Modelling the continental-scale spread of Schmallenberg virus in Europe: Approaches and challenges

ContentslistsavailableatScienceDirect

Preventive

Veterinary

Medicine

jo u r n al h om ep age :w w w . e l s e v i e r . c o m / l o c a t e / p r e v e t m e d

Modelling

the

continental-scale

spread

of

Schmallenberg

virus

in

Europe:

Approaches

and

challenges

Simon

Gubbins

_,

_Jane

_Richardson

_,

_Matthew

_Baylis

_,

_Anthony

_J.

_Wilson

_,

José

Corti ˜

nas

Abrahantes

a_{ThePirbrightInstitute,AshRoad,Pirbright,SurreyGU240NF,UK} b_{EuropeanFoodSafetyAuthority,ViaCarloMagno1A,43126Parma,Italy}

c_{DepartmentofEpidemiologyandPopulationHealth,InstituteofInfectionandGlobalHealth,UniversityofLiverpool,LeahurstCampus,}

ChesterHighRoad,Neston,CheshireCH647TE,UK

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received10September2013 Receivedinrevisedform 12December2013 Accepted5February2014

Keywords: Epidemiology Modelling SBV

Bayesianmethods Under-ascertainment

a

b

s

t

r

a

c

t

FollowingitsemergenceinnorthernEuropein2011Schmallenbergvirus(SBV),a vector-bornediseasetransmittedbythebitesofCulicoidesmidges,hasspreadacrossmuchofthe continent.HerewedevelopsimplemodelstodescribethespreadofSBVatacontinental scaleand,morespecifically,withinandbetweenNUTS2regionsinEurope.Themodelforthe transmissionofSBVbetweenregionssuggeststhatvectordispersalistheprinciple mech-anismfortransmission,evenatthecontinentalscale.Thewithin-regionmodelindicates thatthereissubstantialheterogeneityamongstregionsintheforceofinfectionfor cat-tleandsheepfarms.Moreover,thereisconsiderableunder-ascertainmentofSBV-affected holdings,thoughthelevelofunder-ascertainmentvariesbetweenregions.Wecontrastthe relativelysimpleapproachadoptedinthisstudywiththemorecomplexcontinental-scale micro-simulationmodelswhichhavebeendevelopedforpandemicinfluenzaanddiscuss thestrengths,weaknessesanddatarequirementsofbothapproaches.

©2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCC BYlicense(http://creativecommons.org/licenses/by/3.0/).

1. Introduction

Recently,Europehasexperienced severalmajor out-breaksofemergingvector-bornediseasesoflivestock,allof whichhavebeentransmittedbyCulicoidesbitingmidges. In 2006, bluetongue virus (BTV) serotype 8 appeared near Maastricht in The Netherlands and subsequently spread to Austria, Belgium, Czech Republic, Denmark, France,Germany,Luxembourg,Sweden,Switzerlandand the United Kingdom (Saegerman et al., 2008; Wilson and Mellor, 2009). In 2007, BTV serotype 1 arrived in Spain and then spread northwards across the Iberian

∗ Correspondingauthor.Tel.:+441483232441;fax:+441483232448. E-mailaddress:simon.gubbins@pirbright.ac.uk(S.Gubbins).

PeninsulaandintoFrance(Saegermanetal.,2008;Wilson and Mellor,2009).Finally,Schmallenberg virus(SBV), a novelorthobunyavirus,wasfirstdetectedinGermanyand TheNetherlandsinthesummerof2011(Hoffmannetal., 2012; Muskens et al.,2012)and bythe springof 2013 hadbeenreportedacrossmuchofEurope(EuropeanFood SafetyAuthority,2013).

In this study,we explorethetransmission ofSBV at thecontinentalscaleusingtheavailabledemographicand epidemiologicaldata.Theepidemiologicaldatacomprise thecasesreportedtotheEuropeanFoodSafetyAuthority (EFSA)byEuropeanUnion(EU)memberstates(European FoodSafety Authority,2012,2013; Afonsoetal., 2014). Reflectingthelimiteddataavailableforanewly-emerging disease like SBV, we develop necessarily simple mod-elstoinvestigatepatternsofspreadwithinandbetween

http://dx.doi.org/10.1016/j.prevetmed.2014.02.004

regions in Europe and to assess the potential level of under-ascertainment of SBV-affected holdings. We con-trastourrelativelysimpleapproachwiththemorecomplex continental-scalemicro-simulationmodelsdevelopedfor pandemicinfluenza(Fergusonetal.,2006;Germannetal., 2006) and discuss the strengths, weaknesses and data requirementsofbothapproaches.

2. Materialsandmethods

Thecontinental-scalespreadofSBVwasdescribedat NUTS(NomenclatureofUnitsforTerritorialStatistics)level 2 (NUTS2) (European Union, 2011). This was the level at which caseswerereported toEFSAby eachcountry. Countriesincludedinthemodelwerethe28EUmember states,SwitzerlandandNorway.

2.1. Data

2.1.1. Demographicdata

DemographicdataforeachNUTS2region(numberof holdingswithcattle,numberofholdingswithsheep, num-berofcattle,numberofsheep)for2007wereextracted from Eurostat. Latitude and longitude for thecentroids ofeachregionwereusedtocalculatedistancesbetween regioncentroidsusingthegreatcirclemethod.Inthiscase, thedistance(dij)betweenthecentroidsofregionsiandjis givenby,

dij=2Rsin−1

⎛

⎝

i−j

2 +cosicosjsin 2

i−j

2

⎞

⎠

whereRistheradiusoftheearthandiandiarethe lati-tudeandlongitudeofthecentroidforregioni,respectively.

2.1.2. Epidemiologicaldata

Epidemiologicaldatawerebasedprimarilyonholdings reporting casesof arthrogryposis hydranencephaly syn-drome (AHS) in calves and lambs and consisted of the reportdateand thenumberof holdingsreportingcases (Afonsoetal.,2014).Thedata-setalsoincludedthereport date and number of holdings reporting cases in adult cattle, but thesewere more limited and wereonly for Germany,SwitzerlandandtheUnitedKingdom.Thecases (AHS and adult) were reportedto EFSA by the compe-tentauthorityinthecountry.Thedata-setanalysedinthis paperincludedallcasesreportedtoEFSAbefore21May 2013.

2.2. TransmissionbetweenNUTS2regions

2.2.1. Dataprocessing

Thetimeofinfectionforeach NUTS2regionwas cal-culatedasfollows.Thetimesoftheearliestreportforthe regionofanAHScaseinacalf,anAHScaseinalamband anadultcasewereextractedfromthedata-set.ForAHS cases,thetimeofinfectionwascomputedbysubtracting thegestationperiodforthespecies(280daysincattleor

147daysinsheep)fromthereportdate,thenaddingthe stageofgestationatwhichtheriskofanAHScasebegins (basedonAkabanevirus:64daysincattleor30daysin sheep;Parsonsonetal.,1981).Foradultcases,thetimeof infectionwasassumedtobe4daysbeforethereportdate (i.e.theincubationperiodforSBV;Hoffmannetal.,2012). Thetimeofinfectionfortheregionwastakentobethe ear-liestofthethreedates.Oncearegionwasaffected,itwas assumedtoremainsofortherestoftheyear.The analy-siswasrestrictedtoinfectionsestimatedtohaveoccurred during2011,sothatwecanassumea completelynaïve populationand,hence,donotneedtotakeintoaccount pre-existingimmunitytoSBV.

2.2.2. Modellingapproach

Transmissionbetweenregions wasmodelledusinga kernel-basedapproach,similartothatadoptedpreviously foravianinfluenza(Boenderetal.,2007;Truscottet al., 2007), foot-and-mouthdisease(Chis-Sterand Ferguson, 2007)andbluetongue(deKoeijeretal.,2011).Inthiscase, theforceofinfection,i(t),forregioniondaytisgivenby

i(t)=ˇ(t)

N_C(i)+N_S(i)

j=/i

K

(j)

S

Ij(t),

(1)

whereˇisthetransmissionparameter,

(t)=exp

b0+ 2

n=1

b1,nsin

+b2,ncos

(2)

istheseasonalvectoractivity(Sandersetal.,2011), nor-malised so the maximum value is one (estimates are presentedinTableS1),N(_Ci)andN_S(i)arethenumberof hold-ingswithcattleorsheepinregioni,respectively,andIj(t) isavariableindicatingwhetherregionjisuninfected(0)or infected(1)ondayt.

Weassumedadensity-dependentformulationforthe distancekernelK(dij)(wheredijisthedistancebetweenthe centroidsofregionsiandj),thoughanalternative, density-independentformulationwasalsoexplored(seeelectronic Supplementarymaterial).Threedifferentfunctionalforms forK(d)wereconsidered,reflectingdifferentassumptions abouthowrapidlythekerneldecayswithdistance.These were,

Fat-tailed kernel: K(d)=

d0

,

Gaussian kernel: K(d)=exp

Exponential kernel: K(d)=exp (−˛d). (3)

ParameterswereestimatedinaBayesianframework. Thelikelihoodforthedataisgivenby,

LB=

j∈U

exp

−

t

j(t) ×

j∈I

⎧

⎪

⎨

⎪

⎩

⎛

⎜

⎝

t_inf(j)−1

t=t0

j(t)

⎞

⎟

⎠

−j

tinf(j)

⎫

⎪

⎬

⎪

⎭

whereUisthesetofregionswhichdidnotbecomeinfected, Iisthesetofregionswhichdidbecomeinfected,t0isthe startoftheoutbreakandtinfisthetimeatwhichtheregion becameinfected(cf.Boenderetal.,2007).Thefirsttermis thecontributiontothelikelihoodofregionswhichdidnot becomeinfected,whilethesecondtermisthe contribu-tiontothelikelihoodofregionswhichdidbecomeinfected. Non-informative(andindependent)priors(diffuse expo-nential)wereassumedforallmodelparameters.

A Markovchain-Monte Carlo(MCMC) approach was usedtogenerate samplesfrom thejointposterior den-sityfortheparametersinthemodel(seeSection2.4for details).Twochainsof75,000iterations wererun,with thefirst25,000iterationsdiscardedtoallowforburn-in ofthechain.Thechainswerethenthinned(takingevery tenthsample)toreduceautocorrelationamongstthe sam-ples.Thefitofthemodelsusingthedifferentkernelswere comparedusingthedevianceinformationcriterion(DIC) (Spiegelhalteretal.,2002).

Posteriorpredictivecheckingwascarriedouttoassess model adequacy (Gelman et al., 2004). More precisely, theposteriorpredictivedistributionwasusedtogenerate replicateddatabysamplingparametersetsfromthejoint posteriordistributionandusingthesampledparameters tosimulatedata-setsusingthemodel.Thesewere com-paredtotheobserveddatausingthreemeasures:(i)the numberofregionswhichhadtheirfirstholdingaffectedby SBVeachweek;(ii)thetimeatwhichtheregionbecame infected;and(iii)theproportionofreplicatesinwhicheach regionbecame infected.If theobserved datageneratea moreextremevalueofthemeasuresthanthereplicatedata (asjudgedbytheproportionofreplicateswhichgenerate avalueofthemeasurelessthantheobserveddata;thisis equivalenttoaclassical(i.e.non-Bayesian)P-value),this providesanindicationthatthemodeldoesnotadequately capturethedata.

2.3. IncidencewithinNUTS2regions

2.3.1. Dataprocessing

ForeachNUTS2regionweusedthedata-settocompute thetotal numberofcattleand sheepholdings reporting cases(AHScasesincalvesorlambsorcasesinadultcattle) andthetime-periodoverwhichthereportedcasesbecame infected.Thetimesofinfectionwerecalculatedinthesame wayasdescribedinSection2.2.1,exceptthatthiswasdone forallreportedcasestodeterminethefirstandlastdays onwhichholdingsreportingcasesbecameinfectedineach region.Again,theanalysiswasrestrictedtoinfections esti-matedtohaveoccurredduring2011,sothatwecanassume

acompletelynaïvepopulationand,hence,donotneedto takeintoaccountpre-existingimmunitytoSBV.

2.3.2. Modellingtheincidenceofreportedcases

ThenumberofholdingswithinaregionreportingAHS cases wasassumed todepend ontheforceof infection (whichdependsonbothspeciesandregion),thenumber ofholdingsintheregionandseasonalvectoractivity.More precisely,thenumberofcattleandsheepholdingswithina regionreportingAHScasesweredescribedbyPoisson dis-tributionswithmean(_ir)forspeciesi(cattle(C)orsheep (S))inregionrgivenby,

_i(r)=_i(r)N_i(r)

t

(t), (5)

where,(_ir)istheforceofinfectionforspeciesiinregionr,

N_i(r)isthenumberofholdingskeepingspeciesiinregionr,

(t)istheseasonalvectoractivity(givenbyEq.(2))andthe summationisoverthetimeperiodduringwhichholdings werereported.Toallowforregionalvariationtheforceof infectionforeachregionwasassumedtobedrawnfroma higher-ordergammadistribution(i.e.thereishierarchical structureintheparameters),sothat,

(_ir)∼Gamma (ai,bi), (6)

foreachspeciesi.

ParameterswereestimatedinaBayesianframework. Thelikelihoodforthedatais,

LW=

R(_ir)|(_ir)

, (7)

wherefistheprobabilitydensityfunctionforthePoisson distributionandR(_ir) isthenumberofholdingsreporting AHScasesinspeciesiinregionr.Non-informative(and independent) priors(diffuseexponential)wereassumed forthehierarchicalparameters(i.e.theaisandbisinEq.

(6)).

AnMCMCapproachwasusedtogeneratesamplesfrom thejointposteriordensityfortheparametersinthemodel (seeSection2.4fordetails).Twochainsof2000,000 itera-tionswererun,withthefirst1000,000iterationsdiscarded toallowforburn-inof thechain. Thechainswerethen thinned(takingevery200thsample)toreduce autocorre-lationamongstthesamples.Modeladequacywasassessed by determining whethertheobserved number of hold-ingsreportingAHScasesliewithinthe2.5thand97.5th percentilesoftheposteriorpredictivedistributionforthe numberofreportedholdingsineachregion.

Supplementarymaterialfordetails).Essentially,theuseof twoindependentmeasuresofdiseaseoccurrenceallowsus toinferthelevelofunder-ascertainmentofaffected hold-ings.ThemethodswereappliedtodatafromBelgiumand TheNetherlands,forwhichwehavedataonreportedAHS casesandfromserologicalsurveys(Mérocetal.,2013a,b; Veldhuisetal.,2013).

2.4. MCMCmethods

A Markov chain-MonteCarlo (MCMC) approach was usedtogeneratesamplesfromthejointposteriordensity fortheparametersforeachofthemodelsinSections2.2 and2.3.Morespecifically,weusedanadaptive Metropo-lis algorithm (Haario et al.,2001), modified sothat the scalingparameterwastunedduringburn-intoensurean acceptancerateofbetween20%and40%formoreefficient samplingofthetargetdistribution(AndrieuandThoms, 2008).Convergenceof theMCMC schemewasassessed visually and by using Gelman and Rubin’s convergence diagnostic implemented in thecoda package (Plummer etal.,2006)inR(RCoreTeam,2013).

3. Results

3.1. TransmissionbetweenNUTS2regions

Summary statistics for the marginal posterior distri-butionsoftheparametersinthemodelfortransmission betweenNUTS2regionsarepresentedinTable1.Thebest fit wasobtainedusinga fat-tailedkernel (DIC=1175.2). Thefitusingthiskernelwassignificantlybetterthanfor eithertheGaussiankernel(DIC=1260.5)ortheexponential kernel (DIC=1218.0) (Table 1). Moreover, the density-dependentkernelsprovidedasignificantlybetterfitthan any of the density-independent kernels (see electronic Supplementarymaterial).

Themodeladequatelycapturesthetimecourseofnewly reportingregions,withtheobservedincidencelyingwithin the 95% range of the posterior predictive distribution (Fig.1;seealsoFig.S1).Themodelalsocapturesthe geo-graphicspreadofSBV,withthoseregionsreportingcases havingahighpredictedprobabilityofinfection,exceptfor theUK(Fig.1).Therewere,however,someregionswhich didnotreportcases,butforwhichthepredictedprobability ofinfectionwasatasimilarleveltothosewhichdidreport cases(Fig.1).Possiblereasonsfortheseobservationsare exploredinthediscussion.

Foralmostallregionsreportingcases,themodel pre-dictionsforthetimeofinfectionwereconsistentwiththat estimatedfortheregion(Fig.S2).Inaddition,themodel predictedthehighest probabilitiesofinfectionfor those regionswhichreportedcases,whilethepredicted proba-bilityofinfectionforthoseregionswhichdidnotreport casesweretypicallylow(Fig.S3;cf.Fig.1).

3.2. IncidencewithinNUTS2regions

Forallregionstheobservednumberofholdings repor-ting AHS cases lies within the 95% prediction interval (Fig.2),indicatingagoodagreementbetweenmodeland

data.Themodelpredictedthattheforceofinfectionwas markedly higher (>10 times) for sheep than for cattle (Fig. 3a), and that there was considerable variation in theforceofinfectionamongstregions(Fig.S4).However, estimatesof theforceof infectionare confoundedwith under-ascertainmentofcases.Consequently,speciesand regionaldifferencesarelikelytoreflectbothdifferencesin epidemiologyandincaseascertainment.

For Belgium and The Netherlands it waspossible to adjusttheestimatesfortheforceofinfectiontoallowfor under-ascertainment.Inthiscase,therewerestill differ-encesintheforceofinfectionbetweencattleandsheep holdings,thoughthedifferencewasmuchsmaller(Fig.3c; see also Fig. S5). There were also differences amongst regionsintheforceofinfectionforbothspecies(Fig.S5). Under-ascertainmentofSBV-affectedholdingswasmuch higherincattlecomparedwithsheepfarms.Weestimated that0.5%of affectedcattleholdingsreportedAHS cases (Fig.3e),whereas2%ofaffectedsheepholdingsreported AHScases(Fig.3f).However,therewassubstantial vari-ationamongstregionsinunder-ascertainment,especially forsheepholdings(Fig.S5).

4. Discussion

Therearetwomainissueswhenattemptingto inves-tigate the continental-scale spread of SBV. First, the epidemiologicaldatadonotprovidedirectinformationon whenregions(orholdings)becomeinfected,ratherthey providethedatesonwhichholdingsineachNUTS2region reportAHS cases.Second,there is likely tobe substan-tialunder-ascertainmentof cases,becauseclinicalsigns arerelativelymildinadultcattleandinapparentinadult sheep(Gariglianyetal.,2012;Doceuletal.,2013),because notallaffectedholdingswillexperienceAHScases(e.g.if theyarenotinfectedduringtheriskperiod)andbecause SBVisnotanotifiablediseaseinmanycountries.Indeed, under-ascertainmentmayaccountfortherebeinga num-berofregionswhichdidnotreportdisease,butforwhich thepredictedprobabilityofbecominginfectedwassimilar toregionswhichdidreport(Fig.1andFig.S3).Moreover, itcouldalsoaccountforthepossibleunder-predictionof newly-reportingregions duringthelaterweeksof 2011 (Fig.1andFig.S1).

Fromthereportingdatesitispossibletoinferanearliest datewhenSBVmusthavebeencirculatingintheregionby back-calculatingtothestageofgestationatwhichafoetus isatriskofinfection.AlthoughthisisnotknownforSBV,it canbeassumedtobesimilartoAkabanevirus(Parsonson etal., 1981).Thispartly mitigatestheimpactof under-ascertainmentwhen modellingspread betweenregions, butcannotaccountfornon-reportingfarmsinfectedbefore thoseholdings whichdo reportdisease.However, addi-tionaldata,suchasfromserologicalsurveys,areessentialto accountforunder-ascertainmentwhenmodellingspread withinaregion.

Fig.1. ObservedandpredictedspreadofSchmallenbergvirus(SBV)inEuropeduring2011.Resultsareshownforamodelassumingdensity-dependent (a)fat-tailed,(b)Gaussianor(c)exponentialdistancekernels.Theleft-handfiguresshowthenumberofNUTS2regionswiththeirfirstcaseofSBVeach week.Barsindicatetheobservednumberofregions,whilecirclesanderrorbarsindicatetheposteriormedianand95%crediblelimitsfortheposterior predictivedistribution.Theright-handfiguresshowthegeographicalspreadofSBV.CirclesmarkthecentroidsoftheNUTS2regionswiththeedgesofthe circlesindicatingtheobservedstatus(red:atleastonecattleorsheepholdingreportingAHScases;blue:nocattleorsheepholdingsreportingAHScases) andthecentreofthecircleindicatingthepredictedprobabilityforthatregionbecominginfected(seescalebar).(Forinterpretationofthereferencesto colorinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

Table1

Posteriormean,medianand95%credibleintervalsforparametersinthemodelforthetransmissionofSBVbetweenNUTS2regionsassuminga density-dependentkernel.

Parameter Mean Median 95%Crediblelimit DIC

Lower Upper

Fat-tailedkernel

Transmissionparameter(ˇ) 1.1×10−8 _9.5×10−9 _3.7×10−9 _2.4×10−8 _1175.2

Kernelparameter(˛) 4.0 4.0 3.6 4.5

Kernelparameter(d0) 48.7 48.2 35.4 65.5

Gaussiankernel

Transmissionparameter(ˇ) 1.5×10−10 _1.4×10−10 _9.0×10−11 _2.3×10−10 _1260.5 Kernelparameter(˛) 4.2×10−3 _4.2×10−3 _3.6×10−3 _4.9×10−3

Exponentialkernel

Transmissionparameter(ˇ) 2.5×10−9 _2.3×10−9 _1.1×10−9 _4.8×10−9 _1218.0 Kernelparameter(˛) 1.8×10−2 _1.8×10−2 _1.4×10−2 _2.2×10−2

importanttransmission route,even atcontinental scale. Alternative routes of transmission may, of course, still playarole,butthosewhichresultindensity-independent transmission,suchasviaequipment,peopleand move-mentsofanimalsandanimalproducts(includingsemen), arelesslikelytobethemainmechanismsofspread.This conclusionisinaccordancewithamoredetailedanalysis ofthespreadofSBVbetweenfarms,whichindicated vec-tordispersalismoreimportantthananimalmovements (Gubbinsetal.,2014).

Intermsoftheformofthedensity-dependentkernel, ourresultssuggestthatafat-tailedkernelbestdescribes

thedata (Table 1).This is oftenthe case in modelsfor thespreadofinfectiousdiseases,suchasavianinfluenza (Boenderetal.,2007;Truscottetal.,2007),foot-and-mouth disease (Chis-Ster and Ferguson, 2007) and bluetongue (deKoeijeretal.,2011;cf.Szmaragdetal.,2009). How-ever,thedataweremodelledatthelevelofNUTS2regions ratherthanatthelevelofholdings,whichwillclearlyhave implicationsforanydescriptionoftransmissionbetween regions.Inparticular,parameterestimatesmaybequite differentfromthoseobtainedifthemodelwereapplied attheholdinglevel(cf.estimatesobtainedbydeKoeijer et al. (2011), where a similarapproach wasapplied to

holding-leveldata for BTVin Europe,a virusfor which mechanismsfortransmissionbetweenfarmsarelikelyto besimilartoSBV).Inaddition,thebetween-regionmodel assumes that the parameters are the same throughout Europe.However,itis likely that therewillbe regional heterogeneitiesintransmission.Forexample,transmission betweenregionswithinmainlandEurope(i.e.overland) is likely tobedifferent than betweenmainland Europe andtheUK(i.e.acrossthesea),giventheabilityof Culi-coidesbitingmidgestodisperseoverlongdistancesover sea(Glosteretal.,2007;Burginetal.,2013).This obser-vationperhapsaccountsfortheunder-estimationofthe probabilityofinfectionforregionsintheUK(Fig.1).

The force of infection for holdings within a region wasshowntovarysubstantiallyamongstregions(Fig3a andFig.S4).Part ofthis variabilitycanbeexplainedby differences amongst regions in under-ascertainment of cases,somethingwhichcannotbeadjustedforwhenonly dataonreportedcasesareavailable.However,asecond analysis focusing onBelgium and The Netherlands (for whichserologicaldataarealsoavailable)alsoidentified substantialdifferencesintheforceofinfectionamongst regions (Fig. 3c and Fig. S5), suggesting that there are indeedregionaldifferences.Thesewillreflectarangeof factors,includinghusbandrypractices,stockingdensities, land-use,localvectorpopulationsandmeteorological con-ditions.

Fromthe analysisof data onaffected holdings from BelgiumandTheNetherlands,weestimatedthatthemean proportionofSBV-affectedholdingswhichexperienceand reportAHScaseswithinaregionwas0.5%forcattleand 2%forsheep(Fig.3).Twofactorscouldhelpexplainthis differencebetweenspecies.First,calvingtendstooccurall yearround(atleastwhenaggregatedataregionallevel) whilelambingtendstobemuchmorestronglyseasonal. Second,calvesinfectedinuterocanclearSBVinfection(and somaynotbeconfirmedasSBVcases),whilelambs can-not(DeReggeetal.,2013).However,extrapolatingthese estimates toother regions willbe complicated because under-ascertainmentofAHScasesinaregionwilldepend ontheseasonalityoflambingandcalvingandthetimeof introductionofSBV,aswellasotherfactorssuchasfarmer willingnesstoreport.

Themodellingapproachadoptedinthepresentstudy wasnecessarilysimple.Inparticular,thedatawere mod-elled at the level of NUTS2 regions rather than at the levelofholdings,areflectionoftheavailabledemographic andepidemiological data.Ineffect,this meanswehave adoptedametapopulationapproachinwhicheachregion istreatedasapatch(orsubpopulation).Inprinciple,amore complexmicro-simulationmodelcouldbedeveloped to describethespreadofSBV,oranothervector-borne dis-ease,inEuropeinthespiritofthemicro-simulationmodels developedforthespreadofpandemicinfluenza(Ferguson etal.,2006;Germannetal.,2006).Preciselywhetherornot suchanenterpriseisworthwhiledependsverymuchon thequestionstobeaddressedbythemodel.Forexample, a micro-simulationapproach would facilitatea detailed explorationoftransmissionscenarios andtheimpactof controlmeasures.Itcouldalsobeusedtoinvestigate sce-nariosforoverwinteringofSBV,whichisproblematicina

modelthatisnotappliedatthelevelofindividualholdings (EuropeanFoodSafetyAuthority,2012).

Model frameworks have already beendeveloped for bluetongue(Szmaragdetal.,2009;Græsbølletal.,2012; Turner et al., 2012), which could be scaled up from a nationaltocontinentallevel.However,thedata require-mentsarequiteonerous.Ataminimum,therequiredinput datawouldbe:thelocationofholdingskeepingcattleand sheep;thenumbersofanimalsofeachspecieskeptatthe location;andthefrequencyofanimalmovementswithin and betweenregions permonth (these couldbe aggre-gated,for example,toNUTS2level).For a virussuchas SBV,wheretheimpactisprimarilyassociatedwith repro-ductivelosses,dataonseasonalityofcalvingandlambing wouldalsoberequired.Itisalsousefultobeableto dis-tinguish between-region movementsfor thepurposeof slaughterfrommovementsforbreeding,astheformerare lesslikelytotransmitinfection.Furthermore,theoutputs fromthepandemicinfluenzamodelpresentedinFerguson etal.(2006)required20,000CPUhourstogenerate,while thosepresentedinGermannetal.(2006)required70CPU years.Finally,itisdifficulttovalidateeveryaspectofthe model,especiallyifdataaresparse.

Conflictofintereststatement

Nonetodeclare.

Acknowledgements

Thisworkwascarriedout undertheauspicesofthe European Food Safety Authority (EFSA) Schmallenberg virusepidemiologyworkinggroup.Theauthorswouldlike toacknowledgethereportingofficersthathave submit-ted data onSBV occurrence in European countries, the EFSA Animal Health and Welfare Network on Schmal-lenberg virus and the experts and EFSA scientific staff on the ad hoc working group on Schmallenberg virus. SG and AJW acknowledge funding by the Biotechnol-ogy and Biological Sciences Research Council (BBSRC) [grant codes: BBS/E/I/00001409 and BBS/E/I/00001717]. MB acknowledges funding from the Leverhulme Trust [ResearchLeadershipAwardF/0025/AC].

AppendixA. Supplementarydata

Supplementarydataassociatedwiththisarticlecanbe found,intheonlineversion,athttp://dx.doi.org/10.1016/ j.prevetmed.2014.02.004.

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