Population effect of influenza vaccination under co-circulation of non-vaccine variants and the case for a bivalent A/H3N2 vaccine component

(1)

ContentslistsavailableatScienceDirect

Epidemics

jo u rn 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 / e p i d e m i c s

Population effect of inﬂuenza vaccination under co-circulation of non-vaccine variants and the case for a bivalent A/H3N2 vaccine component

Colin J. Worby

^a^,∗

, Jacco Wallinga

^b^,^c

, Marc Lipsitch

^a^,^d

, Edward Goldstein

^a

aDepartmentofEpidemiology,CenterforCommunicableDiseaseDynamics,HarvardTHChanSchoolofPublicHealth,Boston,MA02115,USA

bNationalInstituteofPublicHealthandtheEnvironment(RIVM),AntonievanLeeuwenhoeklaan9,3721MABilthoven,TheNetherlands

cLeidenUniversityMedicalCenter,DepartmentofMedicalStatisticsandBioinformatics,2300RCLeiden,TheNetherlands

dDepartmentofImmunologyandInfectiousDisease,HarvardTHChanSchoolofPublicHealth,Boston,MA02115,USA

a r t i c l e i n f o

Articlehistory:

Received19May2016

Receivedinrevisedform15February2017 Accepted17February2017

Availableonline21February2017

Keywords:

Inﬂuenza

Co-circulatingstrains Monovalentvaccine Bivalentvaccine Cross-immunity

a b s t r a c t

Somepastepidemicsofdifferentinfluenzasubtypes(particularlyA/H3N2)intheUSsawco-circulationof vaccine-typeandvariantstrains.Thereisevidencethatnaturalinfectionwithoneinfluenzasubtypeoffers short-termprotectionagainstinfectionwithanotherinfluenzasubtype(henceforth,cross-immunity).

Thissuggeststhatsuchcross-immunityforstrainswithinasubtypeisexpectedtobestrong.Therefore, whilevaccinationeffectiveagainstonestrainmayreducetransmissionofthatstrain,thismayalsolead toareductionofthevaccine-typestrain’sabilitytosuppressspreadofavariantstrain.Itremainsunclear whatthejointeffectofvaccinationandcross-immunityisforco-circulatinginﬂuenzastrainswithina subtype,andwhatisthepotentialbeneﬁtofabivalentvaccinethatprotectsagainstbothstrains.

Wesimulatedco-circulationofvaccine-typeandvariantstrainsunderavarietyofscenarios.Ineach scenario,weconsideredthecasewhenthevaccineefficacyagainstthevariantstrainislowerthanthe efficacyagainstthevaccine-typestrain(monovalentvaccine),aswellthecasewhenvaccineisequally efficaciousagainstbothstrains(bivalentvaccine).

Administrationofabivalentvaccineresultsinasignificantreductionintheoverallincidenceofinfec- tioncomparedtoadministrationofamonovalentvaccine,evenwithlowercoveragebythebivalent vaccine.Additionally,wefoundthatwithgreatercross-immunity,increasingcoveragelevelsforthe monovalentvaccinebecomeslessbeneficial,whileintroducingthebivalentvaccinebecomesmoreben- eficial.

Ourworkexhibitsthelimitationsofinfluenzavaccinesthathavelowefficacyagainstnon-vaccine strains,anddemonstratesthebenefitsofvaccinesthatoffergoodprotectionagainstmultipleinfluenza strains.Theresultselucidatetheneedforguardingagainstthepotentialco-circulationofnon-vaccine strainsforaninfluenzasubtype,atleastduringselectseasons,possiblythroughinclusionofmultiple strainswithinasubtype(particularlyA/H3N2)inavaccine.

1. Introduction

Therecurrenceofseasonalinfluenzaepidemicsisdrivenbya numberoffactorsincludingwaningofimmunity,weather-related changesintransmissibilityofinfluenza(Shamanetal.,2010),and antigenicchangesintheinfluenzavirus(Smithetal.,2004).Anti- genicchangecreatesaneedforanupdateofinfluenzavaccines foreachhemisphere everyyeartoeveryseveralyears (Ampofo

∗ Correspondingauthor.Presentaddress:DepartmentofEcology&Evolutionary Biology,PrincetonUniversity,Princeton,NJ08544,USA.

E-mailaddress:cworby@princeton.edu(C.J.Worby).

etal., 2015).Despite those updates,there is significantcircula- tioninsomeyearsofinfluenzastrainsforwhichthevaccineoffers littleprotection.Themostrecentinstanceofsuchcirculationin theUSand elsewheretookplaceduringthe2014–15 influenza season.Duringthatseason,vaccine-typeA/H3N2viruses(thatis, A/Texas/50/2012-likeviruses)wereamajorityofA/H3N2isolated intheUSearlyintheseason(uptoweek47)(USCDC,2014–2015a);

the vaccine-type strain had declined to about 30% of A/H3N2 specimenscollectedbyweek50(USCDC,2014–2015b),withthe remaindereithershowingreducedtiterstovaccine-derivedantis- eraorbelongingtoageneticlineageshowingsuchreducedtiters.

Thedeclineintheproportionvaccine-typeamongA/H3N2 con- tinuedthroughtherestoftheseason(USCDC,2014–2015c).This

http://dx.doi.org/10.1016/j.epidem.2017.02.008

0/).

(2)

predominanceofthenovelA/H3N2strainalsocontributedtothe verylowvaccineeffectiveness(asmeasuredbythereductionin theriskofclinicaldisease)againstinﬂuenzaA/H3N2duringthe 2014–2015season(USCDC,2005–2015).Theoveralleffectiveness ofvaccinationagainstinﬂuenzaA/H3N2during2014–5intheUS wasunusuallylow at 13%;this overalllow effectiveness wasa combinationof43%effectivenessagainstvaccine-likevirusand9%

effectivenessagainst“vaccine-low”viruses(USInﬂuenzaVaccine EffectivenessNetwork,2014–2015).

Competitionbetweenco-circulatingstrainswithinaninfluenza subtypewas observed during previousseasons as well,with a variety of outcomes. During the 2004–05 season, vaccine-type virusesinitially dominated the 2004–05 A/H3N2 incidence (US CDC,2005a),buttheyweresubsequentlyreplacedbyanon-vaccine strain(USCDC,2005b).Vaccineeffectivenessduringthatseason wasverylow(USCDC,2005–2015).WhentheFujianA/H3N2strain appearedintheUSduringthe2003–2004season,thatstrainhad dominatedthecirculationofinfluenza,andtheproportionofthe vaccinestraindeclinedduringthecourseofthatseason(compare USCDC,2003toUSCDC,2004atoUSCDC,2004b),thoughthe decline in theproportionof thevaccine-type strain amongthe A/H3N2specimens(from25%(USCDC,2003)to11.5%(USCDC, 2004b)),wasnotasdrasticasforthe2004–05season.Moreover, whilevaccineeffectivenessduringthe2003–04seasonwasrela- tivelylow,itwassomewhathigherthanduring2004–05season(US CDC,2004c).Duringthe2007–2008A/H3N2season,anantigenic variantofthevaccinestraincirculatedathigherlevelscompared tothevaccine-typestrain(USCDC,2008a).However,therelative shareofthosetwostrainsvariedlittlethroughthecourseofthe season(USCDC,2008b).Duringthe2011–2012influenzaBseason, overhalfthedetectedBspecimenswerenotofthevaccinetype (USCDC,2012a).Theproportionofvaccineandnon-vaccine-type virusesdidnotseemtochangethroughthecourseofthatseason (USCDC,2012b).

Whenanon-vaccinestrainco-circulatesandvaccineeffective- nessagainstitislow(asin2004–5and2014–5),itiscommonly thoughtthatvaccinationreducestheincidenceofthevaccine-type strain and haslimited impacton mitigating theincidence of a non-vaccinestrain.Anadditionaleffectofvaccinationthatisoften neglectedisapotentialincreaseintheincidenceofanon-vaccine strainthroughreductionoftheincidenceofthevaccine-typestrain, cuttingdownonthemitigatingeffectoftheincidenceofvaccine- type strain onthe incidenceof the non-vaccinestrain through cross-immunity.Thiscross-immunity, which translatesintothe reductionintheriskofinfectionwithoneinﬂuenzastrainfora periodoftimefollowinganinfectionwithanotherinﬂuenzastrain, isbelievedtobeconferredbyavarietyofimmunologicalmech- anisms,and itsconsequences aredocumented intheliterature.

Sonoguchiet al. (1985)studied theimpactof thesame-season circulationofA/H3N2andA/H1N1inﬂuenzainJapaneseschools, concludingthatinfectionwithA/H3N2wasnegativelyassociated with subsequent risk of infection with A/H1N1. Cowling et al.

(2010)havefoundthatthoseinfectedwithseasonalinfluenzaA duringthe2008–2009seasoninHongKong hadalowerriskof laboratory-confirmedpandemicA/H1N1infection.Theresultsin Cowlingetal.(2010)werefurtherextendedtoshowshort-term cross-protectionagainstinfectionbyunrelatedviruses(Cowling andNishiura,2012).Fergusonetal.(2003)andTriaetal.(2005) concludedthatstrong,transient,nonspecificimmunityeffective against all influenza strains was needed in the framework of theirmodelstoproducerealisticpatternsofsequencediversityin simulationsofinfluenzaAandBevolution.Epidemiologicalconse- quencesofcross-immunitybetweendifferentinfluenzasubtypes weredemonstratedinGoldsteinetal.(2011).Thatpaperhasshown thatthemagnitudeofearlypopulationincidenceofsomeinfluenza subtypes is negatively correlated with thecumulative seasonal

incidenceofotherinﬂuenzasubtypes.Whileweareunawareof anystudiesdirectlyaddressingcross-immunitywithina season and within a subtype,it is expected to be even stronger than cross-immunityfordifferentinﬂuenzasubtypes,renderinginfec- tiontwiceinthesameseasonwiththesamesubtypequiteunlikely.

Thoughuntested,thishypothesisseemsplausibleinlightofthe strongevidenceforcross-immunitybetweeninﬂuenzasubtypes.

Given cross-immunity withina subtype,the impact of vac- cinationwhen there is co-circulationof a non-vaccine strainis uncertain,andthedependenceofthatimpactonthestrengthof cross-immunityisunclear.Inthispaper,weexploretheseissues using simulationsof influenza transmissionin an age-stratified populationunderavarietyofscenariosfortransmissionparam- etersandvaccinationcoveragelevels.Whilesomeofthechoices wemakearemotivatedbydatafromrecentepidemicsintheUS, theaimofthisworkisnottocalibratetransmissionmodelstothe actualepidemicdatabutrathertoestablishgeneralprinciplesofthe interactionofvaccinationandcross-immunityforco-circulating influenzastrains.Theultimategoalistheelucidationoftheneedto guardagainsttheco-circulationofnon-vaccinestrains(particularly forinfluenzaA/H3N2)forwhichvaccineefficacyislow,possiblyby employingbivalentvaccinesforcertaininfluenzatypes/subtypes.

Infact,aprecedentforthisexists,ascontinuingco-circulationof theVictoria(vaccine-type)andtheYamagatainﬂuenzaBlineages ledtotheintroductionofaquadrivalentinﬂuenzavaccinecontain- ingbothstrainsstartingwiththe2013–2014season,thoughno bivalentA/H3N2vaccinecomponenthaseverbeenadoptedbythe WHO.

2. Materialsandmethods

2.1. Outline

Wesimulateinfluenzaoutbreaksusingatransmissionmodelin anage-stratifiedpopulationfortwoco-circulatingstrains(which maybeintroducedtothepopulationatdifferenttimes).Thisismost relevanttoascenariowhenoneinfluenzasubtypedominatesthe influenzaseason,andthosetwostrainsaredeemedtobestrains withinthatsubtype.Wecomparetheperformanceofseveraldif- ferent policiesdefined bythevaccinecoverageand thevalency ofvaccineused–thesearethetwovariablesthatareunderthe controlofa policymaker(Table1).Amonovalent vaccinehasa lowerefficacyagainstoneofthetwostrainsthantheother,while abivalentvaccinehasequalefficacyagainstbothstrains.Theout- comeconsideredinthepolicycomparisoniscumulativeincidence ofinfectionoverthecourseofaseason.Thepolicycomparisonis madeacrossasetofscenarios–eachscenariodefinedbyonecom- binationofvaluesfortheparametersnotunderapolicymaker’s control:thedegreeofcross-immunityconferredbynaturalinfec- tionwithonestrainagainstsubsequentinfectionwithanother,and severalparametersthataffectthetransmissiondynamicsofthetwo strains(Table2).Eachpolicyiscomparedagainstabaselinepolicy ofusingthemonovalentvaccinewith40%coverageforchildren, 30%foradults,similartorecentUSdata.Weexaminethescenar- ioswhenthemonovalentvaccineadministrationvaries(iseither reducedorincreasedrelativetothebaselinelevels,seeTable1)and comparethemtothebaseline.Additionally,weconsiderthecase whenabivalentvaccine(withequalefficacyagainstbothstrains) isused,thesamerangeofcoveragelevelsasforthemonovalent vaccine(Table1),againcomparingoutbreaksizewiththebaseline coverageofmonovalentvaccine.Wereportthecomparisonssep- aratelyforthreedifferentvaluesofthecross-immunityparameter

,thedegreeofcross-protectionofferedbynaturalinfection.

Wedeﬁnethefollowingparameters–vaccinecoveragelevels, valencyofvaccineandcrossimmunity–tobe‘primaryparameters’

(3)

Table1

Coveragelevelsconsideredforboththemonovalentandthebivalentvaccinesinoursimulations.

Coveragescenario Monovalentvaccinecoverage Bivalentvaccinecoverage

Uniformcoverage 100%children/100%adults 100%children/100%adults

50%increase 60%children/45%adults 60%children/45%adults

25%increase 50%children/37.5%adults 50%children/37.5%adults

10%increase 44%children/33%adults 44%children/33%adults

Baselinelevel 40%children/30%adults(Baselinecase) 40%children/30%adults

10%reduction 36%children/27%adults 36%children/27%adults

25%reduction 30%children/22.5%adults 30%children/22.5%adults

40%reduction 24%children/18%adults 24%children/18%adults

Table2

Parametersinthetransmissionprocess.

Parameter Meaning Value/source

Cross-immunity:reductioninthesusceptibilitytoonestrainfollowing naturalinfectionwithanotherstrain

90%;70%;50%

V Vaccinevalency “Bivalent”;“Monovalent”

L Vaccinecoveragelevelsinthe5agegroups 40%children,30%adults(baselinescenario);(37%,27%);(30%,22.7%);

(24%,18%)(alternative) ni Populationsize,agegroupi.Agegroupsare(0–4,5–17,18–49,50–64,

65+)

USCDCWonder

cij Contactratebetweenagegroupsiandj Mossongetal.(2008)

s^k_i Susceptibilitytostrainkinagegroupi Drawnuniformlybetween[0.75,1]foragegroups1–3;0.65forage group4;0.4foragegroup5

w() Serialintervaldistribution Cauchemezetal.(2009)

Scalingparameterfortransmission(Eq.(1)) SeedescriptionfollowingEq.(1) D Delay(indays)betweentheintroductionoftheﬁrstinfected

individualsforstrain2vs.1

Drawnuniformlybetween[−35,35]

E Vaccineefﬁcaciesagainstthetwostrainsforthemonovalentandthe bivalentvaccines

Vaccine-typestrain:40%/non-elderly,30%/elderly.Non-vaccinestrain:

40%/non-elderly,30%/elderly(bivalentvaccine);Drawnuniformly between[0,20%]/non-elderly,[0,15%]/elderly(monovalentvaccine)

(T₁), and all remaining parameters governing transmission dynamics‘secondaryparameters’(T2).Inordertoperformthecom- parisonsdescribedinTable1,werepeatedlydrawplausiblevalues ofthesecondaryparameters,T₂,basedonestimatesformthelit- erature(Table2,rows4–10).Foreachsampledsetofsecondary parameters, we calculate thecumulative incidence of infection overthecourseofaseasonforeachofthesixteenvaccinepoli- ciesdescribedinTable1,andforthreelevelsofcross-immunity, givingatotalof48setsofthevaluesoftheprimaryparameters.We notethatwithadeterministicmodelasusedhere,achoiceofthe primaryandsecondaryparametersT₁ andT₂ completelydeﬁnes anepidemicinthecommunity.Foreachlevelofcrossimmunity, theoutcomeundereachofﬁfteenalternativevaccinationpolicies (describedinTable1)iscomparedtotheoutcomewithbaseline coverageofmonovalentvaccine.

2.2. Transmissionmodel

Weconsidertwostrains,1and2,with1beingthetargetofthe monovalentvaccine,whichhaslowerefficacyagainst2.Weuse adeterministic,differenceequationmodelwithadailytimestep, modelingthespreadofthesestrainsinanage-stratifiedpopula- tionwith5agegroups(0–4,5–17,18–49,50–64,65+).Transmission dynamicsaremodeledinthestratifiedmassactiontwo-strainSIR (S,I1,I2,R)framework(Dietz,1979)(withtheparametersdescribed in Tables 2 and 3). Contacts betweenthe different age groups (strata)aredescribedbyasymmetricmatrixC=(c_ij),wherec_ij is theaveragenumberofcontactsperunitoftime(day)betweena pairofindividualsinstrataiandj.WeestimatethecontactmatrixC byaveragingacrossthecountry-specificcontactmatricesprovided bythePOLYMODstudydata(Mossongetal.,2008;Wallingaetal., 2006).Additionally,foreachagegroupi,wehave

A.Populationsizen_i(extractedfromUSCDCWonder,basedonthe 2014USpopulation).

B.Individual relative susceptibility s^k_i ≤1 (per contact with an infectedindividual)forstrainkforeachindividualinstratum i(uniformsusceptibility).Weassumethatfori≤3,s^k_i isdrawn uniformlybetween[0.75,1];s^k₄=0.6,s^k₅=0.45.

Basedonpreviouswork(Cauchemezetal.,2009),weassume that infectivity is age-independent.We furtherassume that an infectorcausesinfectionsinthecommunityfor7daysfollowing his/herowninfection,andthedistributionw()ofinfectiousness overthose7days(serialintervaldistribution)isborrowedfrom Cauchemezetal.(2009).Thus,intheabsenceofvaccination,the numberofinfectionsduringtheearlystageofanepidemicinage groupicausedbyapersoninagegroupjondayd(1≤d≤7)after thatperson’sowninfectionwithstrainkis

·w(d)·s^k_i·ni·cij (1)

TheleadingeigenvalueofthenextgenerationmatrixN(i,j)=

·s^k_i ·ni·cijistheinitialeffectivereproductivenumberforstrain kintheabsenceofvaccination.Weﬁxsowhens^k_i =1fori≤3 (maximalpossiblesusceptibility),theinitialeffectivereproductive number(in theabsenceofvaccination) is1.4 forboth thevac- cineandthenon-vaccinestrains.Wediscardanyparametersets forwhichtheinitialeffectivereproductivenumberisbelow1for eitherstrain.

Basedondataforvaccinationlevelsbeforethestartofseasonal epidemicsinrecentyearsintheUS,weassumethatinthebase- linecase40%ofchildrenand30%ofadultsarevaccinated.Little isknownabouttheefﬁcacyofinﬂuenzavaccineagainstinfection.

TheannualestimatespublishedbytheUSCDCrefertoeffective- nessagainstsymptomatic,PCR-confirmedinfectionepisodes–the latterisexpectedtobehigherthanefficacyagainstinfluenzainfec- tionsincepreventinginfectionpreventsdisease.Ourpreviouswork (Worbyetal.,2015)suggestedthatforsomepathogens,efficacyof vaccinesagainstinfectioncanbesignificantlylowerthanefficacy againstsymptomaticdisease.Weassumethattheinfluenzavaccine

(4)

Table3

ComparativeepidemiologicoutcomeswiththebivalentvaccinecoveragefromTable1comparedtothebaselinecoverageofamonovalentvaccine.

Crossimmunity90% Crossimmunity70% Crossimmunity50%

Coverageforbivalent vaccinerelativeto baseline

%epidemicswith lowercumulative incidencethan baseline

Averageepidemic sizecomparedto baseline (95%CI)

Uniformcoverage 100% −100%

(−100%,−100%)

100% −100%

(−100%,−100%)

100% −100%

(−100%,−100%)

50%increase 100% −87%

(−99.9%,−51.6%)

100% −87.10%

(−99.9%,−31.7%)

100% −87.50%

(−99.9%,−60.3%)

25%increase 100% −63.50%

(−99.7%,−26.6%)

100% −63%

(−99.7%,−31.7%)

100% −62.90%

(−99.7%,−36.7%)

10%increase 100% −51.40%

(−97.2%,−11.4%)

100% −49.80%

(−97.1%,−15.6%)

100% −48.70%

(−97.1%,−22.1%)

Baselinelevel 96.60% −43.70%

(−82.4%,0.1%)

100% −41.30%

(−81.9%,−3.3%)

100% −39.90%

(−80.6%,−9.5%)

10%reduction 89.70% −36.60%

(−67.4%,12.2%)

94.40% −33.80%

(−65.7%,8%)

97% −31.10%

(−63.5%,2.1%)

25%reduction 81.60% −26.10%

(−50%,31.5%)

85.10% −22.50%

(−47.5%,24.9%)

90% −17.90%

(−43.2%,18.6%)

40%reduction 70% −16%

(−35%,53%)

68.40% −10.80%

(−30.4%,42.8%)

59.80% −3.30%

(−25.5%,37%)

reducessusceptibilitytoavaccinestrainby40%fornon-elderly(age groups1–4)andby30%fortheelderly.Forthe“monovalent”vac- cinetype,weassumethatsusceptibilitytonon-vaccinestrainis reducedbyx₁%fornon-elderly,x₂%forelderly,wherex₁isdrawn uniformlybetween[0,20]andx₂drawnuniformlybetween[0,15].

Weassumethatthestarttimeoftheepidemics(introductionof ﬁrstinfectedindividuals)forthetwostrainsdifferbyD,whereD isdrawnuniformlybetween[−35,35]days.Onceastrainisintro- duced,itisseededoveraweekwith500casesadaydistributed amongthedifferentagegroupsaccordingtothepopulationssizes andsusceptibilitytothatstrain.Thus,3500casesareseededinthe populationof318.9million(estimatedUSpopulationin2014).

Onceapersonisinfectedwithonestrain,thatpersonisimmune toitfortherestoftheoutbreak.Moreover,thatperson’ssuscepti- bilitytotheotherstrainisreducedby%.

Table2providesasummaryoftheseconcepts.Parameters,V, LaretheprimaryparametersT₁(withparametersvaccinevalency VandcoveragelevelsLusedinthecomparisonsinTable1),param- etersn_i,c_ij,s^k_i,w(),,D,EaresecondaryparametersT2,asdescribed inSection2.1.

3. Results

We ﬁrst examined the effect of replacing the monovalent vaccinebyabivalentoneunderthebaselinecoveragelevel.Unsur- prisingly,thevastmajorityofsimulatedoutbreakswithabivalent vaccinehadasmallercumulativeincidencecomparedtooutbreaks withmonovalentvaccine distribution(Fig. 2,panelA1), witha 39.9%averagereductionunderacrossimmunityof50%(Table3).

Moreover,the beneﬁt of using a bivalentvaccine compared to a monovalentonehasshownfurther(modest)increasesasthe strengthofcross-immunityincreased.However,athighlevelsof cross immunity(90%), 3.4%of simulated outbreakswere larger withtheimplementationofbivalentvaccinerelativetomonovalent vaccine(Table3).

Next, we considered reducing rates of either monovalent or bivalentvaccination,comparingthe cumulativeincidence of infectionfor thetwo strainstothescenarioof administering a monovalentvaccineatbaselinecoveragelevels(Fig.2).Ourresults suggestthatadministrationofthebivalentvaccine,evenatcov- eragelevelsthatare25%lowerthanthebaselinescenarioforthe monovalentvaccine,leadsonaveragetoasigniﬁcantreductionin thecumulativeincidencecomparedtothebaselinecoverageofa monovalentvaccine.Moreover,underreducedcoveragelevels,the

beneﬁtofboththebivalentandthemonovalentvaccinesincrease withincreasingstrengthofcross-immunity(Tables3and4).Inrare cases(about1%ofsimulationswithhighcross-immunity),reduc- ingcoverageforthemonovalentvaccineresultedinslightlysmaller outbreaks(Table4).

We considered increasingvaccination coverage for both the bivalentandthemonovalentvaccinesabovethebaselinecoverage level(Fig.1).Ourresultssuggestthathighercoveragelevelsforthe bivalentvaccinepreventthemajorityofincidentcasesofinfec- tioncomparedtothebaselinecoverageofamonovalentvaccine (Table3).Forexample,increasingcoverageforthebivalentvaccine by50%relativetothebaselinecompletelysuppressestransmission forabout30%ofsimulatedepidemics(Fig.3);onaverage,itleads toan87%reductioninepidemicsize(cumulativeincidence)com- paredtoadministrationofamonovalentvaccineatthebaseline coveragelevel.Atthesametime,wefoundthatevenincreasing monovalentvaccinationtounrealisticlevelscouldnotprovidethe samelevel ofprotectionasthebivalentvaccineatthebaseline coveragelevel.Evenuniversalcoverageofthemonovalentvaccine providedasomewhatloweraveragereductionincumulativeinci- dencecomparedtotheadministrationofthebivalentvaccineat baselinecoveragelevels(Tables3and4).Additionally,thebeneﬁt ofincreasingcoveragelevelsforthemonovalentvaccinedecreases somewhatwiththeincreasingstrengthofcross-immunity.

Wenotedabovecertainrareoccurrenceofsomecounterintu- itiveresults,suchasincreaseinepidemicsizewhenthemonovalent vaccineisreplacedbythebivalentone,ordecreaseinepidemicsize whencoveragelevelforthemonovalentvaccinedecreases.Those counterintuitivechangesinthecumulativeincidence(Fig.2,points abovethediagonalinpanelA1,belowthediagonalinpanelsB2–B4) areveryrareandquitesmall,withtheirmagnitudebeingsome- whatlargerforthedecreaseincoveragelevelsforthemonovalent vaccine(panelsB2–B4)comparedtotheintroductionofabiva- lentvaccine(panelA1).Reasonsforthosecounterintuitiveresults, aswellasthepotentialexplanatoryprinciplesbehindourmain ﬁndingsarepresentedinthe3rdparagraphofSection4.

4. Discussion

Inthispaperwestudiedthedynamicsofco-circulatinginfluenza strainsanditsrelationtovaccination.Theseanalysesweremoti- vatedbytheexperiencefromsomeofthepastinfluenzaepidemics intheUSwhenco-circulationofavaccine-typeandnon-vaccine strainswithincertaininfluenzatypes/subtypestookplace(USCDC,

(5)

Table4

Comparativeepidemiologicoutcomeswiththemonovalentvaccineathigherorlowercoveragelevelscomparedtothebaselinecoveragelevel(Table1).

Crossimmunity90% Crossimmunity70% Crossimmunity50%

Vaccinecoverage relativetobaseline

averageepidemic sizecomparedto baseline (95%CI)

Uniformcoverage 100% −37.20%

(−99.8%,−0.8%)

100% −38.40%

(−99.8%,−9.1%)

100% −40.30%

(−99.8%,−9.5%)

50%increase 100% −8.90%

(−47.1%,−1.7%)

100% −10.30%

(−47.7%,2.5%)

100% −11.80%

(−49.4%,−2.8%)

25%increase 99.90% −4.40%

(−27.1%,−0.8%)

100% −5.40%

(−26.3%,−1.3%)

100% −6.40%

(−27.8%,−1.4%)

10%increase 99.10% −1.80%

(−11.9%,−0.3%)

100% −2.20%

(−11.4%,−0.5%)

100% −2.80%

(−11.4%,−0.6%)

10%reduction 1.30% 1.80%

(0.3%,12.2%)

0.10% 2.40%

(0.5%,11.6%)

0% 3.40%

(0.6%,11.6%)

25%reduction 1.00% 4.60%

(0.7%,31.9%)

0% 6.60%

(1.4%,29.9%)

0% 9.70%

(1.7%,30%)

40%reduction 0.90% 7.70%

(1.2%,52.3%)

0% 11.50%

(2.3%,49.1%)

0% 17.70%

(2.9%,49.5%)

2014–2015a,b,c, 2005a,b, 2003, 2004a,b, 2008a,b, 2012a,b).For someofthoseseasons,incidenceofnon-vaccinestrainsincreased significantlyrelativetotheincidenceofvaccine-typesstrains(US CDC,2014–2015a,b,c,2005a,b,2003,2004a,b);duringothersea- sons,littlerelativechangeintheincidenceofthedifferentstrains was observed (US CDC, 2008a,b, 2012a,b). We examined how administrationofvaccines(thatoftenhavehigherefficacyagainst vaccine-typestrainscomparedtonon-vaccinestrains),combined withcross-immunityfromnaturalinfections(whichisexpectedto behigh)canaffecttherelativedynamicsofthetwostrains.We alsoconsideredthepotentialbenefitsofadministering vaccines thatimpartgoodprotectionagainstboththevaccine-typeandthe non-vaccinestrains.

Weinvestigatedtheimpactoftheinteractionofcross-immunity andvaccinationonthedynamicsof co-circulatingstrainsusing numericalsimulationsinanage-stratifiedpopulation.Inoursim- ulations, we considered thebaseline scenario of a monovalent vaccine(whichwasparameterizedtoreflect therealismofepi- demicswherevaccinewaspoorforthenon-vaccinestrain,e.g.the 2004–05and2014–15A/H3N2epidemics)withvaccinationcover- agelevelsof40%forchildrenand30%foradults.Wematchedthese outcomestoepidemicsforwhichvaccinetypeandcoveragelev- elsvary,whileallotherparametersarethesame.This(pair-wise) comparisonofthebaselineandmatchedepidemicsdemonstrated thatadministrationofa bivalentvaccineresultsin asignificant reductionintheoverallincidencecomparedtoadministrationofa monovalentvaccine,oftenevenwithreducedcoveragelevelsofthe bivalentvaccine.Moreover,wefoundthatthehigherthedegree ofcross-immunity,thesmallerthereductionintheincidenceof infectionthatcanresultfromincreasesincoveragelevelsforthe monovalentvaccine(Table4),andthemorebeneficialtheusage ofabivalentvaccine(Table3).Theseresultsareprimarilymeant tosuggestthebenefitofincludingmultipleA/H3N2strainsin a vaccinewhensuchstrainsareexpectedtocirculate.

Ourmainresultsareconsistentwithtwosimpleexplanatory principles.The qualitative finding in Table3 is that when two strainscompeteforhosts,itismorebeneficialtouseabivalentthan amonovalentvaccine.Moreover,thisbenefitgenerallyincreases withincreasingdegreeofcross-immunitybetweenthedifferent strains(whichisexpectedtobehigh,asindicatedinSection1).

Webelievethatthereasonforthisisthatusageofamonovalent vaccinereducestheincidenceofonestrain,decreasingthemiti- gatingeffectofthatincidenceontheincidenceoftheotherstrain, withthestrengthofmitigationbeinghighestforhigherdegreeof cross-immunity.Incertainrareinstances,particularlywhenthe

epidemicassociatedwiththevaccine-typestrainprecedestheone causedbythenon-vaccinestrain,andtheformerepidemichasa smallereffectivereproductivenumber,vaccinationwithamono- valentvaccinecan evenresult in theincreaseof thecombined incidenceofinfectionforthetwostrains,thoughsuchincreases inoursimulationareverymodest(andhighlyrare).Table4shows thatreducingcoverageofthemonovalentvaccinetypicallyreduces thepopulation-levelbeneﬁtofvaccination;however,thisreduc- tionofbeneﬁtislessstrikingwhencross-immunityisstrong,as theincreaseinincidenceofthevaccine-typestrainispartlyoffset byadeclineinthatofthesecondstrain.Wealsonotethatwhileall thoserulesholdonaverage,neitheroftheserulesofthumbholds universally.

Thiswork is meant to illustratethe basicprinciples under- lying the interaction of cross-immunity and vaccination under co-circulationofdifferentstrains,ratherthanmakeclaimsabout theactualpastinfluenzaepidemicsintheUS.Duringthoseepi- demics,even the simplerquestionof which strain would have dominated had the vaccine not been administered is not easy to answer, much less predict in advance. For example, during the process of vaccine selection for the 2014–15 season, the A/Switzerland/9715293/2013A/H3N2strainwasalreadyknown tocirculate,buttheA/Texas/50/2012A/H3N2strainwaschosen, withthenon-vaccinestrainoutstrippingthevaccine-typestrain throughthecourseoftheseason.InEurope,wherevaccination levelsarelowerthanintheUS,higherlevelsofcirculationofthe vaccine-typeA/H3N2straintookplacecomparedtotheUS(ECDC, 2014–2015vs.USCDC,2014–2015c).Wenotethatregardlessofthe questionwhichA/H3N2strainwouldhavebeenmoredominantin theabsenceofvaccinationduringthe2014–15season,andwhat theimpactoftheadministeredvaccinewas,itisclearthatavac- cinethatcontainedboththeSwitzerland/2013andtheTexas/2012 A/H3N2strainswouldhavebeensignificantlymorebeneficialthat avaccinethatonlycontainedoneofthosestrains.

Ourworkhasseverallimitations.Itisunclearhowwelltherange oftransmissionparametersemployedherereflectstherealityof influenzaepidemics.Inourmodel,vaccineisadministeredprior tothebeginningofinfluenzaseasonswhileinreality,someaddi- tionalvaccineadministrationcontinuestotakeplacethroughthe courseofinfluenzaepidemics,atleastintheUS.Theeffectofsea- sonalforcingonthetransmissionparametersisnotmodeledinour study,thoughthiseffectshouldoperateindependentlyofthephe- nomenaexaminedhereandpresumablyhasaratherlimitedimpact ontheresults.Whileweconsideredthreedifferentvaluesforthe strengthofcross-immunityparameters,andevidencesuggeststhat

(6)

Fig.1. Changeincumulativeincidenceresultingfromincreasedvaccinationcoveragestrategies,relativetobaselinecoverageofthemonovalentvaccine.Eachpanelrepresents avaccinationscenario;bivalent(left)andmonovalent(right)vaccinationatincreasingcoveragelevels(toptobottom)arecomparedtothebaselinecoverageofmonovalent vaccine.Pointsdenoteindividualsimulations;pointsbelowthediagonalrepresentsimulationsinwhichthealternativevaccinationstrategyreducedthesizeoftheoutbreak relativetothebaselinescenario.

this parameter shouldbe fairly large, it is difﬁcult to estimate usingepidemiologicalorgeneticdata.Moreover,inoursimulations thisparameterwasselectedindependentlyoftheefﬁcacyofthe

“monovalent”vaccineagainstthenon-vaccinestrain.Giventhat significantcross-immunityexitsbetweendifferentinfluenzasub- types,thisassumptionforstrainswithinaninfluenzasubtypeisnot unreasonable,thoughpossiblynotentirelyaccurate.Inoursimu- lations,theefficacyofamonovalentvaccineagainstnon-vaccine

strainsisassumedtobesignificantlylowcomparedtoitsefficacy againstthevaccine-type strain.While this wasindeedthecase duringcertaininfluenzaepidemics,suchasthe2014–15A/H3N2 epidemicintheUS(USInfluenzaVaccineEffectivenessNetwork, 2014–2015), this might not be thecase when thenon-vaccine strainbelongstoacloselyrelatedlineage.Finally,weconsidered theimpactofvaccinationoninfluenzaincidenceduringonesea- son.Incidenceofinfluenzaduringagivenseasonhasaneffecton

(7)

Fig.2. Changeincumulativeincidenceresultingfromreducedvaccinationcoveragestrategies,relativetobaselinecoverageofthemonovalentvaccine.Eachpanelrepresents avaccinationscenario;bivalent(left)andmonovalent(right)vaccinationatreducingcoveragelevels(toptobottom)arecomparedtothebaselinecoverageofmonovalent vaccine.PanelB1representsthebaselinecase.Pointsdenoteindividualsimulations;pointsbelowthediagonalrepresentsimulationsinwhichthealternativevaccination strategyreducedthesizeoftheoutbreakrelativetothebaselinescenario.

(8)

0.0 0.2 0.4 0.6 0.8 1.0 0.0

0.5 1.0 1.5 2.0

Monovalent vaccine

Quantile

Relative outbreak size

Relative vaccine coverage 0.6 0.9 1.1 1.5

Cross Immunity 0.9 0.7 0.5

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.5 1.0 1.5 2.0

Bivalent vaccine

Quantile

Relative outbreak size

Relative vaccine coverage 0.6 0.9 1.1 1.5

Cross Immunity 0.9 0.7 0.5

Fig.3.(Inverted)cumulativedistributionfunctions(CDFs)fortherelativesizesofoutbreakscomparedtotheadministrationofamonovalentvaccineatthebaselinecoverage level.Foreachpolicy(deﬁnedbyvaccinevalency,coveragelevel,andstrengthofcross-immunity),apoint(X,Y)onthegraphsuggeststhatfortheproportionXofsimulated epidemicswiththelowestrelativesize(attackratecomparedtotheadministrationofamonovalentvaccineatthebaselinecoveragelevel),thisrelativesizeisatmostY.

incidenceduringsubsequentseasonsthrough long-termimmu- nity,andcorrespondingly,vaccinationhasmulti-seasoneffectson incidenceaswell,evenifdirectimmunityconferredbythevaccine wanes.

5. Conclusions

Ourworkprovidesaframeworkforunderstandingseveralgen- eralprinciplesrelatedtovaccination(includingtheadministration ofbivalentvaccines)duringco-circulationofdifferentinfluenza strains. It illustratesthesignificantlimitations thatmonovalent vaccines(thosethathavepoorefficacyagainstnon-vaccinestrains) carryandsuggestsamajorimprovementinoutcomeswhenbiva- lentvaccinesforagiveninfluenzasubtypeareadministered.We hopethatthisworkcanbeusedtoguidevaccineselection.When thereisevidence(eitherbasedonepidemiologicaldataand/oron theanalysisoftheevolutionoftheinfluenzavirus,e.g.Neheretal., 2014,2015)thatmajorcirculationonmultiple,reasonablydistinct influenzastrainsislikelyduringtheupcomingseason,ourwork stressesthebenefitofincludingmultiplestrainswithinaninfluenza subtype,especiallyinfluenzaA/H3N2,inavaccine.

Fundingsources

ResearchreportedinthispaperwassupportedbytheNational InstituteofGeneralMedicalSciencesoftheNationalInstitutesof HealthunderawardnumberU54GM088558.Thecontentissolely theresponsibilityoftheauthorsanddoesnotnecessarilyrepresent theofﬁcialviewsoftheNationalInstituteofGeneralMedicalSci- encesortheNationalInstitutesofHealth.Thefundershadnorole instudydesign,datacollectionandanalysis,decisiontopublish,or

preparationofthemanuscript.Thisresearchwasalsosupportedby theDutchMinistryofHealth,WelfareandSports,andcarriedout withintheframeworkoftheRIVMStrategicProgramme(SPRgrant numberS/113005/01/PT),preparingtheNationalInstituteforPub- licHealthandtheEnvironment(RIVM)torespondtofutureissues inhealthandsustainability.

Conﬂictsofinterest

ML has received honoraria from Affinivax and Pfizer and researchfundingthroughHarvardfromPfizerandPATHVaccine Solutions.

Acknowledgements

WethankJenniferMichaels,SheridaKipp,andBrianArnoldfor theirhelpwiththispaper.

References

Ampofo,W.K.,Azziz-Baumgartner,E.,Bashir,U.,Cox,N.J.,Fasce,R.,etal.,2015.

Strengtheningtheinﬂuenzavaccinevirusselectionanddevelopmentprocess:

reportofthe3rdWHOInformalConsultationforImprovingInﬂuenzaVaccine VirusSelectionheldatWHOheadquarters,Geneva,Switzerland,1–3April 2014.Vaccine33,4368–4382.

Cauchemez,S.,Donnelly,C.A.,Reed,C.,Ghani,A.C.,Fraser,C.,etal.,2009.

Householdtransmissionof2009pandemicinﬂuenzaA(H1N1)virusinthe UnitedStates.N.Engl.J.Med.361,2619–2627.

Cowling,B.J.,Nishiura,H.,2012.Virusinterferenceandestimatesofinﬂuenza vaccineeffectivenessfromtest-negativestudies.Epidemiology23,930–931.

Cowling,B.J.,Ng,S.,Ma,E.S.,Cheng,C.K.,Wai,W.,etal.,2010.Protectiveefficacyof seasonalinfluenzavaccinationagainstseasonalandpandemicinfluenzavirus infectionduring2009inHongKong.Clin.Infect.Dis.51,1370–1379.

(9)

Dietz,K.,1979.Epidemiologicinterferenceofviruspopulations.J.Math.Biol.8, 291–300.

ECDC,2014–2015.Summarisingthe2014–2015inﬂuenzaseasoninEurope.http://

ecdc.europa.eu/en/press/news/layouts/forms/NewsDispForm.

aspx?ID=1231&List=8db7286c-fe2d-476c-9133-18ff4cb1b568-sthash.

Duog50bJ.dpuf.

Ferguson,N.M.,Galvani,A.P.,Bush,R.M.,2003.Ecologicalandimmunological determinantsofinﬂuenzaevolution.Nature422,428–433.

Goldstein,E.,Cobey,S.,Takahashi,S.,Miller,J.C.,Lipsitch,M.,2011.Predictingthe epidemicsizesofinﬂuenzaA/H1N1,A/H3N2,andB:astatisticalmethod.PLoS Med.8,e1001051.

Mossong,J.,Hens,N.,Jit,M.,Beutels,P.,Auranen,K.,etal.,2008.Socialcontactsand mixingpatternsrelevanttothespreadofinfectiousdiseases.PLoSMed.5,e74.

Neher,R.A.,Russell,C.A.,Shraiman,B.I.,2014.Predictingevolutionfromtheshape ofgenealogicaltrees.Elife,3.

Neher,R.A.,Bedford,T.,Daniels,R.S.,Russell,C.A.,Shraiman,B.I.,2015.Prediction, dynamics,andvisualizationofantigenicphenotypesofseasonalinﬂuenza viruses.arXiv:1510.01195.

Shaman,J.,Pitzer,V.E.,Viboud,C.,Grenfell,B.T.,Lipsitch,M.,2010.Absolute humidityandtheseasonalonsetofinﬂuenzainthecontinentalUnitedStates.

PLoSBiol.8,e1000316.

Smith,D.J.,Lapedes,A.S.,deJong,J.C.,Bestebroer,T.M.,Rimmelzwaan,G.F.,etal., 2004.Mappingtheantigenicandgeneticevolutionofinﬂuenzavirus.Science 305,371–376.

Sonoguchi,T.,Naito,H.,Hara,M.,Takeuchi,Y.,Fukumi,H.,1985.Cross-subtype protectioninhumansduringsequential,overlapping,and/orconcurrent epidemicscausedbyH3N2andH1N1inﬂuenzaviruses.J.Infect.Dis.151, 81–88.

Tria,F.,Lassig,M.,Pelitl,L.,Franz,S.,2005.Aminimalstochasticmodelfor inﬂuenzaevolution.J.Stat.Mech.Theor.Exp.,P07008.

USCDC,2003.WeeklyReport:InﬂuenzaSummaryUpdate.Weekending December20,2003–Week.http://www.cdc.gov/ﬂu/weekly/

weeklyarchives2003-2004/weekly51.htm.

USCDC,2004a.WeeklyReport:InﬂuenzaSummaryUpdate.WeekendingJanuary 31,2004–Week4.http://www.cdc.gov/ﬂu/weekly/weeklyarchives2003-2004/

weekly04.htm.

USCDC,2004b.WeeklyReport:InﬂuenzaSummaryUpdate.WeekendingMay15, 2004–Week19.http://www.cdc.gov/ﬂu/weekly/weeklyarchives2003-2004/

weekly19.htm.

USCDC,2004c.Assessmentoftheeffectivenessofthe2003–04inﬂuenzavaccine amongchildrenandadults–Colorado,2003.MMWRMorb.MortalWklyRep.

53(August(31)),707–710.

USCDC,2005–2015.SeasonalInﬂuenzaVaccineEffectiveness,2005–2015.http://

www.cdc.gov/ﬂu/professionals/vaccination/effectiveness-studies.htm.

USCDC,2005a.WeeklyReport:InﬂuenzaSummaryUpdate.WeekendingJanuary 15,2005–Week2.http://www.cdc.gov/ﬂu/weekly/weeklyarchives2004-2005/

weekly02.htm.

USCDC,2005b.WeeklyReport:InﬂuenzaSummaryUpdate.WeekendingMay14, 2005–Week19.http://www.cdc.gov/ﬂu/weekly/weeklyarchives2004-2005/

weekly19.htm.

USCDC,2008a.FluView.2007–2008InﬂuenzaSeasonWeek19,endingMay10, 2008.http://www.cdc.gov/ﬂu/weekly/weeklyarchives2007-2008/weekly19.

htm.

USCDC,2008b.FluView.2007–2008InﬂuenzaSeasonWeek8,endingFebruary23, 2008.http://www.cdc.gov/ﬂu/weekly/weeklyarchives2007-2008/weekly08.

htm.

USCDC,2012a.FluView.2011–2012InﬂuenzaSeasonWeek20endingMay19, 2012.http://www.cdc.gov/ﬂu/weekly/weeklyarchives2011-2012/weekly20.

htm.

USCDC,2012b.FluView.2011–2012InﬂuenzaSeasonWeek4endingJanuary28, 2012.http://www.cdc.gov/ﬂu/weekly/weeklyarchives2011-2012/weekly04.

htm.

USCDC,2014–2015a.FluView.2014–2015InﬂuenzaSeasonWeek46ending November15,2014.http://www.cdc.gov/ﬂu/weekly/weeklyarchives2014- 2015/week46.htm.

USCDC,2014–2015b.FluView.2014–2015InﬂuenzaSeasonWeek50ending December13,2014.http://www.cdc.gov/ﬂu/weekly/weeklyarchives2014- 2015/week50.htm.

USCDC,2014–2015c.FluView.2014–2015InﬂuenzaSeasonWeek20endingMay 23,2015.http://www.cdc.gov/ﬂu/weekly/weeklyarchives2014-2015/week20.

htm.

USCDCWonder.http://wonder.cdc.gov/.

USInﬂuenzaVaccineEffectivenessNetwork,2014–2015.Endofseasoninﬂuenza vaccineeffectivenessestimatesforthe2014–15season.http://www.cdc.gov/

vaccines/acip/meetings/downloads/slides-2015-06/ﬂu-02-ﬂannery.pdf.

Wallinga,J.,Teunis,P.,Kretzschmar,M.,2006.Usingdataonsocialcontactsto estimateage-speciﬁctransmissionparametersforrespiratory-spread infectiousagents.Am.J.Epidemiol.164,936–944.

Worby,C.J.,Kenyon,C.,Lynﬁeld,R.,Lipsitch,M.,Goldstein,E.,2015.Examiningthe roleofdifferentagegroups,andofvaccinationduringthe2012Minnesota pertussisoutbreak.Sci.Rep.5,13182.