within-host competition determines vaccine impact on ... · correspond to is not explicitly...

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Within-hostcompetitiondeterminesvaccineimpactonantibioticresistanceNicholasG.Daviesa,b,c,*,StefanFlaschea,b,c,MarkJita,b,c,d,KatherineE.Atkinsa,b,c,ea.CentreforMathematicalModellingofInfectiousDiseases,LondonSchoolofHygieneandTropicalMedicine,London,UK.b.VaccineCentre,LondonSchoolofHygieneandTropicalMedicine,London,UK.c.DepartmentofInfectiousDiseaseEpidemiology,FacultyofEpidemiologyandPopulationHealth,LondonSchoolofHygieneandTropicalMedicine,London,UK.d.ModellingandEconomicsUnit,PublicHealthEngland,London,UK.e.CentreforGlobalHealth,UsherInstituteofPopulationHealthSciencesandInformatics,TheUniversityofEdinburgh,Edinburgh,UK.*Correspondingauthor.E-mail:[email protected]|Vaccinescouldhelpmitigatetheburdenofantibiotic-resistantinfectionsbypreventingpeoplefromcontractinginfectionsinthefirstplace.Butthelong-termimpactofvaccinesuponantibioticresistanceisunclear,becausewedonotknowhowvaccinationmayitselfalterselectionforresistance.Thislackofclarityiscompoundedbyuncertaintyoverwhichmechanismsdriveresistanceevolutioninbacteria.Specifically,thereisdisagreementoverwhatstablymaintainsobservedpatternsofcoexistencebetweenresistantandsensitivestrainsovertime.Usingamathematicalmodellingframework,weshowthatcontemporarypatternsofpenicillinresistanceinthecommensalpathogenStreptococcuspneumoniaeacrossEuropecanbeexplainedeitherbywithin-hostcompetition,bydiversifyingselectionforbacterialcarriageduration,orbywithin-countryheterogeneityintreatmentrates.However,thesealternativemechanismsvaryconsiderablyintheirpredictionsoftheimpactofvaccineinterventions.Specifically,weidentifythetestablehypothesisthattheoutcomeofwithin-hostcompetitionbetweensensitiveandresistantstrainscriticallydetermineswhethervaccinationpromotesorinhibitstheevolutionofresistance.Thesepredictionsvaryforsettingsdifferingincarriageprevalenceandtreatmentrates.Hence,calibrationtopathogen-andcountry-specificdataisrequiredforevidence-basedpolicy.

author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (which was not peer-reviewed) is the. https://doi.org/10.1101/610188doi: bioRxiv preprint

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Inanageofwidespreadantibioticresistance,thereisgrowinginterestinusingvaccinestopreventbacterialinfectionsthatwouldotherwisecallfortreatmentwithantibiotics(1–4).Thisinterestarisesfortwomainreasons:first,vaccinesareeffectiveagainstbothantibiotic-resistantandantibiotic-sensitivebacteria;andsecond,successfulprophylaxisremovestheneedforacourseofantibiotictherapythatmightpromotemoreresistance(2–5).Overthepasttwodecades,theuseofpneumococcalconjugatevaccines(PCV)hasseeminglyborneouttheseadvantages.AdministeringPCVtoyoungchildrenhassubstantiallyreducedpneumococcaldisease(5–8)anddecreaseddemandforantibiotictherapy,largelybyreducingcasesofotitismediarequiringtreatment(5,9).ButbecausePCVtargetsonlyafractionofthe~100knownpneumococcalserotypes,thenicheithasvacatedhasbeenfilledbynon-vaccineserotypes,andpneumococcalcarriagehasreturnedtopre-vaccinelevels(10,11).Concomitantly,diseasecausedbynon-vaccineserotypes(12)andthelevelofresistanceamongnon-vaccineserotypes(5,13)haveriseninmanysettings.Concernoverserotypereplacement—alongwiththehighcostofmanufacturingPCV—hasspurreddevelopmentof“universal”whole-cellorprotein-basedpneumococcalvaccinesprotectingagainstallserotypes,whicharenowinclinicaltrials(14).However,itisunclearhowuniversalvaccinationmayitselfimpactupontheevolutionofantibioticresistanceinS.pneumoniae.Whilemathematicalmodelsareausefultoolforgeneratingpredictionsfromnonlineartransmissiondynamics(15,16),existingmodelsfocusonserotype-specificvaccinesand,eventhen,disagreeovertheexpectedimpactofvaccinationonresistanceevolution(17–23).Comparingandinterpretingtheresultsofthesemodelsishamperedbythefactthatnonestartsfromapositionofrecapitulatingcontemporary,large-scalepatternsofantibioticresistance.Themainchallengeinreplicatingthesepatternsliesinidentifyingthemechanismsthatmaintainlong-termcoexistencebetweensensitiveandresistantstrainsacrossawiderangeofantibiotictreatmentrates,likethoseseenacrossEuropeandtheUnitedStates(24,25).Robustpredictionsofthelong-termimpactofvaccinationonresistantpneumococcaldiseaserequireamechanisticunderstandingofthesepatterns.Here,weidentifyeighthypothesesthathavebeenproposedtoexplaincoexistencebetweensensitiveandresistantstrainsofpathogenicbacteria.WefindthatfourofthesehypothesesareconsistentwithempiricalpatternsofpenicillinresistanceinthecommensalpathogenStreptococcuspneumoniae(pneumococcus)across27Europeancountries.Then,weshowthateachofthesefourmodelsmakedifferentpredictionsfortheimpactofvaccinationuponthelong-termevolutionofantibioticresistance.Inparticular,weshowthatwhethervaccinationpromotesorinhibitsresistanceevolutiondependsuponthenatureofwithin-hostcompetitionbetweensensitiveandresistantstrains.Wedemonstratehowourpredictionscanbeappliedmoregenerallybyextendingourmodeltohigh-carriagesettings.Ourworkemphasizesthatanunderstandingofthemechanismsthatgovernresistanceevolutioniscrucialforpredictingthepotentialforusingvaccinestomanageantibioticresistance.


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ResultsFourmodelsofresistanceevolution.Usingaliteraturesearch,weidentifyeightcandidatemechanismsthathavebeenhypothesisedtomaintaincoexistencebetweensensitiveandresistantbacterialstrains.WefindthatfourofthesemechanismscouldplausiblyreproducepatternsofcoexistenceasseeninS.pneumoniae(Table1).Accordingly,weembedthesefourmechanismsinthefollowingmodelframeworkofpneumococcaltransmission.Ourmodelcalculatesthecountry-specificequilibriumfrequencyofresistanceinpneumococcicirculatingamongchildrenunderfiveyearsofage—theagegroupresponsibleforthemajorityofpneumococcalcarriage(26).Weassumethathostsmixrandomlywithinapopulation,witheachhostmakingeffectivecontactwithanotherrandomhostatrateβpermonth,therebypotentiallyacquiringacarriedstrain(eithersensitiveorresistant)fromthecontactedhost.Withprobabilityc,resistantstrainsfailtotransmit,wherecrepresentsthetransmissioncostofresistance(27,28).Wemodelimportationofstrainsfromoutsideacountryatalow,constantrateψ,assumingthatwithprobabilityρ(equaltotheaverageresistancefrequencyinEurope)animportedstrainisresistant.Ahostnaturallyclearsallcarriedstrainsatrateu,andisexposedtoantibiotictherapyatacountry-specificrateτ,whichclearsthehostofsensitivestrainsonly.Weassumethatthetreatmentrateisindependentofcarriagestatus(29).Intheabsenceofanymechanismmaintainingcoexistencebetweensensitiveandresistantcells,competitiveexclusionisexpected—inotherwords,eitherresistantorsensitivestrainsareexpectedtogotofixationinthepopulation(24,30).Eachofthefourmodelsbuildsuponthisframeworkandinvokesanalternativemechanismformaintainingcoexistence.


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Table1.MechanismsformaintainingcoexistenceMechanism

Modeofaction

Modelledinthisstudy?

Consistentwithempiricalpatterns?

Within-hostcompetition

(A:transmissioncost)

Within-hostcompetitioncreatesfrequency-dependentselectionforresistance(24,25,31–33)

Yes

Within-hostcompetition

(B:growthcost)

" Yes

Diversesubtypes

Subtypesmaintainedbydiversifyingselectiondifferinpropensityforresistance(34)

Yes

Treatmentvariation

Assortatively-mixingsubpopulationsdifferintreatmentrates(24,35–38)

Yes

Treatedclass

Individualscurrentlyintreatmentmaintainresistantstrains(24,32,35,39)

No:Onlysupportsasmallamountofcoexistence(24)

Separateniches

Sensitiveandresistantstrainsexploitseparateniches(40,41)

No:Resistantandsensitivestrainsareknowntooccupythesameniches(30)

Mutationpressure

Mutation-selectionbalancemaintainsintermediateresistancefrequency(38,41,42)

No:DenovoacquisitionofresistanceinS.pneumoniaeisnotfrequentenough(24)

Prescriptionfeedback

Doctorsreduceprescribingofadrugasresistancetoitincreases(38,39)

No:Doesnotexplainhowcoexistenceismaintainedoverarangeofdifferenttreatmentrates


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Fig.1.Fourmodelsofresistanceevolution.(a–d)Wecontrastfourmodels,whosestructuresareshownhere.Themechanismpromotingcoexistenceineachmodelisillustrated.SeeMethodsformodelimplementationdetails.(e)ModelfitswithassociatedWAIC.Verticallinesshowthe95%HDIsforthereportedproportionofinvasiveS.pneumoniaeisolatesthatareresistanttopenicillinplottedagainsttheantibioticconsumptionrateinunder-5s.Ribbonsshowthe50%and95%HDIsforresistanceprevalencefromeachfittedmodel.(f)Thetoprowshowsestimatedposteriordistributionsforthefreeparametersineachmodel;thebottomrowshowsmodeloutputsassociatedwiththeseparameterstoaidinterpretation.Inthefirsttwo“Within-hostcompetition”models(Fig.1a&b),individualscanbecolonisedbybothsensitiveandresistantstrains.Antibiotictreatmentbenefitsresistantstrainsbyclearingawaytheirsensitivecompetitors.Thisbenefitismorepronouncedwhenresistantstrainsarerare,becausewhenraretheytendtocompetemorewithcommonsensitivestrainsthanwithotherrareresistantstrains.Thiscreatesfrequency-dependentselectionforresistancethatcanmaintaincoexistence(25).The“Within-hostcompetitionA”modelassumesthatonlyantibiotictherapymediateswithin-hostcompetition,whilethe“Within-hostcompetitionB”modelassumesthatsensitivestrainscangraduallyoutcompeteresistantstrainswithinthehostintheabsenceofantibiotics,whichoccursatrateb(25).Weassumethatthereisnotransmissioncostofresistanceinthislattermodel(c=0),withthewithin-hostgrowthadvantagebofsensitivestrainsaccountingcompletelyforthecostofresistance.Accordingly,thetwomodelsprimarilydifferinhowthecostofresistanceispresumedtooperate.Thekeyparametergoverningcoexistenceinthesetwomodelsisk,therelativerateofco-colonisationcomparedtoprimarycolonisation.


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Inthethird“Diversesubtypes”model,pneumococciaredividedintosubtypes(“D-types”)(34)thatvaryintheirmeandurationofnaturalcarriage.DiversifyingselectionactingontheD-typelocusensuresthatallsubtypesaremaintainedincirculationdespitethevariabilityincarriageduration.Inturn,thevariabilityincarriagedurationcausesresistancetobeselectedinsomesubtypes,butnotothers(Fig.1c).WhatD-typescorrespondtoisnotexplicitlyspecifiedbythismodel,butserotypevariationisonecandidate.Forexample,ifhostimmunitypromotesantigenicdiversitythroughacquiredimmunitytocapsularserotypes,anddifferentserotypestendtodifferintheirintrinsicabilitytoevadeclearancebytheimmunesystem,thenintermediateresistancecanbemaintainedbecauseselectionforresistancetendstobegreaterinstrainsthathaveaprolongeddurationofcarriage.Long-lastingserotypeswilltendtoevolveresistance,whileshorter-livedserotypeswilltendnotto—apatternobservedinS.pneumoniae(34).Thismodelassumesthatindividualsalreadycarryingpneumococcuscannotbeco-colonised.Theparametersgoverningcoexistenceinthismodelarea,thestrengthofdiversifyingselectiononstraintype,andδ,thevariabilitybetweensubtypesinclearancerate.Finally,inthe“Treatmentvariation”model,heterogeneityintheconsumptionofantibioticsbetweensubpopulationsofhostswithinacountrymaintainscoexistence(24,35,36)(Fig.1d).Subpopulationsinwhichconsumptionishightendtopromoteresistance,andsubpopulationsinwhichconsumptionislowtendtoinhibitresistance.Providedthattheinterchangeofstrainsbetweenhigh-consumptionandlow-consumptiongroupsisnottoofrequent,astable,intermediatefrequencyofresistancecanbemaintainedacrossthewholepopulation.Again,co-colonisationisnotmodelled.Subpopulationswithinacountrycouldcorrespondtogeographicalregions,socioeconomicstrata,hostageandriskclasses,oracombinationofthese.Thekeyparametersgoverningcoexistenceinthismodelareκ,whichmeasuresthevariabilityinantibioticconsumptionbetweensubpopulations,andg,therelativerateatwhichcontactbetweenhostsismadewithinratherthanbetweensubpopulations,ameasureof‘assortativity’.FulldetailsofallmodelimplementationsareprovidedintheMethods.Allmodelscanreproduceobservedpatternsofresistance.TheEuropeanCentreforDiseasePreventionandControl(ECDC)monitorsantibioticconsumptionandresistanceevolutionacrossEuropeancountriesfor26combinationsofdrugandbacterialspecies(13,43).Thesedatacaptureanaturalexperimentinresistanceevolution:foreachmonitoreddrugandpathogen,eachcountryreportsadifferentrateofantibioticconsumptioninthecommunityandexhibitsadifferentfrequencyofresistanceamonginvasivebacterialisolates.Overall,resistancetendstobemorecommonincountrieswheremoreantibioticsareconsumed(44),andthefractionofinvasiveisolatesthatareresistantismaintainedatastable,intermediatelevelovertime(25).Fittingmodelstodatafrommultiplecountriesallowsonetoruleoutmodelsthatcannotreproducethislarge-scalepattern(25).


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WeuseBayesianinferencetoindependentlyfitthefourmodelstoECDCdataforcommunitypenicillinconsumptionandpenicillinresistanceinS.pneumoniaeacross27Europeancountries,withanassumed50%carriageprevalenceinchildrenunderfiveyears(11,26).Weassumethatcountriesonlydifferintreatmentrateandreportedresistancefrequency,withothermodelparameterssharedacrosscountries.Wefindthateachmodelcanfitequallywelltotheempiricaldata(Fig.1e,ΔWAIC<2.0)andrecoverplausibleposteriorparameterdistributions(Fig.1f).Modelsdifferinthepredictedimpactofvaccination.Usingourfourfittedmodels,wepredicttheimpactoftwoalternativevaccinesthateachreducecarriageprevalencebyadifferentmode(Fig.2).Wemodelan“acquisition-blocking”vaccinethatpreventspneumococcalacquisitionwithprobabilityεa,anda“clearance-accelerating”vaccinethatshortensthedurationofpneumococcalcarriagebyafractionεc,reflectingalternativemodesofacquiredimmunitythatmightbeelicitedbyapneumococcalvaccine(45,46).Forsimplicity,weassumethatallchildrenunderfivearevaccinatedandrefertoεaorεcasthevaccineefficacy.Tocomparevaccineswithantibioticstewardship,wealsoevaluatetheimpactofreducingtherateofantibiotictherapybyafractionεs.Wereporttheeffectofeachinterventiononcarriageprevalenceandonresistancefrequency(Fig.2).Asexpected,pneumococcalcarriageprevalenceisdecreasedbybothvaccines,andismoderatelyincreasedbyantibioticstewardship(Fig.2a),withconsistenteffectsacrossmodels.Incontrast,predictionsforresistancefrequencyvaryacrossbothmodelsandvaccinetypes(Fig.2b).Theacquisition-blockingvaccineselectsstronglyagainstresistanceinthe“Within-hostcompetitionA”modelbecausebyloweringtransmission,itreducesco-colonisationandthusdecreaseswithin-hostcompetition,whichinthismodelbenefitstheresistantstrain(Fig.2d).Conversely,in“Within-hostcompetitionB”,within-hostcompetitiontypicallybenefitsthesensitivestrain,andsothevaccinestronglypromotesresistance(Fig.2d).Thismirrorsourpreviousfindingthatincreasedtransmissionofstrainsmodulatesresistanceevolutionthroughitsimpactuponwithin-hostcompetition(25).Inthe“Diversesubtypes”and“Treatmentvariation”models,theacquisition-blockingvaccinehasarelativelyminorinhibitingeffectuponresistance.Thisstemsfromvaccineshavingarelativelygreaterimpactupontransmissioninpopulations(whethercountriesorsubpopulationswithinacountry)wherecarriageislower,leadingtovariabilitybetweenpopulationsintheinterplaybetweentransmissionandimportationthathaveamildimpactuponresistanceevolution.Alloftheseeffectsarealsoseenfortheclearance-acceleratingvaccine,whichhasanadditionalresistance-inhibitingeffectacrossallmodels,becauseashorterdurationofcarriage—whethernaturalorvaccine-induced—selectsagainstresistance(Fig.2d)(34).Antibioticstewardshipselectsagainstresistance,asexpected.


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Fig.2.Impactofinterventions.Pointsgivethemean,andverticalbarsgivethe95%HDI,for(a)carriageprevalence,(b)resistancefrequency,and(c)resistantcarriageunderdifferentinterventions.Notethatasvaccinesreducewithin-countrytransmissiontonearzero(ε≥50%;dashedline),carriageisincreasinglydominatedbyimportedstrains,whichhavearesistancefrequencyof14%,theempiricalaverageacrossEurope.(d)Illustrationofthestrongestforcesselectingforgreaterorlesserresistanceacrossmodels.Thepredictedresistantcarriage(Fig.2c)istheproductofcarriageprevalenceandresistancefrequency.Notethatunderthe“Within-hostcompetitionB”model,vaccinationatintermediateefficacyisexpectedtomarginallyincreasetheoverallrateofresistantcarriage.Inothermodels,vaccinationalwaysreducesresistantcarriage,particularlyunderthe“Within-hostcompetitionA”model.Implicationsforpolicy.Reducinginappropriateantibioticuseiscurrentlytheprimarymeansofmanagingresistance.Accordingly,weevaluatetheaveragereductioninantibioticusewhichisequivalent,intermsofreducingresistantcarriage,toarolloutofeachvaccineforincreasingvaccineefficacies(Fig3a).Wefindthattherelativeeffectofreducinginappropriateantibioticuseandintroducingavaccineisconsiderablydependentontheunderlyingmodel.Forexample,thevaccineefficacyrequiredtoachievetheequivalentofa15%reductioninantibioticconsumption—thecurrenttargetforantibioticstewardshipintheUK(48)—islowestinthe“Within-hostcompetitionA”model(εa=11%;εc=7%)andhighestunderthe“Within-hostcompetitionB”model(εa=47%;εc=45%).Ofinterestforclinicaltrialsisthelengthoftimethatisexpectedforvaccine-mediatedchangesinresistancetooccur;wefindthatittakes5–10yearsforthefulleffectsofresistanceevolutiontobeseen(Fig.3b).


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Fig.3.Policyimplications.(a)Medianequivalentreductioninprescriptionrateacrossfourmodelsofresistanceevolution,intermsoftheirefficacyatreducingtheincidenceofresistantpneumococcalcarriage.Thisdemonstratesthevaccineefficacyrequiredtoachieveasimilardecreaseinresistantcarriagetoagivenreductioninantibioticprescriptionrates.Theimpactonoverallpneumococcalcarriageisnotconsideredhere.Theshadedbarshowsan8.8–23.1%reductioninprescriptions,anestimateofthepercentageofprescriptionswhichareclinicallyinappropriateintheUK(47).Thedashedlineshowsa15%reductioninprescriptions,whichhasrecentlybeenannouncedasatargetbytheUKgovernment(48).(b)Theimpactofvaccinationisnotimmediate,buttakesabout5–10years,dependinguponthemodel.Dashedlinesshowequilibriumresistantcarriageaftervaccinationat30%efficacy,whilesolidlinesandribbonsshowmeanand95%HDIs.(c)Per-countryimpactofvaccines.CountriesreportingtoECDCareorderedfromlowest(NL)tohighest(CY)reportedrateofpenicillinconsumption.Opendiamondsshowthechangeinallpneumococcalpneumoniacases,whilefilleddistributionsshowthechangeinresistantcases.


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Fig.4.Vaccineimpactinahigh-burdensetting.Adjustingfittedmodelstobeconsistentwithahigh-burdensettingyieldsdifferentpredictionsforvaccineimpact,highlightingboththeincreasedchallengesandgreateropportunitiesforresistancemanagementviavaccination.Wealsoevaluatetheimpactofeachinterventiononanationallevel,focusingontheconcreteoutcomeofchildhoodpneumococcalpneumoniacases(Methods).Whileinterventionshaveaconsistentimpactfromcountrytocountryonthetotalpneumoniacaserate,theimpactonresistantpneumoniacasesisgreatestinthosecountrieswhereresistanceishighest(Fig.3c).Vaccinationinahigh-burdensetting.Highcarriageandresistanceratesareobservedinsomesettings.Forexample,a90%pneumococcalcarriagerate,with81.4%ofisolatesresistanttopenicillin,hasbeenobservedamongchildrenunderfiveinwesternKenya(49).Thisincreasedcarriageratemaybepartlyattributabletoalongeraveragedurationofcarriageinthissetting,consistentwitha71.4-daymeandurationofnaturalpneumococcalcarriagemeasuredinKilifi,easternKenya(50)(SupplementaryMaterial).Tomodelasimilarhigh-burdensetting,weadjustmodelparametersestimatedfromEuropeandata:decreasingtherateofnaturalclearanceto71.4days–1,increasingthetransmissionratetogeneratea90%carriageprevalence,increasingthetreatmentratetoyieldaresistancefrequencyof81.4%,andignoringstrainimportation(ψ=ρ=0),whilekeepingotherparameters(c,b,k,a,δ,g,andκ)thesame.Inrelativeterms,acomparativelygreatervaccineefficacyisneededtoreducetherateofresistantcases,particularlyunderthe“Within-hostcompetitionB”model(Fig.4).However,vaccinationisexpectedtohaveacomparativelygreaterimpactinabsolutetermsbecauseofacomparativelyhigherrateofdiseaseinsuchsettings:forexample,Kenyaisestimatedtohavean8.8-foldhigherrateofseverepneumococcalpneumoniathantheaverageinEurope(51).

ConclusionsWehaveidentifiedfourmechanismsthatcanexplainpatternsofpenicillinresistanceinS.pneumoniaeacrossEurope.Thesemechanismsarenotmutuallyexclusive,buttherelativeimportanceofeachwillhaveasubstantialimpactuponpredictionsforresistanceevolutionundervaccination.Inparticular,the“directionality”ofwithin-hostcompetition—thatis,whether,onaverage,within-hostcompetitionbenefitsresistantorsensitivestrains—hasasubstantialimpactuponwhetherimmunisationselectsfora


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decreaseoranincreaseinantibioticresistanceinthelongterm.Thisdirectionalitywillvarybetweenpathogens,butisalsosensitivetotheantibiotictreatmentrate,andsomayalsovarybetweensettings.AlthoughwehavefocusedoncompetitionbetweensensitiveandresistantstrainsofS.pneumoniaeonly,competitionbetweenserotypes(23)andamongothernasopharyngealcoloniserswillalsoimpactuponresistanceevolution,anddeterminingtheimportanceoftheseothersourcesofwithin-hostcompetitioniscrucial.Wehavealsoshownthatthemodeofvaccineprotection—whetheracquisition-blockingorclearance-accelerating—isimportant.Whole-cellandpurified-proteinpneumococcalvaccinesmayinduceantibody-mediatedhumoralimmunity,CD4+Thelper-17cell-mediatedimmunity,orboth(45,46).Bymodellingbothmodesofvaccineaction,wehavehighlightedthatclearance-acceleratingvaccineshavespecialpotentialforpreventingthespreadofresistance.Ourfocushasbeenontheimpactofthefouridentifiedmechanismsperseuponresistanceevolution.Modelsthatcouldmakemoreaccuratecountry-specificpredictionswouldneedtoaccountfortheeffectsofdemographicstructure,differencesincarriageprevalenceanddiseaseratesbetweensettings,andvariablevaccineprotectionamongindividuals.Wehaveassumedthatantibiotictreatmentratesamongpneumococcalcarriersremainsconstantaftertheintroductionofavaccine,eventhoughtreatmentratesdroppedinmanysettingsfollowingPCVintroduction(5,9).However,forauniversalpneumococcalvaccinethatreducesantibiotictreatmentratesbecauseitreducescarriageandtherebypreventsantibiotic-treatabledisease,anyreductionintreatmentwillonlyoccuramongindividualswho,becauseofvaccineprotection,arenotpneumococcalcarriers,allelsebeingequal.Accordingly,itmightbeexpectedthattreatmentratesincarrierswouldremainequallyhighamongthoseindividualsforwhomvaccineprotectionhasfailed.Ahighlyefficaciousnext-generationpneumococcalvaccinecanindeedreducetheoverallburdenofantibiotic-resistantpneumococcaldisease.However,thelong-termeffectofavaccinewithintermediateefficacyuponresistanceislesscertain,asvaccineimpactdependscruciallyuponthemechanismsthatdriveresistanceevolution.Thus,empiricalinvestigationofpathogencompetitivedynamics—andtheimpactofsetting-specificfactorsonthesedynamics—isneededtomakeaccuratepredictionsofvaccineimpactonresistantinfections.


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MethodsMechanismsdrivingresistance.Weconductedaliteraturesearchtoidentifymechanismsthroughwhichanintermediatefrequencyofresistancecanbemaintainedacrossahostpopulation.WesearchedPubMedusingtheterms:(AMRORABROR((antimicrobialORantibiotic)ANDresist*))AND((modelORmodellingORmodeling)AND(dynamic*ORtransmi*ORmathematical))AND(coexist*ORintermediate).Thisyielded93papers(SupplementaryMaterial).Weincludedallpaperscontainingadynamichost-to-hostpathogentransmissionmodelanalysingbothsensitiveandresistantstrainswithstablecoexistenceasanoutcomeofthemodel.Fromthe11studiesmeetingthiscriterion,weidentifiedsevenuniquemechanisms.Fouroftheseweruledoutbecauseofimplausibilityorbecausepreviousworkshowsthatthemechanismdoesnotbringaboutsubstantialcoexistence,leavingfourmechanisms(Table1).Modelframework.Weanalysetheevolutionofantibioticresistancebytrackingthetransmissionofresistantandsensitivebacterialstrainsamonghostsinapopulationusingordinarydifferentialequations.Inasimplemodel,hostscaneitherbenon-carriers(X),carriersofthesensitivestrain(S),orcarriersoftheresistantstrain(R).Modeldynamicswithinacountryarecapturedby dS/dt=λSX–(u+τ)S dR/dt=λRX–uR X=1–S–R, (1)whereλS=βS+ψ(1–ρ)istheforceofinfectionofthesensitivestrain,λR=β(1–c)R+ψρistheforceofinfectionoftheresistantstrain, βisthetransmissionrate,cisthetransmissioncostofantibioticresistance,uistherateofnaturalclearance,τisthetreatmentrate,ψistherateofimportation,andρisthefractionofimportedstrainsthatareresistant.Themodelswecompareinthispaperextendthissimplemodel.The“within-hostcompetition”models(25)allowhoststocarryamixofbothstrains.Hostscancarrythesensitivestrainwithasmallcomplementoftheresistantstrain(SR)ortheresistantstrainwithasmallcomplementofthesensitivestrain(RS).Dynamicswithinacountryare dS/dt=λSX–(u+τ)S–kλRS+b0bSR dSR/dt=kλRS–(u+τ)SR+bRS–b0bSR dRS/dt=kλSR–(u+τ)RS–bRS dR/dt=λRX–uR–kλSR+τ(SR+RS) X=1–S–R–SR–RS, (2)


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whereλS=β(S+SR)+ψ(1–ρ)istheforceofinfectionofthesensitivestrain,λR=β(1–c)(R+RS)+ψρistheforceofinfectionoftheresistantstrain,kistherateofco-colonisationrelativetoprimarycolonisation,bisthewithin-hostgrowthbenefitofsensitivity,andb0istherateoftheSR→StransitionrelativetotheRS→SRtransition.“Within-hostcompetitionA”assumesthecostofresistanceisincurredbyreducedtransmissionpotential(b=0andc>0),while“Within-hostcompetitionB”assumesthatthecostofresistanceisincurredthroughdecreasedwithin-hostgrowth(b>0andc=0).The“Diversesubtypes”modelextendsthesimplemodel(eq.1)bystructuringthepathogenpopulationintoDdifferent“D-types”(weassumeD=25),eachwithadifferentnaturalclearancerate,whereeachtypeiskeptcirculatingbydiversifyingselectionactingonD-type(34).Dynamicswithinacountryare dSd/dt=qdλS,dX–(ud+τ)Sd dRd/dt=qdλR,dX–udRd X=1–Σd(Sd+Rd) (3)whereλS,d=βSd+ψ(1–ρ)/DistheforceofinfectionofthesensitivestrainofD-typed,λR,d=β(1–c)Rd+ψρ/DistheforceofinfectionoftheresistantstrainofD-typed,𝑞" =(1 − '()*(

∑ ,'-)*-.-+ 0

1)3isthestrengthofdiversifyingselectionforD-type𝑑 ∈ {1,2, … , 𝐷}

and𝑢" = 𝑢 >1 + 𝛿 @2 "A01A0

− 1BCistheclearancerateforD-typed(34).

Finally,the“Treatmentvariation”modelextendsthesimplemodel(eq.1)bystructuringthepopulationintomultiplesubpopulationsthatexhibitdifferentratesofantibiotictreatmentandmakecontactwitheachotheratunequalrates(21,26,27,38).Ineachcountry,wemodelNrepresentativesubpopulationsindexedby𝑖 ∈ {1,2, … , 𝑁},whereweassumeN=10.Dynamicswithinacountryare dSi/dt=λS,iX–(u+τi)S dRi/dt=λR,iX–uR Xi=1–Si–Ri (4)whereλS,i=β(ΣjwijSj)+ψ(1–ρ)istheforceofinfectionofthesensitivestraininsubpopulationi,λR,i=β(1–c)(ΣjwijSj)+ψρistheforceofinfectionoftheresistantstraininsubpopulationi,andwijisthe“whoacquiresinfectionfromwhom”matrix,capturingtherelativerateofcontactbygroup-iindividualstogroup-jindividuals.Weassumethatwij=g+(1–g)/Nwheni=j,andwij=(1–g)/Nwheni≠j,suchthatgistheassortativityofsubpopulations.Finally,weassumethattreatmentratesofsubpopulationswithinacountryapproximatelyfollowagammadistributionwithshapeparameterκandmeantreatmentrateτ.Accordingly,therateofantibioticconsumptioninsubpopulationiis


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𝜏G = ∫ 𝑡𝑃K(𝑡|𝜅)𝑑𝑡NO@

PQ|RB

NO@PSTQ |RB

,where𝑄K(𝑞|𝜅)isthequantileqofthegammadistribution

withshape𝜅and𝑃K(𝑡|𝜅)istheprobabilitydensityattofthesamegammadistribution.Dataandmodelfitting.Weextractedcommunitypenicillinconsumptionandpenicillinnon-susceptibilityinS.pneumoniaeinvasiveisolatesfromdatabasesmadeavailablebytheECDC(13,43).Weusedatafrom2007,becausechangesinpneumococcalresistancereportingstandardsforsomecountriesafterthisyearhamperthecomparabilityofECDCdatapoints.Weassumethatcommunitypenicillinconsumptiondrivespenicillinresistance,thatantibioticconsumptionisindependentofwhetheranindividualiscolonisedbypneumococcus,andthatresistanceamonginvasivebacterialisolatesisrepresentativeofresistanceamongcirculatingstrainsmorebroadly.Countriesreportcommunitypenicillinconsumptionindefineddailydoses(DDD)perthousandindividualsperday.Totransformthisbulkconsumptionrateintotherateatwhichindividualsundertakeacourseofantibiotictherapy,weanalysedprescribingdatafromeightEuropeancountries,estimatingthat5DDDinthepopulationatlargecorrespondtoonetreatmentcourseforachildunder5yearsofage.OurmodelframeworktrackscarriageofS.pneumoniaeamongchildrenaged0-5years,theagegroupdrivingbothtransmissionanddisease.InEuropeancountries,weassumethattheprevalenceofpneumococcalcarriageinunder-5sis50%(11,26)andtheaveragedurationofcarriageis47days(52,53).WecalculatetheaverageincidenceofS.pneumoniae-causedseverepneumoniarequiringhospitalisationas610permillionchildrenunder5peryear(51)acrosstheEuropeancountriesinourdataset.Tomatchmodelpredictionstoahigh-burdensetting,weincreasethedurationofcarriageto71.4days;increasethetransmissionratebyafactorof3.61(Within-hostcompetitionA),3.20(Within-hostcompetitionB),3.62(Diversesubtypes),or3.49(Treatmentvariation)sothatcarriageprevalencereaches90.0%;andincreasetheantibioticconsumptionrateto1.138,5.887,1.458,or1.670coursesperpersonperyear,respectively,sothatresistanceprevalencereaches81.4%.SeeSupplementaryMaterialfordetailsofcalculationsrelatingtopneumococcalcarriageanddisease.WeuseBayesianinferenceviadifferentialevolutionMarkovchainMonteCarlo(54)toidentifymodelparametersthatareconsistentwithempiricaldata.Countrymhasantibiotictreatmentrateτmandreportsrmofnmisolatesareresistant.OverallMcountries,thesedataaredenoted𝜏 = (𝜏0, 𝜏V, … , 𝜏W),𝑟 = (𝑟0, 𝑟V, … , 𝑟W),and𝑛 =(𝑛0, 𝑛V, … , 𝑛W),respectively.Theprobabilityofagivensetofmodelparameters𝜃isthen

𝑃(𝜃|𝜏, 𝑟, 𝑛) ∝ 𝑃(𝜏, 𝑟, 𝑛|𝜃)𝑃(𝜃),

where𝑃(𝜃)isthepriorprobabilityofparameters𝜃and


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𝑃(𝜏, 𝑟, 𝑛|𝜃) = 𝐶,𝑌 = 𝑌(𝜏|𝜃).^𝑅,𝑟 = 𝑟 , 𝑛 = 𝑛`, 𝜌 = 𝜌(𝜏`|𝜃).bc/be

W

`f0

.

isthelikelihoodofdata𝜏, 𝑟, 𝑛givenmodelparameters𝜃.Above,𝑌(𝜃)istheaveragemodel-predictedprevalenceofcarriageacrossallcountriesand𝜌(𝜏`|𝜃)isthemodel-predictedresistanceprevalenceforcountrym.C(Y)isthecredibilityofprevalenceofcarriageYandR(r,n,ρ)isthecredibilityofroutofnisolatesbeingresistantwhenthemodel-predictedresistanceprevalenceisρ.ForC(Y),weuseanormaldistributionwithmean0.5andstandarddeviation0.002.ForR(r,n,ρ),weuse𝑅(𝑟, 𝑛, 𝜌) = ∫ 𝑇,𝑥|𝜇 =0

k

𝜌, 𝜎 = 𝜎(𝜃).,mn.𝑥n(1 − 𝑥)mAn𝑑𝑥,abinomialdistributionwheretheprobabilityof

successismodelledasa[0,1]-truncatednormaldistributioncentredonρandwithstandarddeviationσ.Theparameterσcapturestheunexplainedbetween-countryvariationinresistancefrequency.Here,𝑇(𝑥|𝜇, 𝜎) = o(p|q,r)

,s(0|q,r)As(k|q,r).,where𝜑(𝜇, 𝜎) =

0√Vvrw

𝑒𝑥𝑝 @− (pAq)w

VrwBistheuntruncatednormalPDFand𝛷(𝜇, 𝜎) = 0

V(1 + 𝑒𝑟𝑓 @pAq

r√VB)is

theuntruncatednormalcumulativedistributionfunction.Finally,Nmisthepopulationsizeofcountrymand𝑁eistheaveragepopulationsizeacrossallcountries;theexponent𝑁`/𝑁eallowsustoweighttheimportanceofeachcountrybyitspopulationsize,whichallowsacloserfitwiththeoverallresistanceprevalenceacrossallcountries.Weadopt𝑐 ∼ 𝐵𝑒𝑡𝑎(𝛼 = 1.5, 𝛽 = 8.5),𝑏 ∼ 𝐺𝑎𝑚𝑚𝑎(𝜅 = 2, 𝜃 = 0.5),𝛽 ∼ 𝐺𝑎𝑚𝑚𝑎(𝜅 =5, 𝜃 = 0.35),𝑘 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(𝜇 = 1, 𝜎 = 0.5),𝑎 ∼ 𝐺𝑎𝑚𝑚𝑎(𝜅 = 2, 𝜃 = 5),𝛿 ∼ 𝐵𝑒𝑡𝑎(𝛼 =20, 𝛽 = 25),𝑔 ∼ 𝐵𝑒𝑡𝑎(𝛼 = 10, 𝛽 = 1.5),and𝜅 ∼ 𝐺𝑎𝑚𝑚𝑎(𝜅 = 4, 𝜃 = 2)asweaklyinformativepriordistributionsformodelfitting.Wesettheunexplainedbetween-countryvariationinresistancefrequencyσto0.06acrossallmodelsbasedonapreliminaryroundofmodelfittingwithσasafreeparameter,andsettherateofimportationψto0.0075permonthbasedonratesoftravelwithintheEU.SeeSupplementaryMaterialforMCMCdiagnostics.Interventions.Interventionshavethefollowingimpactonmodelparameters:fortheacquisition-blockingvaccine,thetransmissionratebecomesβ′=(1–εa)β;fortheclearance-acceleratingvaccine,theclearanceratebecomesu′=u/(1–εc);andunderantibioticstewardship,theaveragetreatmentrateincountrymbecomesτm′=τm(1–εs).

Acknowledgements

N.G.D.,M.J.andK.E.A.werefundedbytheNationalInstituteforHealthResearchHealthProtectionResearchUnitinImmunisationattheLondonSchoolofHygieneandTropicalMedicineinpartnershipwithPublicHealthEngland.TheviewsexpressedarethoseoftheauthorsandnotnecessarilythoseoftheNHS,NationalInstituteforHealthResearch,


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DepartmentofHealthorPublicHealthEngland.S.F.wassupportedbyaSirHenryDaleFellowshipjointlyfundedbytheWellcomeTrustandRoyalSociety(grantnumber208812/Z/17/Z).

References1. O’NeillJ(2016)Vaccinesandalternativeapproaches:reducingourdependenceon

antimicrobialsAvailableat:http://amr-review.org/sites/default/files/Vaccinesandalternatives_v4_LR.pdf.

2. LipsitchM,SiberR(2016)HowCanVaccinesContributetoSolvingtheAntimicrobialResistanceProblem ?7(3):1–8.

3. AtkinsKE,LipsitchM(2018)Canantibioticresistancebereducedbyvaccinatingagainstrespiratorydisease?LancetRespirMed6(11):820–821.

4. SevillaJP,BloomDE,CadaretteD,JitM,LipsitchM(2018)TowardeconomicevaluationofthevalueofvaccinesandotherhealthtechnologiesinaddressingAMR.ProcNatlAcadSci115(51):12911–12919.

5. KlugmanKP,BlackS(2018)Impactofexistingvaccinesinreducingantibioticresistance:Primaryandsecondaryeffects.ProcNatlAcadSci115(51):12896–12901.

6. KyawMH,etal.(2006)EffectofIntroductionofthePneumococcalConjugateVaccineonDrug-ResistantStreptococcuspneumoniae.NEnglJMed354(14):1455–1463.

7. ThorringtonD,AndrewsN,StoweJ,MillerE,vanHoekAJ(2018)Elucidatingtheimpactofthepneumococcalconjugatevaccineprogrammeonpneumonia,sepsisandotitismediahospitaladmissionsinEnglandusingacompositecontrol.BMCMed16(1):1–14.

8. ChenC,etal.(2019)Effectandcost-effectivenessofpneumococcalconjugatevaccination:aglobalmodellinganalysis.LancetGlobHeal7(1):e58–e67.

9. WilbyKJ,WerryD(2012)Areviewoftheeffectofimmunizationprogramsonantimicrobialutilization.Vaccine30(46):6509–6514.

10. HanageWP,etal.(2010)EvidencethatpneumococcalserotypereplacementinMassachusettsfollowingconjugatevaccinationisnowcomplete.Epidemics2(2):80–84.

11. FlascheS,etal.(2011)Effectofpneumococcalconjugatevaccinationonserotype-specificcarriageandinvasivediseaseinEngland:across-sectionalstudy.PLoSMed8(4):e1001017.

12. LewnardJA,HanageWP(2019)Makingsenseofdifferencesinpneumococcalserotypereplacement.LancetInfectDis3099(18).doi:10.1016/s1473-3099(18)30660-1.

13. EuropeanCentreforDiseasePreventionandControl(2018)Antimicrobialconsumptionratesbycountry.Availableat:http://ecdc.europa.eu/en/healthtopics/antimicrobial_resistance/esac-net-database/Pages/Antimicrobial-consumption-rates-by-country.aspx.


https://doi.org/10.1101/610188

17

14. WorldHealthOrganization(2019)WHOvaccinepipelinetracker.Availableat:https://www.who.int/immunization/research/vaccine_pipeline_tracker_spreadsheet/en/[AccessedApril10,2019].

15. AtkinsKE,etal.(2018)Useofmathematicalmodellingtoassesstheimpactofvaccinesonantibioticresistance.LancetInfectDis18:e204–e213.

16. AtkinsKE,FlascheS(2018)Vaccinationtoreduceantimicrobialresistance.LancetGlobHeal6(3):e252.

17. TemimeL,GuillemotD,BoëllePY(2004)Short-andlong-termeffectsofpneumococcalconjugatevaccinationofchildrenonpenicillinresistance.AntimicrobAgentsChemother48(6):2206–2213.

18. TemimeL,BoëllePY,ValleronAJ,GuillemotD(2005)Penicillin-resistantpneumococcalmeningitis:Highantibioticexposureimpedesnewvaccineprotection.EpidemiolInfect133(3):493–501.

19. OpatowskiL,etal.(2008)AntibioticInnovationMayContributetoSlowingtheDisseminationofMultiresistantStreptococcuspneumoniae:TheExampleofKetolides.PLoSOne3(5):e2089.

20. VanEffelterreT,etal.(2010)AdynamicmodelofpneumococcalinfectionintheUnitedStates:Implicationsforpreventionthroughvaccination.Vaccine28(21):3650–3660.

21. DeCellèsMD,etal.(2015)Interactionofvaccinationandreductionofantibioticusedrivesunexpectedincreaseofpneumococcalmeningitis.SciRep5(June):1–11.

22. MitchellPK,LipsitchM,HanageWP(2015)Carriageburden,multiplecolonizationandantibioticpressurepromoteemergenceofresistantvaccineescapepneumococci.PhilosTransRSocBBiolSci370(1670):3–9.

23. ObolskiU,etal.(2018)VaccinationcandriveanincreaseinfrequenciesofantibioticresistanceamongnonvaccineserotypesofStreptococcuspneumoniae.ProcNatlAcadSci115(12):3102–3107.

24. ColijnC,etal.(2010)Whatisthemechanismforpersistentcoexistenceofdrug-susceptibleanddrug-resistantstrainsofStreptococcuspneumoniae?JRSocInterface7(47):905–919.

25. DaviesNG,FlascheS,JitM,AtkinsKE(2019)Within-hostdynamicsshapeantibioticresistanceincommensalbacteria.NatEcolEvol.doi:10.1038/s41559-018-0786-x.

26. BogaertD,etal.(2004)ColonisationbyStreptococcuspneumoniaeandStaphylococcusaureusinhealthychildren.Lancet363(9424):1871–1872.

27. AnderssonDI(2006)Thebiologicalcostofmutationalantibioticresistance:anypracticalconclusions?CurrOpinMicrobiol9(5):461–465.

28. AnderssonDI,HughesD(2010)Antibioticresistanceanditscost:Isitpossibletoreverseresistance?NatRevMicrobiol8(4):260–271.

29. TedijantoC,OlesenS,GradY,LipsitchM(2018)Estimatingtheproportionofbystanderselectionforantibioticresistanceamongpotentiallypathogenicbacterialflora.ProcNatlAcadSciUSA115(51):E11988–E11995.


https://doi.org/10.1101/610188

18

30. LipsitchM,ColijnC,CohenT,HanageWP,FraserC(2009)Nocoexistenceforfree:Neutralnullmodelsformultistrainpathogens.Epidemics1(1):2–13.

31. HastingsIM(2006)Complexdynamicsandstabilityofresistancetoantimalarialdrugs.Parasitology132(5):615–624.

32. BeamsAB,TothDJA,KhaderK,AdlerFR(2016)Harnessingintra-hoststraincompetitiontolimitantibioticresistance:mathematicalmodelresults.BullMathBiol78(9):1828–1846.

33. SergeevR,ColijnC,CohenT(2011)Modelstounderstandthepopulation-levelimpactofmixedstrainM.tuberculosisinfections.JTheorBiol280(1):88–100.

34. LehtinenS,etal.(2017)Evolutionofantibioticresistanceislinkedtoanygeneticmechanismaffectingbacterialdurationofcarriage.ProcNatlAcadSci114(5):1075–1080.

35. BlanquartF,LehtinenS,LipsitchM,FraserC(2018)Theevolutionofantibioticresistanceinastructuredhostpopulation.JRSocInterface15(143).doi:10.1098/rsif.2018.0040.

36. KriegerMS,HillAL(2018)Long-termcoexistenceandregionalheterogeneityofantibiotic-resistantinfectionsreproducedbyasimplespatialmodel.bioRxiv14:469171.

37. KouyosR,KleinE,GrenfellB(2013)Hospital-CommunityInteractionsFosterCoexistencebetweenMethicillin-ResistantStrainsofStaphylococcusaureus.PLoSPathog9(2).doi:10.1371/journal.ppat.1003134.

38. BoniMF,FeldmanMW(2006)EvolutionofAntibioticResistanceByHumanandBacterialNicheConstruction.Evolution(NY)59(3):477.

39. AustinDJ,KristinssonKG,AndersonRM(1999)Therelationshipbetweenthevolumeofantimicrobialconsumptioninhumancommunitiesandthefrequencyofresistance.ProcNatlAcadSci96(3):1152–1156.

40. GræsbøllK,NielsenSS,ToftN,ChristiansenLE(2014)Howfitnessreduced,antimicrobialresistantbacteriasurviveandspread:Amultiplepig-multiplebacterialstrainmodel.PLoSOne9(7).doi:10.1371/journal.pone.0100458.

41. RodriguesP,GomesMGM,RebeloC(2007)Drugresistanceintuberculosis-areinfectionmodel.TheorPopulBiol71(2):196–212.

42. Patterson-LombaO,AlthouseBM,GoergGM,Hébert-DufresneL(2013)OptimizingTreatmentRegimestoHinderAntiviralResistanceinInfluenzaacrossTimeScales.PLoSOne8(3):1–11.

43. EuropeanCentreforDiseasePreventionandControl(2016)DatafromtheECDCSurveillanceAtlas-Antimicrobialresistance.Availableat:https://ecdc.europa.eu/en/antimicrobial-resistance/surveillance-and-disease-data/data-ecdc[AccessedFebruary24,2018].

44. GoossensH,FerechM,VanderSticheleR,ElseviersM(2005)OutpatientantibioticuseinEuropeandassociationwithresistance:Across-nationaldatabasestudy.Lancet365(9459):579–587.

45. CobeyS,LipsitchM(2012)Nicheandneutraleffectsofacquiredimmunitypermitcoexistenceofpneumococcalserotypes.Science(80-)335(6074):1376–1380.


https://doi.org/10.1101/610188

19

46. JochemsSP,WeiserJN,MalleyR,FerreiraDM(2017)Theimmunologicalmechanismsthatcontrolpneumococcalcarriage.PLoSPathog13(12):1–14.

47. SmieszekT,etal.(2018)PotentialforreducinginappropriateantibioticprescribinginEnglishprimarycare.JAntimicrobChemother73(Suppl2):ii36-ii43.

48. UKDepartmentofHealthandSocialCare(2019)Tacklingantimicrobialresistance2019to2024:theUK’s5-yearnationalactionplanAvailableat:https://www.gov.uk/government/publications/uk-5-year-action-plan-for-antimicrobial-resistance-2019-to-2024.

49. KobayashiM,etal.(2017)Pneumococcalcarriageandantibioticsusceptibilitypatternsfromtwocross-sectionalcolonizationsurveysamongchildrenaged<5yearspriortotheintroductionof10-valentpneumococcalconjugatevaccine-Kenya,2009-2010.BMCInfectDis17(1):1–12.

50. LipsitchM,etal.(2012)EstimatingratesofcarriageacquisitionandclearanceandcompetitiveabilityforpneumococcalserotypesinKenyawithaMarkovtransitionmodel.Epidemiology23(4):510–519.

51. RudanI,etal.(2013)Epidemiologyandetiologyofchildhoodpneumoniain2010:estimatesofincidence,severemorbidity,mortality,underlyingriskfactorsandcausativepathogensfor192countries.JGlobHealth3(1):S114-010401.

52. MelegaroA,GayNJ,MedleyGF(2004)Estimatingthetransmissionparametersofpneumococcalcarriageinhouseholds.EpidemiolInfect132(3):433–441.

53. HögbergL,etal.(2007)Age-andserogroup-relateddifferencesinobserveddurationsofnasopharyngealcarriageofpenicillin-resistantpneumococci.JClinMicrobiol45(3):948–952.

54. TerBraakC(2006)AMarkovChainMonteCarloversionofthegeneticalgorithmDifferentialEvolution:EasyBayesiancomputingforrealparameterspaces.StatComput16(3):239–249.


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