Epidemics19(2017)43–52
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Epidemics
jo u r n al h om ep ag e :w w w . e l s e v i e r . c o m / l o c a t e / e p i d e m i c s
Acomparativeanalysis ofChikungunyaandZikatransmission
JulienRiou∗,ChiaraPoletto,Pierre-YvesBoëlle
SorbonneUniversités,UPMCUnivParis06,INSERM,InstitutPierreLouisd’EpidémiologieetdeSantéPublique(IPLESPUMRS1136),75012Paris,France
a r t i c l e i n f o
Articlehistory:
Received30September2016 Receivedinrevisedform 23December2016 Accepted3January2017 Availableonline18January2017 Keywords: Zikavirus Chikungunyavirus Outbreakanalysis Multilevelanalysis Weather a b s t r a c t
TherecentglobaldisseminationofChikungunyaandZikahasfosteredpublichealthconcernworldwide. Tobetterunderstandthedriversoftransmissionofthesetwoarboviraldiseases,weproposeajoint analysisofChikungunyaandZikaepidemicsinthesameterritories,takingintoaccountthecommon epidemiologicalfeaturesoftheepidemics:transmittedbythesamevector,inthesameenvironments, andobservedbythesamesurveillancesystems.WeanalyseeighteenoutbreaksinFrenchPolynesia andtheFrenchWestIndiesusingahierarchicaltime-dependentSIRmodelaccountingfortheeffectof virus,locationandweatherontransmission,andbasedonadiseasespecificserialinterval.Weshow thatChikungunyaandZikahavesimilartransmissionpotentialinthesameterritories(transmissibility ratiobetweenZikaandChikungunyaof1.04[95%credibleinterval:0.97;1.13]),butthatdetectionand reportingratesweredifferent(around19%forZikaand40%forChikungunya).Temperaturevariations between22◦Cand29◦Cdidnotaltertransmission,butincreasedprecipitationshowedadualeffect,first reducingtransmissionafteratwo-weekdelay,thenincreasingitaroundfiveweekslater.Thepresent studyprovidesvaluableinformationforriskassessmentandintroducesamodellingframeworkforthe comparativeanalysisofarboviralinfectionsthatcanbeextendedtoothervirusesandterritories.
©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCC BY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction
Arboviralinfectionsareincreasinglybecomingaglobalhealth problem(WHO,2016).Denguefeverandyellowfeverviruseshave beenre-emerginginmanytropicalareassincethe1980s(Gubler, 2004),but new epidemic waveshave recentlybeen caused by lesserknownarboviruses:theChikungunyavirus(CHIKV)since 2005(Renaultetal.,2007),andtheZikavirus(ZIKV)since2007 (Duffyetal.,2009).Interestingly,thespreadofZIKVandCHIKVhave sharedmanyepidemiologicalcharacteristics.Whilediscoveredin the1940–50s,theglobalspreadofthesevirusestopreviously unaf-fectedareashasonlybeguninrecentyears,andlargeoutbreaks haveaffectedtheimmunologicallynaivepopulationsoftheIndian andPacificoceansandoftheAmericas(WeaverandLecuit,2015; Musso et al.,2015; Zhang et al., 2016).Case identificationand countinghasbeenanissueforepidemiologicalsurveillancesince symptomscausedby ZIKVandCHIKVinfectionare mostof the timesmildandnotspecific.Finally,bothdiseasescanbe transmit-tedbythesamemosquitoesoftheAedesgenus(Richardetal.,2016;
Lietal.,2012).Themostcommonvector,Ae.aegypti,iswelladapted tothehumanhabitat(Brownetal.,2011),isresistanttomany insecticides(Limaetal.,2011),and bitesduringthedaysothat
∗ Correspondingauthor.
E-mailaddress:julien.riou@iplesp.upmc.fr(J.Riou).
preventionbybednets,forexample,isineffective(Christophers etal.,1960).
Obviously,transmissionofthediseasehasbeenfacilitateddue to thejointoccurrence of largesusceptible humanpopulations andcompetentvectors.However,otheraspectsareinvolvedinthe transmissionofarboviruses,sincevectorabundanceandbehavior changewiththeenvironment.AjointanalysisofCHIKVandZIKV epidemicsmayprovideabetterunderstandingofthe commonali-tiesanddifferencesamongthesetwoAedes-transmitteddiseases. Up tonow, thesediseases havebeenstudiedseparately,witha special focuson thereproduction ratio of CHIKV (Boëlle et al., 2008; Polettiet al.,2011;Yakob and Clements,2013; Robinson et al., 2014) orZIKV (Kucharskiet al.,2016; Champagneet al., 2016;Nishiuraetal.,1010;Chowelletal.,2016).Theuncertainty regarding severalparameters,suchastheunder-reportingratio and therateofasymptomaticindividuals,havemadeitdifficult toassesstheattackratesinnaivepopulations,therelative trans-missibilityoftheviruses,andwhethermeteorologicalconditions mayaltertheseparameters.
Here, building oncommonaspects in location and vectorial transmission,westudyindetail themainfactorsthatimpacted diseasespread.Withthisobjective,weproposeajointmodelof ChikungunyaandZikatransmissionbasedonthetime-dependent susceptible-infectious-recovered(TSIR)framework(Perkinsetal., 2015),usingdatafromninedistinctterritoriesinFrench Polyne-siaand theFrench WestIndies,whereboth diseases circulated http://dx.doi.org/10.1016/j.epidem.2017.01.001
1755-4365/©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/ 4.0/).
Wealsoconsidertheinfluenceofmeteorologicalconditionsduring theoutbreaks.Thisapproachallows todiscriminatethe respec-tiveinfluenceontransmissibilityof:(i)propertiesofeach virus itselfinatypicalsituation,(ii)factorsthatdependonthe char-acteristicsofagivenareathatmaybeconsideredasstableover time(e.g.humanpopulationdensityandorganization,mobilityof humansandvectors,environmentalcomposition),and(iii)weather conditions.
2. Materialsandmethods
Weanalysed theZikaand Chikungunyaepidemics occurring between2013and2016insixislandsorsmallarchipelagoesof FrenchPolynesiaandthreeislandsoftheFrenchWestIndiesby fittingweeklyincidencedatawithacommonhierarchical trans-missionmodel.Thetwomaincomponentsofthisanalysiswere: (1)amechanisticreconstructionofthedistributionoftheserial intervalofthediseases(thetimeintervalbetweendiseaseonset inaprimaryandsecondarycase),includingtheinfluenceof tem-perature;and (2) a TSIR model for thegeneration of observed secondarycases,thatincludedcoefficientsdependingonthe ter-ritory,thediseaseandthelocalweatherconditions.Theanalysis allowedfortheidentificationoftheparametersofinterest,suchas thereportingrate,thereproductionratioandtheattackrateofeach outbreak.
2.1. Data
Incidenceofclinicaldiseasewasavailablefromlocalsentinel networksofhealthpractitioners.Weeklydatawerecollectedfor thewholedurationoftheoutbreaks,exceptfortheZikaepidemics in the French West Indies that were still ongoing at the time ofwriting(theperiodbeforeOctober2nd,2016wasconsidered fortheanalysisinthatcase).InFrenchPolynesia,bothZikaand ChikungunyaepidemicsweremonitoredbytheCentred’Hygiène etde SalubritèPublique de PolynésieFranc¸isefor sixislands and archipelagoesofFrench Polynesia:theAustralIslands (abbrevi-atedAUS),theMarquesasIslands(MRQ),Mo’oreaIsland(MOO), theSous-le-ventIslands(SLV,alsonamedLeewardIslands),Tahiti (TAH),andtheTuamotus(TUA)(Directiondelasanté,Bureaude veillesanitaire,2015;Centred’hygièneetdesalubritépubliquede Polynésiefranc¸aise,2014).IntheFrenchWestIndies,thetwo epi-demicsweremonitoredbytheCIREAntilles-GuyaneforGuadeloupe (GUA),Martinique(MRT), andSaint-Martin(STM)(CIREAntilles Guyane,2015,2016).
Foreachdisease,weobtainedaggregatednumbersofsuspected casesbyweekofdiseaseonsetforeacharea.Inthecaseof Saint-Martin,whereCHIKVcirculatedatlowintensityforseveralmonths afteraninitialpeak,weonlyconsideredthefirstwaveofthe out-break(25weeks).SuspectedcasesofZIKVinfectionweredefined asa rashwith or without feverand at least two signs among conjunctivitis,arthralgia, or oedema. Suspected cases of CHIKV infectionweredefinedasafeverwitharthralgia.Asthenumber ofactivesentinelcentreschangedfromweektoweek,weused theprojectednumbersofcasesextrapolatedfromthenumberof reportinghealth practitionersin theareaprovided bythelocal authorities(Kucharskietal.,2016).Weatherdatawerecollected foreachlocationandoutbreakperiodfromthenearestweather stationavailablein theWeatherUndergroundwebsite (Weather undergroundwebsite,2016).Dailyreportsofmeantemperature (in◦C)andtotalprecipitation(incm)wereaggregatedbyweekon thesamegridasincidencedata.
WeextendedtheapproachusedinBoëlleetal.(2008)toobtain thedistributionoftheserialintervalbetweenonsetofdiseasein aprimaryandsecondary caseforZikaandChikungunya.Inthis framework,theserialintervalissplitinfourparts:(i)theinfectious periodbeforesymptomsintheprimarycase;(ii)thetimefrom infectiousnessintheprimarycasetoaninfectiousmosquitobite; (iii)thetimefromtheinitialcontaminatingbitetoatransmitting biteinthemosquito–thatdependsontheextrinsicincubation period(EIP)and themosquitogonotrophiccycle–;and(iv)the incubationperiodinthesecondarycase.
Thecharacteristicsofeachpartarewellinformedinthe liter-atureand putsforwardtheimportanceoftemperatureinthree respects. First, theduration of theEIPshortensas temperature increases. FollowingJohanssonet al. (2014),Alex Perkins et al. (2016),wecomputedthemeanEIPdurationattemperatureTas (T)=28×exp(−0.21(T−28))(Chanand Johansson,2012),with base value 28 measured at 28◦C fixed at 3 days for Chikun-gunya(Dubrulleetal.,2009;Dupont-Rouzeyroletal.,2012)and at 6 days for Zika (Boorman and Porterfield, 1956; Li et al., 2012).Second,themeanduration ofonegonotrophiccyclealso decreaseswithtemperature,fromabout5daysat22◦Cto2days at 28◦C (Carrington et al., 2013) but increases again at higher temperatures.Thisassociationwasdescribedusingthefunction (T)=56.64−3.736×T+0.064×T2(Carringtonetal.,2013).Third, mosquitomortalityrateisaffectedbytemperature,buttheeffect measuredinfieldstudiesisverylimitedwithintherangeofvalues relevantinthisstudy.Hence,thedailymortalityratewasfixedto 0.29(Bradyetal.,2013).
Taking allinformationintoaccount, wecomputed theserial intervaldistributionsasafunctionoftemperatureT.Thesewere characterizedbytheirmeanSI(T),standarddeviationSI(T)and cumulativedistributionfunctionG(t,T).Furtherdetailsare avail-ableintheSupplementaryInformation.
2.3. Transmissionmodel
TheBayesianmodelforanalysingoutbreakswasbasedonthe modelpresentedbyPerkinsetal.(2015).Here,wefirstdescribe analysisforonediseaseinonelocation,thenextendthe frame-worktoahierarchicalmodelencompassingCHIKVandZIKVinall locations.
2.3.1. Oneisland,onedisease
We are interested in modelling the time series O={Ot}t= 1,...,Koftheweeklynumber ofincidentcasesreportedtothe surveillancesystems,whereKisthedurationoftheepidemicin weeks.Oconsistsofthecaseswhosoughtclinicaladviceandwere diagnosed,afractionofthe(unobserved)incidentinfectedcases I={It}t=1,...,K.Wethereforewrite,inthe“observation”level ofthemodel,thatOtisaproportionofallcasesItaccordingto:
Ot|It,∼Binom(It,), (1)
whereistheprobabilitythataninfectedcaseconsultedwitha healthprofessional,wasdiagnosedandreported.
In the “transmission” level, we link incidence It with past observedincidencesO− t = O1,...,Ot−1 as: It|O− t,ˇ,∼Binom St,ˇt N 5 n=1 wt,nOt−n , (2)
where N the total population of the island and ˇt is a time-dependent transmission parameter. The term 5
n=1wt,nOt−n/ summarizesexposuretoinfectiousmosquitoesattimet:itisan
J.Riouetal./Epidemics19(2017)43–52 45
averageofpastincidencewithweightsdefinedbytheserial inter-valdistributionwt,n=G(n+0.5; ¯Tt)−G(n−0.5; ¯Tt)computedat themeantemperature ¯Ttoverthe5weeksprecedingt.The num-berofsusceptibleindividualsSt=N−t−1
u=1Iuatthebeginningof periodtiscomputedasN−t−1
u=1Ou/,notingthatOu/isafirst orderapproximationtoIu.
ToavoiddataaugmentationwiththeunobservedIduring esti-mation,wecollapsethe“observation”and“transmission”levels intoasinglebinomialdistribution:
Ot|O− t,ˇ,∼Binom St,ˇt N 5 n=1 wt,nOt−n . (3)
Ina finalstep,weaccountfor theimprecisenatureoftheO data,sinceobservedcasesOhavebeenextrapolatedfromlimited informationprovidedbyanetworkoflocalhealthpractitioners. Wethereforeallowforover-dispersionusinganegativebinomial distributioninsteadofthebinomial,as:
Ot|O− t,,ˇ∼Neg−Binom Stˇt N 5 n=1 wt,nOt−n, , (4)
wherevarianceiscomputedasthemeandividedby. Thejointprobabilityofdataandparametersisfinally Pr(O,ˇ,)= t Pr(Ot|O− t,ˇt,) Pr()Pr(ˇ) =Pr(O|O−,,ˇ)Pr()Pr(ˇ), (5)
wherePr(ˇ)andPr()arepriordistributionsdescribedlater. 2.3.2. Severalislands,severaldiseases
Weintroducedahierarchicalstructureinthemodelfor repor-tingratesandtransmission.Reportingratesijinislandifordisease jweremodelledusingalogistic-normalmodel
ln ij
1−ij =ri+Vjlnω, (6)
whereri∼N(,2
)isarandomislandeffect,Vjis1forZIKVand0 forCHIKVandωistheodds-ratioofreportingZIKVcasesrelative toCHIKVcasesduringanepidemic.Threeparameters ={,, ω}definethemodel.
Likewise,we allowed for a random island coefficient in the transmissiontermandfixedeffectsfordiseaseandweather covari-ates,asfollows: lnˇijt=bi+VjlnˇD+ 8 l=0 Tt−llnˇT,l+ 8 l=0 Pt−llnˇP,l (7) wherebi∼N(B,2
B)isanisland-specificrandomparameter,ˇDis therelativetransmissionofZIKVcomparedtoCHIKV,andthelast twotermscapturetheinfluenceoftemperatureTandprecipitation Pforthelastnineweeksontransmissionwithninetransmission effectseach,ˇT,landˇP,l–wechosetoconsideratimelaguptoeight weeksbasedonpreviousknowledgeondengueecology(Barrera etal.,2011).Transmissionthusdependsonparameters ˇ={B, B,ˇD,ˇT,0,ˇT,1,...,ˇT,8,ˇP,0,ˇP,1,...,ˇP,8}.
WritingOij=
Oijt
theobservedincidenceintheoutbreakin islandianddiseasej,andOthewholedataset,wehave:
Pr(O, ) = ⎧ ⎨ ⎩ i,j Pr(Oij|O− ij,ˇijt,ij)Pr(ij| )Pr(ˇijt| ˇ) ⎫ ⎬ ⎭Pr( )Pr( ˇ). (8) Table1 Priordistributions.
Parameter Meaning Priordistribution
Island-averagedreporting parameter ∼Normal(=0,=1) Between-islandsSDin reporting ∼Inv-Gamma(˛=10, ˇ=10)
ω Odds-ratioofreportingfor
ZIKVrelativetoCHIKV
lnω∼Normal(=0,=1) B Island-averagedbaseline transmissionparameter B∼Student(=5,=0, =2.5) B Between-islandsSDfor transmission B∼half-Cauchy(x0=0, =2.5)
ˇD RelativetransmissionofZIKV
withrespecttoCHIKV
lnˇD∼Student(=5,=0,
=2.5)
ˇT,l Relativetransmission
accordingtotemperature
(withtimelagl)
lnˇT,l∼Student(=5,=0,
=2.5)
ˇP,l Relativeprecipitation
accordingtotemperature
(withtimelagl)
lnˇP,l∼Student(=5,=0,
=2.5)
Overdispersioninreported
cases
∼half-Cauchy(x0=0,=2.5)
where ={ , ˇ}isthewholesetofparameterstobeestimated. 2.3.3. Modelsandoutcomes
Wedefinedasetofmodelstostructureourinvestigationofthe effectofdiseaseandweathercovariatesontransmission:
• thebaselinemodelconsideredasingletransmissionrateforthe entiretyofeachoutbreakirrespectiveofweatherconditions(i.e. parametersˇT,landˇP,lweresetto1);
• thefreemodel,withthesamehypothesesasthebaselinemodel, butwithindependentrandomtermsbijforeachdiseaseinstead ofthecombinationbi+lnˇDVjinthetransmissionterm,dropping theassumptionofdependencebetweentwooutbreaks occur-ringinthesamearea(seeSupplementaryInformationformore details);
• theweathermodelsbuiltonthebaselinemodelbyincludinga dependenceoftransmissiononweatherconditions.We consid-ered3possibilities:temperaturealone(weatherT),precipitation alone(weatherP),andbothatthesametime(weatherT&P).
Model fitswere compared usingtheleave-one-out informa-tioncriterion(LOOIC),aBayesianinformationcriterionespecially adaptedtohierarchicalmodels(Vehtarietal.,2015).To summa-rizetheintensityoftransmission,wecomputedreproductionratios basedonthegeneralformulaR(i,j,t)=5
n=1wt,nˇi,j,t+n(Perkins
etal.,2015).Inparticular,wecomputedforeachdiseasean island-averagedbasicreproduction ratio ¯R0(j)=exp(B+VjlnˇD),and for each island a disease-specific basic reproductive ratio R0(i, j)=exp(bi+VjlnˇD).
2.3.4. Priorinformation&estimation
Weusedthick-tailed,weaklyinformativepriordistributionsas showninTable1andinSupplementaryInformation(Gelmanetal., 2014,2006).Thejointposteriordistributionsof theparameters wereexploredwiththeHamiltonianMonteCarloNUTSalgorithm, asimplementedinStan2.9.0(Carpenteretal.,2015).Weusedeight chainswith10,000iterationseachanddiscardedthefirst25%as burn-in.Eachchainwassampledevery10-thiterationtoreduce autocorrelation.Convergenceofthechainswasassessedboth visu-allyandbyinspectingtheGelman-Rubinratio ˆR foreveryestimated parameter.Theposteriordistributionsweresummarisedbytheir meansand95%credibleintervals(95%CI).
Wecheckedthatallparameterswereidentifiableusing simu-lateddatasets(seeSupplementaryInformation).Importantly,we
Fig.1.(A)ProfilesofCHIKV(red)andZIKV(blue)outbreaksinthenineterritoriesunderstudy(eachrowisscaledindependentlytoitsmaximum).(B)and(C)Distributions ofweeklymeantemperatures(in◦C)andprecipitation(incm)duringthecorrespondingepidemicperiods.(Forinterpretationofthereferencestocolorinthisfigurelegend, thereaderisreferredtothewebversionofthearticle.)
Table2
Territoriesincludedinthe2013–2016ZIKVandCHIKVoutbreaksinFrenchPolynesia andtheFrenchWestIndies,withtheobservedcumulatedincidence.
Territory Territory
code
Population ZIKVcases CHIKVcases
Number % Number %
Polynesia
AustralIslands AUS 7,000 1,208 17% 1,321 19%
Mo’oreaIsland MOO 16,000 1,235 8% 3,830 24%
MarquesasIslands MRQ 9,000 994 11% 4,762 53% Sous-le-ventIslands SLV 33,000 3,912 12% 8,046 24% Tahiti TAH 184,000 21,406 12% 45,722 25% Tuamotus TUA 16,000 1,211 8% 5,017 31% WestIndies Guadeloupe GLP 400,000 30,454a 8% 81,321 20% Martinique MTQ 385,000 37,295a 10% 72,539 19% Saint-Martin MAF 36,000 2,519a 7% 3,309 9%
aAsofOctober2nd,2016(stillongoing).
foundthatevenwhenepidemicswerenotobservedtotheirend, theresultsweresensible.
3. Results
3.1. CHIKVandZIKVoutbreaksinFrenchPolynesiaandFrench WestIndies
InFrenchPolynesia,ZIKVoutbreaksoccurredbetweenOctober, 2013andMarch,2014,followedoneyearlaterbyCHIKVoutbreaks (October,2014–March,2015). Overall,there wereabout30,000 observedclinicalcasesofZikaand 69,000ofChikungunya, cor-respondingtoanobservedcumulatedincidenceof11%and26% (Table2).Thedynamicsoftheoutbreaksweresimilarinmostof thesixstudiedareas,withasteepincreaseafterthefirstreported casesandameanoutbreakdurationof20weeks(Fig.1A).Except intheAustralislands,thereweremorereportsofCHIKVcasesthan ofZIKVcases(2.1–4.5timesmore).
In the French West Indies, CHIKV outbreaks occurred first (betweenDecember, 2013andApril, 2015)and ZIKVoutbreaks
startedinJanuary,2016andwerestillongoingbyOctober,2016. Overall,therewere159,000reportedclinicalcasesofChikungunya and70,000ofZika. Ifwe consideronlythefirstepidemicwave inSaint-Martin,theCHIKVepidemicslastedfrom25to59weeks, withanobservedcumulatedincidencebetween9%and20%.Asof October2nd,2016,i.e.36–39weeksafterthefirstreportedcases, ZIKVwasstillcirculatinginthethreeconsideredislandsatalow pace.
The weather conditions over the outbreak periods showed diversebehavioracrossislands(Fig.1BandC).Thetemperature inFrenchPolynesiaislandswasalmostconstantaround27–28◦C, exceptintheAustralIslandswherethetemperaturewascolder (around24–26◦C).IntheWestIndies,therangeofvariationwas larger and the average temperature was around 27◦C, slightly higherduringtheperiodsofZIKVcirculation.Rainfallshowedan oppositetrend,withmorevariationinthePacificislandsthanin theWestIndies.
3.2. Reconstructedtemperature-dependentserialinterval
Themeanserialintervalrangedfrom1.5to2.7weeksforCHIKV andfrom2.2to4.7weeksforZIKVaccordingtothechangein tem-perature over theperiods(Fig.2).Thechanges werelimitedin mostPolynesianislands,reflectingstabletemperatureovertime, exceptfor theAustralislands.Onthecontrary,theserial inter-val tended to be longer on average and more variable in the WestIndies.
3.3. Modelfitandparameterestimates
Thebaselinemodelcapturedtheessentialcharacteristicsofthe outbreaks,asshowninFig.3.Overall,thetimecourseoftheCHIKV outbreakswasfittedmoreaccuratelythanthatoftheZIKV out-breaks:somepredictedpeaksinincidencewereslightlyofftarget, forexampleinTahitiortheMarquesasIslands.Thefitwasalsovery goodforthethreeZIKVepidemicsstillunderwayintheFrench WestIndies.Thebaselinemodel,withanadditiveeffectofdisease andislandontransmissionperformedsimilarlytothefreemodel
J.Riouetal./Epidemics19(2017)43–52 47
Fig.2. Mean,2.5%and97.5%quantilesoftheserialintervaldurationforCHIKV(A) andZIKV(B)accordingtotemperature(in◦C).
accordingtotheLOOIC(difference=+5; standarderror=9), sug-gestingthatthisdescriptionoftransmissionwasindeedadequate. ThetwomodelsyieldedsimilarR0 values,despitedifferencesfor someZikaepidemicsandingenerallargerfluctuationspredicted bythefreemodel(seeSupplementaryInformation).
TheparametersofthebaselinemodelarereportedinTable3. Theisland-averagedreportingrate¯differedaccordingtothe dis-ease,estimatedat40%[29%;54%]forCHIKVand19%[12%;28%] forZIKV.ThetransmissibilityratiobetweenZIKVandCHIKVwas ˇD=1.04[95%CI:0.97;1.13],showingnosignificantdifferencein transmissibilitybetweenthediseases.Indeed,theisland-averaged reproductiveratiowas ¯R0=1.80[1.54;2.12]forCHIKVand1.88 [1.59;2.22]forZIKV.
Thevariance for therandom island effectsin reporting and in transmissionweredifferent from0,indicating heterogeneity betweenlocations(Fig.4).Theisland-specificreproductionratios