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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.
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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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14
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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15
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,
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
16
DepartmentofHealthorPublicHealthEngland.S.F.wassupportedbyaSirHenryDaleFellowshipjointlyfundedbytheWellcomeTrustandRoyalSociety(grantnumber208812/Z/17/Z).
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