimac,respectively;figure5 b ).Interestingly,VBR 0 ( a ) ( b ) 2003–2006 first reported rabies rabies outbreaks 2007–2010 2011–2014 0 <10 10–50 50–100 100–200 >200 –5 –10 –15 50 suspected outbreak laboratory confirmed250 100 0 200320092014 year40no. outbreaksno. outbreaks30 20 10 0 –80 2003200520072009201120132015 y ear –75 –70 longitudelatitude Figure1. SpatialandtemporalpatternsofVBRoutbreaksinPeru.( a )TimesofVBRonsetatthedistrictlevel(mainmap)andthenetnumberofconfirmed outbreaksattheregionallevel(inset).RedlinesshowtheAAC,includingtheApurimac,AyacuchoandCuscoregions.( b )Patternofmonthly(mainfigure) andyearly(insetfigure)outbreakreportsacrossPeru,excludingregionswheredograbiesisenzootic(Puno)andtworegionsonthecoast(LimaandAn cash) thatreportedsmallnumbersofunconfirmedoutbreaks. rspb.royalsocietypublishing.org Proc.R.Soc.B 283 :20160328 4

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isspreadingthroughbatpopulationsnearlytwiceasrapidly intheRioApurimacvalleyasinChalhuanca(17.2kmyr2 1(95%confidenceinterval(CI):15.3–19.7)versus9.1kmyr2 1(95%CI:8.6–9.7);figure5 a ).Uncertaintyintheoriginlocations hadlittleinfluenceonwavefrontspeeds.Bootstrapestimates revealedsimilarspeedsacrossallplausibleoriginlocations, withestimationsrangingfrom14.3to20.4kmyr2 1( R2:0.87– 0.98)inRioApurimacandfrom6.7to11.2( R2:0.96–0.99)in Chalhuanca(electronicsupplementarymaterial,figureS1). Likewise,estimatesofwavefrontspeedswereinsensitiveto elevationthresholdsinthelandscaperesistancemodels,with valuesacrossthresholdsintherangeof16.5–17.9kmyr2 1( R2: 0.92–0.93)inRioApurimacand7.8–9.2( R2:0.97–0.98)in Chalhuanca(electronicsupplementarymaterial,figureS2). Theconsistencyofwavefrontspeedswithineachvalley suggeststhatVBRspreadspredominatelybyshortdistance dispersalthroughacontinuouslyoccupiedlandscape,rather thanbypunctuatedspreaddrivenbylongdistanceflightsof infectedbats.Censusdatashowednosignificantdifference betweenvalleysinthenumberoftownsper5kmgrid cell(Chalhuanca:mean + s.d.:12.9 + 11.5;RioApurimac: 12.5 + 12.2;Wilcoxontest, W ¼ 838, p ¼ 0.6)orinthepercentageofsurveyedcommunitiesreportinganimalsbitten bybats(Chalhuanca:71%(36/51communities)andRio Apurimac:78%(92/118);electronicsupplementarymaterial, figureS4).Thetwovalleyshadequivalentprevalenceofbat bites( W ¼ 267, p ¼ 0.8)andthepresence/absenceofbites (linearmodelwithbinomialerrordistributioncontrollingfor thenumberoftownsandthenumberofinspectionspercell: valleyeffect, t -value1,44¼ 0.74, p ¼ 0.4).Togetherthesedata suggestwidespreadpresenceofbatsineachvalleywithsimilar distributionsofcommunitiesandsurveyeffort.(c)Spatialforecastsofcross-speciestransmission tolivestockOurquestionnairesconfirmedthepresenceofvampirebats (asincidenceofbatbites)aheadofadvancingwavefronts, whichwillenablethespreadofVBRintocurrentlyrabiesfreepartsofeachvalley(figure5 a ).Moreover,only25% (Chalhuanca)and3%(RioApurimac)ofrespondentsknew thatbatscouldtransmitrabiesandfewerthanhalf(47%: Chalhuancaand40%:RioApurimac)knewtheappropriate governmentagencyforreportingrabies.Only1outof90 farmershadvaccinatedanyanimalsagainstrabies. Giventhepresenceofvampirebatsandthelowpreparednessforoutbreaksaheadofwavefronts,weusedourspatial modelstoforecastdatesofrabiesarrivaltocurrentlyuninfectedareas.Thepredictivepowerofourmodelswas supportedbyourwithin-datavalidation.Thetruearrivalof rabiesfellwithinthepredictedCIsinalloutbreaks(electronic supplementarymaterial,figureS3),withanaveragedifferenceof6.4and3.3monthsbetweenthepredictedand actualarrivaldatesinChalhuancaandRioApurimac, respectively( n ¼ 5and7hexagonalcellstopredict,respectively).Byforwardprojectingourfullmodels,wepredict VBRarrivaltovampirebatpopulationsinsixcurrently uninfecteddistrictsbytheendof2015,13by2016and22 by2017inthetwovalleyscombined(figure5 a ;electronic supplementarymaterial,tableS1).4.DiscussionUsingahigh-resolutionspatiotemporaldatasetofrabiesoutbreaks,weillustratethepowerofcombiningsentinelanimal datafromnationalsurveillancesystemswithstatistical modelstopredictthetimeandplaceoffuturecross-species transmissionsofbatviruses.InPeru,weobservearecentdoublingofVBRoutbreaksinlivestock,whichisassociatedwith spatialexpansionsofthevirusintopreviouslyuninfectedbat populations.Intheregionofthecountrywheremostoutbreaks occur,theexpansionformsmultipleindependentwavesof infectionthataretravellingatconsistentratesandtrajectories towardscommunitieswherewedocumenthighcontactrates betweenbatsandunvaccinatedlivestockandpoorknowledge ofrabies.Widespreadinvasionsintonewareasandincreasesin theburdentohumanandanimalhealthrevealVBRasanemergingratherthananenzooticzoonosisandmandatenew strategiesforrabiescontrolinLatinAmerica. TheconsistentdetectionofVBRinonepreviouslyuninfecteddistrictpermonthoverthelast12yearsisanalarming signalofthegrowinghumanandanimalhealththreatposed byVBR.Thetrigger(s)oftheseexpansionsareuncertain,but theyareoccurringthroughoutthecountryintransitionzones betweentheAmazonandAndesandinvalleyswithinthe Andes(figure3).Onepossibilityisthatgrowinglivestock populationscouldhaveincreasedthesizeorconnectivityof vampirebatpopulations,facilitatingviralintroduction[5]. However,livestockcensusdatafrom1994and2012indicate nochangeinlivestockdensitiesinthenewlyinfecteddistricts (PeruvianNationalLivestockCensus,CENAGRO).Another hypothesisisthatrisingtemperaturesduetoclimatechange couldexpandbatpopulationsandthusVBRtohigher elevations[17].Indeed,ourGLMMshowsthatVBRisspreadingonaveragetohigherelevations.Importantlyhowever, expansionsoccurredinareaswellbelowthemaximum elevationofVBRinotherpartsofthePeru(3600mts),and theelevationofoutbreaksdidnotincreaseinhighelevation regionswhereVBRwasenzooticthroughoutthetimeseries (i.e.ApurimacandAyacucho;figure3).Thus,wearguethat 200420062008201020122014 y ear 20 30annual no. infected districts40 50 60200420062008201020122014 yearcumulative no. infected districts0 50 100 150 R2=0.99 slope=12.6 districts yr–170 Figure2. NationalspatialexpansionofVBR.Annual(mainfigure)and cumulative(insetfigure)numberofgovernmentaldistrictsreportingVBRoutbreaksfrom2003until2014.Linesshowvaluespredictedbytheloess functioninR. rspb.royalsocietypublishing.org Proc.R.Soc.B 283 :20160328 5

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theemergenceofVBRintheseregionsiscausednotbyclimatedrivenchangesinthevampirebatdistribution,butinsteadan epidemiologicalprocessofprotractedviralinvasionofa relativelynewvirusinvampirebatpopulations,ahypothesis supportedbymolecularclockestimatesofthemostrecent commonancestorofvampirebatrabies[26].Infurthersupport 4000 ApurimacAyacuchoCusco**Cajamarca** Amazonas JuninPascoMadre de diosLoreto San Martin**Ucayali**Huanuco 3000 2000 1000 0 4000outbreak elevation3000 2000 1000 0 4000 y ear 3000 2000 10002004 2006 2008 2010 2012 2014 2004 2006 2008 2010 2012 2014 2004 2006 2008 2010 2012 2014 2004 2006 2008 2010 2012 20140 Figure3. Changesinthegeographicalelevationofrabiesoutbreaksineachregion.Eachpanelshowstheannualdistributionoftheelevationofobservedoutbr eaks ineachregionbetween2003and2014.Regionsaresortedbydecreasingorderofaverageelevation.Boxplotsshowmedian,secondandthirdquartiles,w hereas greydotspresenttherawdata.AsteriskshighlightregionswhereincreasesinoutbreakelevationweresignificantinourGLM( p , 0.05).(Onlineversionincolour.) Siviaelevation (m) 50002003–2006 2007–2010 2011–20144000 3000 2000 10002014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003–72.5 –73.0 longitude –73.5( b ) ( a ) ( c )–74.0Ayacucho Apurimac Cusco144 72 month since 2003 0 80 70 60area (×1000 km2)50 100no. outbreaks50 0Santa Rosa Anco Tambo San_Miguel Saurama Chilcas Acos Inchos Luis Carranza Chungui Ocros Concepcion Vilcashuaman Carhuanca Huambalpa Accomarca Belen Chalcos Independencia Chilcayoc Querobamba San Pedro de Cachora Huaccana Ongoy Huanipaca Andarapa Ranracancha Ocobamba Kaquiabamba Anco-huallo Chincheros Curahuasi Tamburco Talavera Pacobamba Pacucha Kishuara Uranmarca Cocharcas Abancay Huancarama San Antonio de Cachi Andahuaylas Santa Maria de Chicmo Huancaray Pichirhua Lambrama Chacoche Circa Lucre Tintay San Juan de Chacña Chapimarca Colcabamba Echarate Quimbiri Yanatile Kosñipata Limatambo Mollepata Vilcabamba Figure4. SpatialexpansionsandincreasingburdenofVBRinAndeanvalleysofApurimac,AyacuchoandCusco(AAC).( a )MonthlyVBRoutbreaksfrom2003to2014 in61infecteddistrictsinAAC.Eachrowrepresentsthenumberofoutbreaksinanindividualdistrictthroughtime.Districtsweresortedaccordingt othelatitudeof theircentroid(withthemostnortherndistrictatthetopofthepanel)withineachregion.Darkerredsindicatelargernumbersofcases(maximum ¼ 8),white indicatestheabsenceofVBRdetections.Arrowsillustratethebeginningofthewave-likespreadfortheChalhuanca(blue)andRioApurimac(red)val leysshownin figure5.( b )Detailedspatiallocationsofoutbreaksfrom2003to2014.( c )Numberofoutbreaksperyearandestimatedareacoveredaccordingtokerneldensity estimates. rspb.royalsocietypublishing.org Proc.R.Soc.B 283 :20160328 6

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fortheslowinvasionhypothesis,thetravellingwavesinthe twofocalvalleysofAACwereinitiatedonlyinthelastfew yearsdespitemolecularevidencethatVBRwaspresentin northwesternpartsoftheregionsincetheearly1970sandthe evidencefromourquestionnairestudythatvampirebatsare alreadypresentinrabies-freepartsofeachvalley[14] (figure5 a ). Theslowwavefrontspeedsthatweobserveinvampirebats relativetootherrabiesreservoirs(e.g.30–100kmyr2 1inraccoons)andtheirlowvariabilityismoreconsistentwithshort distancedispersalofinfectedbatsthaninvasiondrivenby rarelongdistanceflights[27].Indeed,althoughtranslocation experimentsshowthatvampirebatsarephysiologically capableoflongdistancemovements,homerangesizesare typically , 10km2[9,24,28].Oneremainingquestioniswhy wavesaretravellingatdifferentratesindifferentvalleys. Differentpatternsofbetween-colonybatmovementsineach valleydrivenbyunderlyingdifferencesinthedistributionof batcoloniescouldinfluencewavespeeds.However,valleys hadsimilardistributionsoffarmsandintensitiesofbites(electronicsupplementarymaterial,figureS5),suggestingthatlong distancedispersalofVBRisunlikelytobealimitingfactorin eithervalley.Anthropogenicdisturbances,particularlythe intensityofbatculls,couldalsoconceivablyinfluenceviral spread.Ontheonehand,cullscouldreducetheprobability ofdispersalbyaninfectedbatbyreducinginfectionprevalence orcompetition-drivendispersal.Ontheotherhand,dispersal bysurvivorsofcullscouldfacilitateviralinvasioninto uninfectedareas.Asimilarexampleofdisturbance-driven pathogenspreadwasobservedintheUK,wheredisruption ofbadgerterritorialboundariesbycullingfacilitatedthespatial spreadofbovinetuberculosis[29].Finally,differencesin wavefrontspeedscouldpotentiallyariseifviralstrains withdifferentinfectionphenotypescirculateineachvalley. However,previousworkshowedthatonlyonegeographically isolatedvirallineagehascirculatedintheAACsincetheearly 1970s[14].Therefore,wesuspectthatthewavesdescribedhere haveacommonevolutionaryorigin,andrecentevolutionis unlikelytoexplaintheobservedvariationinwavefrontspeeds. Intheabsenceofintervention,thearrivalofVBRtocurrentlyuninfectedareaswillcauseconsiderablelivestock mortality,majoreconomiclossesandanewpublichealth threattofarmerswhohandleinfectedbatsorlivestock.Itis difficulttoquantifytherealimpactoftheseviralinvasions onagriculture,becauseunder-reportingofVBRisthought tobesignificantbutremainsunquantifiedinmostareasof LatinAmerica,precludingestimationofthetrueburden ofthediseaseonlivestock[30].InthetwoAACvalleys alone,weforecastthatover11600small-scalefarms,containingatleast339000livestock(93715cows,215707sheep, 15690goatsand13774pigs)willnewlybeatriskofrabiesin thenext3years.Vaccinationoftheseanimalswouldcostat leastUS$373000peryear(US$1.1pervaccine);asignificant financialburdentosmall-scalefarmerswhorelyonlivestock salestopayforhousemaintenanceandchildhoodeducationandforlocalgovernmentsthathavenotpreviously beenaffectedbyrabies.Thehighcostofvaccines,together withlowlocalknowledgeofrabiesindicatedbyourquestionnaires,presentsamajorchallengetoovercomewithepizootic invasionimpending. Toaidplanningofinterventions,weprovideaforecastof rabiesarrivaldatestopresentlyuninfectedareas.Likeallpredictivemodels,ourprojectionuncertaintyincreasesfurther intothefuture;thus,itwillbeusefultoupdatemodelsas additionaldatabecomeavailable.Nevertheless,theconsistencyofwavefrontspeeds,evenafterconsideringuncertainty inoriginlocations,andtheabilityofourmodeltosuccessfully predictknowndatesofrabiesarrivalprovideconfidenceinour forecasts.Althoughourphenomenologicalmodelsofrabies spreadaccountforhabitatheterogeneityusingaleast-costdistancealgorithm,othermethodsexistforestimatingwavefront speed.Statisticalmethodssuchastrendsurfaceanalysisare usedoverlargerspatialandtimescalesthanourdata,where outbreaksaredistributedalongrelativelyshortvalleys. –13.22015 2015 2016 2016 2017 10km 2017–13.6 –14.0 –14.6 –73.4–73.0–72.5 10 20 30 40 50 60 70 lon g itude least-cost distance from ori g in (km) –72.0 10p -value<0.001 dispersal rate=17kmyr–1R2=0.93 p -value<0.001 dispersal rate=9kmyr–1R2=0.9820 30 40 50 10 20 30month of first outbreak since 2012 month of first outbreak since 200940latitude( b ) ( a ) Figure5. Wave-likespreadandoutbreakforecastingintwovalleysofPeru.( a )MapsofChalhuanca(left)andRioApurimac(right)valleysshowingtheleast-cost paths(blueandredlines)fromthecentreofeachcellwhereanoutbreakoccurredtothepredictedoriginofeachwave(triangles)andthepredictedlim itsof outbreaksfortheendof2015,2016and2017,respectively.Predictedlocations(blueandredcolourpalettes)weredrawnbysimulatingrandomcoordi natesthat matchedthepredictedleast-costdistancefromlinearmodels.Greyshadingindicatesaltitudesbelow3600m,wherevampirebatsoccur.Piechartssh owthe percentage(green)offarmswherevampirebatbitesoccurredonlivestockforeachofninecommunities(10questionnairespercommunity).( b )Linearregressions betweenthemonthofthefirstconfirmedVBRoutbreakineachcellandtheleast-costdistancefromtheinferredoutbreakoriginsintheChalhuanca(le ft,blue points)andRioApurimac(right,redpoints)valleys. rspb.royalsocietypublishing.org Proc.R.Soc.B 283 :20160328 7

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Spatiallyexplicitmechanisticmodelshavealsobeenwidely usedtomodelrabiesspreadincarnivoresinheterogeneous landscapes(e.g.[27,31]).Unfortunately,thedispersaldistancesofinfectedbatsandthesizesofcoloniesareunknown,so parameterizationofsuchamodelforVBRwouldnotbe straightforward.Moreover,withoutadditionaldata,such modelswouldnotbeexpectedtoalterourmeanpredictions. Wethereforeargueourapproachisideallysuitedtoinform rapidresponsesinapublichealthandveterinaryemergency. Travellingwaveshavebeenidentifiedinseveralotherwildlifezoonoses(e.g.Ebolavirus[23],rabiesinraccoons[32]and plagueinrodents[33]).ThewavesofVBRthatweidentify areimportant,becausetheyareoccurringinrealtimeand arepredictableinspeedandtrajectory,creatingapowerful opportunitytodirectthedistributionofvaccinesandeducationalcampaignstoareaswhereinfectionisimminent (electronicsupplementarymaterial,tableS1).Ourresults furtheropennewpossibilitiesforthecontrolofabat-borne zoonosisinitsreservoir.Whileinterventionssuchasculling havehistoricallyfocusedonenzooticareas,ourfindings enabletargetingofhealthybatpopulationsbeforeviralinvasion.SuchastrategywasattemptedinArgentinainthe1970s, butevenwithadramatic95%reductionofvampirebatpopulationsusingcyanidepoisoning,theepizooticadvanced[34]. Thisfailurecouldreflectanabsenceofnaturalgeographicalbarriersallowingthevirustocircumnavigatetheinterventionzone orthechallengesofusingpopulationreductiontocontrola pathogenwithfrequency-dependenttransmission[9,10,35]. Anappealingalternativewouldbetoincreasetheproportion ofimmunizedbatswhilemaintainingtheagestructureand relativelysedentarydispersalbehaviourofvampirebats. Atransmissiblegel-basedtopicalrabiesvaccinewaseffective incaptivevampirebatsbuthasneverbeenreleasedinwild populations[36].Vaccinationaheadoftheepizooticfront couldbeparticularlyeffectivewhenpairedwithnatural geographicalbarrierssuchasthehighAndeanpeaksthat occurintheAAC. Thisstudydemonstratesthepowerofanimalhealth surveillancesystemstogeneratehigh-resolutioninsightsinto thespatiotemporaldynamicsofzoonoticvirusesthatwould probablybeimpossibletodetectrelyingonstudieswithina wildlifereservoiralone.Thetravellingwavesthatwedetected inPerudirectlyinformmanagementofviralspilloverfrombats byprovidingrecommendationsforwhereandwhenlivestock shouldbevaccinatedandeducationalcampaignsshouldbe carriedout,whilecreatingauniqueopportunitytotrailexperimentalinterventionsinbatpopulationstoblockspatially replicatedadvancingepizootics. Dataaccessibility.DatausedinthisstudywereprovidedbytheServicio NacionaldeSanidadAgraria(SENASA)ofPeru,publiclyavailable onlineathttp://www.senasa.gob.pe/senasa/reportes-epidemiologicos-semanales.BatbitedatamayberequestedfromtheApurimac RegionalProjectforRabiesControl.Authorscontributions.J.A.BandD.G.S.designedresearch;J.A.Band D.G.S.analyseddataandJ.A.B,D.G.S.andW.Vwrotethepaper.Competinginterests.Wehavenocompetinginterests.Funding.D.S.wassupportedbyaSirHenryDaleFellowship,jointly fundedbytheWellcomeTrustandRoyalSociety(grantno: 102507/Z/13/Z).Acknowledgement.WethankRomanBiek,KatieHampson,RolandKao, RichardReeveandMafaldaVianaforhelpfulsuggestionsonthe manuscript.WethanktheNationalServiceofAgrarianHealthof theMinistryofAgricultureofPeruforcollectingandproviding accesstonationalsurveillancedataonrabiesandotherlivestockdiseases,ElizabethRojasPaniaguaforconductingthequestionnaires, andMBZRubyNin ˜ odeGuzmanMonteroandMBZEduardoSanchez fortheirvaluableknowledgeofvampirebatrabiesinApurimac.References1.CalisherCH,ChildsJE,FieldHE,HolmesKV, SchountzT.2006Bats:importantreservoirhosts ofemergingviruses. 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