Seven challenges in modelling pathogen dynamics within host and across scales

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Original citation:

Gog, Julia R., Pellis, Lorenzo, Wood, James L.N., McLean, Angela R., Arinaminpathy,

Nimalan and Lloyd-Smith, James O.. (2015) Seven challenges in modelling pathogen

dynamics within-host and across scales. Epidemics, Volume 10 . pp. 45-48. ISSN

1755-4365

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ContentslistsavailableatScienceDirect

Epidemics

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

Seven

challenges

in

modeling

pathogen

dynamics

within-host

and

across

scales

Julia

R. Gog

a,b,∗

_,

_Lorenzo

_Pellis

c

_,

_James

_L.N.

_Wood

a,d

_,

_Angela

_R.

_McLean

e

_,

Nimalan

Arinaminpathy

f

_,

_James

_O.

_Lloyd-Smith

a,g

a_Fogarty_{International}_Center,_National_Institutes_of_Health,_Bethesda,_MD_20892,_USA

b_Department_of_Applied_Mathematics_and_Theoretical_Physics,_Centre_for_Mathematical_Sciences,_University_of_Cambridge,_Cambridge_CB3_0WA, UnitedKingdom

c_Warwick_Infectious_Disease_Epidemiology_Research_Centre_(WIDER)_and_Warwick_Mathematics_Institute,_University_of_Warwick,_Coventry_CV4_7AL, UnitedKingdom

d_Disease_Dynamics_Unit,_Department_of_Veterinary_Medicine,_University_of_Cambridge,_Cambridge_CB3_0ES,_United_Kingdom e_Department_of_Zoology,_Oxford_Martin_School,_University_of_Oxford,_South_Parks_Road,_Oxford_OX1_3PS,_United_Kingdom

f_Department_of_Infectious_Disease_{Epidemiology,}_School_of_Public_Health,_Imperial_College_London,_Exhibition_Road,_London_SW7_2AZ,_United_Kingdom g_Department_of_Ecology_and_Evolutionary_Biology,_University_of_California,_Los_Angeles,_CA_90095,_USA

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received11March2014 Receivedinrevisedform 19September2014 Accepted21September2014 Availableonline30September2014

Keywords:

Within-host Multiplescales Superinfection Transmissionbottlenecks Deep-sequencing

a

b

s

t

r

a

c

t

Thepopulationdynamicsofinfectiousdiseaseisamaturefieldintermsoftheoryandtosomeextent, application.Howeverformicroparasites,thetheoryandapplicationofmodelsofthedynamicswithin asingleinfectedhostisstillanopenfield.Further,connectingacrossthescales–fromcellulartohost level,topopulationlevel–haspotentialtovastlyimproveourunderstandingofpathogendynamicsand evolution.Here,wehighlightsevenchallengesinthefollowingareas:transmissionbottlenecks, hetero-geneitywithinhost,dynamicfitnesslandscapeswithinhosts,makinguseofnext-generationsequencing data,capturingsuperinfectionandwhenandhowtomodelmorethantwoscales.

Introduction

Drivenbynewdatasourcesandnewquestions,modelersare increasingly tryingtolinkwithin-hostdynamicsto population-leveldynamicsusingcross-scalemodels.Thisisatime-honored traditioninmacroparasitemodels,wherethelinkbetween within-hostparasiteabundanceand transmissibilitycannotbeignored, butitismuchlesswell-developedformicroparasites.Herewe out-linesomeofthecurrentandfuturechallengesinwithin-hostand cross-scalemodeling ofmicroparasites.Weare focusingin par-ticularonthewithin-hostquestionsthatmayinformcross-scale dynamics.

∗_{Corresponding}_author_at:_Department_of_Applied_Mathematics_and_Theoretical

Physics,CentreforMathematicalSciences,UniversityofCambridge,CambridgeCB3 0WA,UnitedKingdom.Tel.:+441223760429.

E-mailaddress:[email protected](J.R.Gog).

1. Newmodelsandnewdatatoelucidatetheprocesses

underlyingtransmissionprobabilitiesandbottlenecks

Transmissionisthedeﬁningcharacteristicofinfectiousdiseases, andisthefundamentalpointofcontactbetweenwithin-hostand population-scalemodels.Despiteconsiderableattentioninrecent years,therearemajoroutstandingchallengesinlinking within-hostdynamicstoprobabilitiesoftransmission,andunderstanding

howtransmissioneventsseedthedynamicsinanewlyinfected

host.

Focusing ﬁrst on the donor host, how does infectiousness

(interpretedas probabilityof infectiongiven acontact) depend onpathogen load? This relationshipis crucial tolinking scales but as yet little understood. The experimental literature gives

some insight from dose–response experiments with particular

pathogens,butoftenaninsufﬁcientcontextisgivenfor general-ization,combinedwithroutesofexposurethatdonotrepresent whathappensnaturally(e.g.,virusinjectedundertheskinrather thanintranasalexposureforrespiratorypathogens)limitutility. Experimentaltransmissionstudiesinquasi-naturalsettingssuch

http://dx.doi.org/10.1016/j.epidem.2014.09.009

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46 J.R.Gogetal./Epidemics10(2015)45–48

ascontacttransmissionofmammalianinﬂuenzaofferclear poten-tialtoenrichourunderstanding,ifappropriatemeasuresofviral loadaretaken(Imaietal., 2012;Murcia etal., 2010).Valuable insightshavebeengainedfromstudiesofHIV-1indiscordant cou-ples(Grayetal.,2001),butitisnotclearthatthesecanbeappliedto acuteinfectionsordifferenttransmissionroutes.Overall,itwould bedesirabletoidentifyclassesoffunctionalrelationships–andto understandwhenandwhytheserelationshipsapply.Thisrequires considerationofhowpathogenloadinthesampledbodysitelinks topathogenexcretionbytherelevantroute(s), andthenhow a givenexcretedloadrelatestotheprobabilityofestablishinganew infection.

Next,focusingontherecipienthost,initialinfectionisan inva-sionprocessacrossparticularcellandtissuetypes,dependingon thepathogen.Thepathogenpopulationisseededbyagivendose, routeoftransmissionandperiodoverwhichexposureoccurs.Here, stochasticandspatialinvasionmodelsmayofferinsightinto

impor-tantmechanisms of establishment,and couldbe usedto make

inferencefromavailabledata.Detailedspatialknowledgeof infec-tioninitiationinvivomaybeﬁrmlyoutofreachformostsystems,

butinsightsmaybegained frominvitroexperimentscombined

withstochasticspatialmodels(Howatetal.,2006).Anexample ofabasicquestioniswhethertheinfectiousparticlesinagiven doseoperateindependentlyfromoneanother,suchthattheeffect ofdoseiseasilycalculatedfromprobabilistic considerations,or whethersomeinteractionsarisethroughcooperativity,local sat-urationofimmuneresponseortargetcells,orothermechanisms (Woodetal.,2014;Zwartetal.,2009).Anotherexample:invasion modelscouldhelpinunderstandingthebasisforthe phylogenet-icallyderivedresultthatmostHIV-1infectionsarefoundedbya singlevirus(Keeleetal.,2008).Isthisbecauseinfectioneventsare veryrareorbecauseoneofmanyinfectinglineageswinsoutin earlycompetition?

Alloftheseprocessesconvergetodeterminetheprobabilityof infectionandthenumberanddiversityofpathogenparticles trans-ferredtothenewlyinfectedhost,i.e.,thetransmissionbottleneck. Thetransmissionbottleneckisvitaltocouplingwithin-host mod-elstobetween-hostmodels,whichwillbeparticularlyimportant

whenconsideringpathogenevolutionarydynamics.

Mathematicalandcomputationalmodelsmayalsoplayarole indesigningexperimentstoexplorebottlenecks.Infection experi-mentsbothinvitroandinvivoareoftenchallengingandthenumber ofreplicatesmaybelimited,soitcanbeextremelyvaluabletouse modelsinadvancetohelpplanthemostinformativeapproaches. Forexample,intransmissionexperimentsinvolvinginfectionwith isogenictaggedpathogens(Cowardetal.,2008),modelscanmake useofpreliminarydataandassumptionstosuggesttherangeof doses,mixofstrainsandsamplingtimestogainthemost informa-tiononthesizeofthebottleneck.

2. Heterogeneitywithinasinglehost

Manywithin-hostmodelstreatthehostasasinglepopulation oftargetcellswithoutanystructure,asifwearewell-mixed uni-formcellcultures.Thisisobviouslynotthecaseinpractice,and heterogeneitiesincelltype,celldemography,immuneresponse, andthespatialstructureofthehostwillallplayimportantrolesin shapingthedynamicsofinfection.Likepopulationecology,while

thehomogeneousmodelscomeﬁrstandrevealmanykeyideas,

moredetailedmodelsarelesstractablebutforsomephenomena mayproveessentialinunderstandingthefulldynamics.

Weknowfrompopulationdynamicsthatspatialstructurecan

fundamentally change the range of possible system behaviors

(Bolkerand Grenfell,1995).For awithin-hostmodel,spacecan beanythingfromhost-scale,e.g.,a metapopulationwhere sites aredifferentorgans,downtoﬁnecell-to-celltransmission,e.g.,a

latticeofepithelialcells.ForexampleininﬂuenzaAinmammals, infection dynamics mayinvolve small distinct foci of infection in the respiratory epithelium (Saenz et al., 2010). Broad-brush non-spatialcompartmentalmodelsmaybesuccessfulincapturing

generaldynamics when thebiological readouts for comparison

arethemselvesbroad,suchasantibodylevelsintheblood(Handel etal.,2010).Howeverthespatialorganizationoftherespiratory systemmustbemodeledtounderstandtheselectivepressureson thevirusfromtissuetropismand hence,crucially,transmission ratesbetweenhosts(Reperantetal.,2012).Studyofchronicviruses fromHIV-1(Sanjuánetal.,2004)toPlumpox virus(Jridietal., 2006)hasrevealedpopulationgeneticstructureamongdifferent

tissuecompartments; therearemany openquestions regarding

how such structure inﬂuences transmission and evolutionary

dynamics,acrosspathogenandhosttypes.

Whiletheimpactofthepathogenonthehostcellpopulationis usuallyconsidered,theeffectofthehostcelldemographicsonthe

pathogendynamicsareoftenoverlooked,againincommonwith

populationdynamics.Thismaybeascellulardynamics(otherthan thosedrivendirectlybyinfection)areassumedtobeirrelevanton thetimescalesconsidered,ortoohardtocaptureintermsof math-ematicaltractabilityorlackofsuitableparameterization,oreven thelackofknowledgeofaplausibleformofthedynamics. How-everagainthereareknownexampleswheredetailsoftargetcell demographyshapespathogendynamics.Forexample,the recruit-mentrateofredbloodcellsisacrucialdriverofmalariaparasite abundance(Metcalfetal.,2011).Forchronicviralinfections,the probabilityofdenovodrugresistancedepends ontheinterplay

betweenappearanceofnewresistantmutantsandtimeneeded

forhostcellregrowth(AlexanderandBonhoeffer,2012).

Theissueofhowmuchdetailoftheimmunesystemtoinclude ismorespeciﬁctocurrent within-hostmodelsofinfection.Any

attempttoconstructacomprehensivemodelofallknown

vari-etiesofimmunecells,secretedproteinsandsignalingmolecules, aswellastheimmunodynamicsoftargetcells,willbecertainly

doomed:themodelswillbeintractable,unparameterisableand

almostcertainlywillmisrepresentsomeimmunologicalsubtleties. Conversely, entirely neglecting any form of adaptive or innate immunity(asisoftendoneinwithin-hostmodels)maybe appro-priateforsomequestionsandapplications,butoftenthecoreof within-hostinfectionkineticsisfoundinthedynamicinterplay betweenthepathogenandtheimmunesystem.Thisismost appar-entinchronicinfectionssuchasHIV(NovakandMay,1991)but eveninacuteinfections,ignoringanyformofdynamicimmunity cangivemisleadingresults,suchasinfectionsonlybeingresolved bytotaltargetcelldepletion(Saenzetal.,2010).Whencanthe

immunesystembemodeledinasimplewaysuchastargetcells

beingabletomoveintoaprotectedantiviralstate,andwhendo

weneedtograpplewithfullerdetailofimmunedynamics?Are

theregeneralitieshere,perhapsaccordingtotimescale,pathogen type,orsomethingelse?

3. Dynamicﬁtnesslandscapes

A‘fitnesslandscape’isessentiallyamappingfromapathogen’s genotype,toitsreproductivephenotype.Here,‘fitness’canbeseen eitherinreplicationterms(within-host)orasatransmissionfitness (atthepopulationlevel).Fitnesslandscapesareimportantdrivers ofnaturalselection:anunderstandingofhowandwhytheycome aboutwouldthereforeplayanimportantroleinunderstandingthe forcesshapingpathogenevolution.Theseideasarecloselylinked withissuesdescribedinchallenge2,above,butoverthecourseof infectionthelandscapechanges,hencedynamicfitnesslandscapes.

Current models of within-host evolution typically operate

on a genotype space, adopting simpliﬁed scenarios for the

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valley’ scenarios. However, there remains a need to address importantcaseswhereﬁtnesslandscapeschangeovertime:akey examplebeingevolutionforimmuneescape.ForHIV,replication ﬁtnesslandscapeschangeontimescalesshorterthantheinfectious periodofthevirus(daSilvaetal.,2010).Meanwhile,theevolution

of humaninﬂuenza is clearly shaped by populationimmunity,

butthereareindicationsthattheimmunitybuiltupoverahost’s lifetimeismorecomplexthanisoftenassumed(Lessleretal.,2012). Modelingtheselandscapesintheirfullmechanisticdetailwould arguablybeneitherfeasiblenorhelpful, giventheprohibitively highdimensionalityoftheimmunological,virologicalandgenetic spacesinvolved(Kouyosetal.,2012).Therefore,akeychallenge willbetonarrowthisspacetomoremanageableproportions(e.g., assuggestedinBedfordetal.,2012).Couldtransmissionﬁtness landscapeseverbestudiedinalaboratorysetting?Theabilityto dosowouldgenerateawealthofbiologicaldatafor understand-ingtheselandscapes,e.g.,underdifferentconditionsofimmunity. Achievingbettercorrelatesoftransmission(seechallenge1,above) couldpavethewayforsuchexperimentalapproachesinfuture.

4. Interfacingmodelswithdeep-sequencingdata

Empiricalstudieshave demonstratedfor both acute(Murcia etal.,2010;Hughesetal.,2012)andchronicinfections(hepatitisC, HIV,SIV),thatthereismassivegeneticvariationofviralpathogens withininfectedhosts.Recentevidenceshowsthatthisistruefor

Plasmodiumaswell(Manskeetal.,2012).Insomecasesthisgenetic diversityistransmitted,andinothercasesitisnot,sothe bottle-neckwidthisitselfnotconstant.Alsointerestingisthespeedat whichthemostcommonvariant,ortheconsensuspathogenvariant canestablishitselfwithin-andthenbetween-hosts.ForHIV,these processesmaytakedaysorweeks,whereasverylimiteddatafor mammalianinﬂuenzasuggestthatthiscanhappenin24h(Murcia etal.,2010).Theimplicationsofthisforscalingfromwithinhost,to betweenhost,toglobalphylogeniesremainessentiallyunexplored. Quantitativemethodshavebeenestablishedforepidemiclevel, orgloballevelphylogeneticdata,typicallybasedaroundconsensus sequenceofpathogens,andsomemethodsalsoexistforthecontact tracinganalysisofwellsampledepidemics,butthereseemtobeno wellestablishedmethodsforanalysisofpathogendeepsequence datathatusetherichnessofdeepsequencedatatoallowinference abouttheepidemicandevolutionarycharacteristicsofthe trans-missionprocessinquestion.Thisshouldbeamassivefrontierfor within-hostmodeling,sinceinprinciplethedataprovideanewand

higher-resolutionwindowintowithin-hostandindeed

between-hostdynamics.Buthowshouldwejudgewhichapparentsignals

canbetrusted(McKinleyetal.,2011)?Whatarerobustsignalsthat canbeextracted?Howshouldthesehugelyhigh-dimensionaldata berepresentedinmodels?Whatarethegeneralitieshere?Further deepsequencingdatawillsurelychallengeourunderstandingas weseenewpatternswhichdonotﬁtourcurrenttheory.

5. Whenandhowtomodelsuperinfection

Superinfectionisdefinedastheintroductiontoahost,afteran infectionthathastriggeredsomeimmuneresponse,ofasecond (heterologous)strain(Smithetal.,2005).Ignoringsuperinfection greatlysimplifiesmodelanalysisasitallowsamodeling frame-workbasedontheconceptoftime-since-infection,whichallows theapplicationofthewell-developedtheoryofnext-generation matricestothestudyofendemicequilibria(Lythgoeetal.,2013) andepidemicfinalsize.

Itremainsunclear,however,whenneglectingsuperinfectionis avalidapproximationandwhatitsimplicationsare.Superinfection is knowntooccurin HIVinfections, where it couldpotentially

increase viralloadand hasten progressiontoAIDS(Korenromp et al., 2009), although biological mechanistic explanations and reliablequantiﬁcationarestilllacking.Highentomological inoc-ulationratestypicalofmalariasuggestopportunitiesformultiple infections, which canaffect within-hoststrain competitionand alterdynamicsandoutcome.InthecaseofTB,thereisanongoing debateaboutrelative importanceof reinfection versus reactiva-tion,butperhapsmodelingwillhelpdisentangletheseprocesses (Gomesetal.,2012).

Inaddition,evenincontextswheresuperinfectionisshownto bevitaltounderstandingtheobserveddynamics,thechallenge wouldremainofhowtoinfersuperinfectionratesfromobtainable data.Thegrowingbodyofsequencedata(bothacrosshostsandin deepsequencingwithinasinglehost)mayopenthepossibilityof inferringrecombinationandreassortmentrates,though elucidat-inghowtheyconnecttosuperinfectionratesstillremainsanopen challenge.

6. Whentousemorethantwoscales

While thebottleneckof transmissionnaturally distinguishes

within-andbetween-hostdynamics,itmustberecognizedthat

bothofthesescalesinvolvefurthernestedlevelsoforganization, e.g.,fromcelltotissuetohost,orfromhouseholdtocitytocountry (seeotherpapersinthisissue).

Multi-scalemodelsatthepopulationlevelarecommon,mostly becauseoftheclearimpactofspatialheterogeneityinhumanand animal populationondiseasespread (seeBall et al.,2015)and because datacan becollected relatively easily.However, these modelsgenerallyignorethewithin-hostcomponents.

On the other hand, within-host multi-scale models are less

commonmostly becausesolittlehasbeenmeasuredregarding

between-cellororganinfectionratesinvivo.However, microbiolo-gistsandvirologistshavewell-resolvedunderstandingofmanykey processesatcellularscales,suchasgenomereplicationorvirion

assembly, andif wehopetodevelop moremechanistic models

ofhowgeneticdiversityisgeneratedthenwewillneedto con-sidermolecularinteractions.Thereisaneedtosynthesizethese processes(e.g.,modelingthecellcycleofavirus)tounderstand whetheroursimplerrepresentationsareaccurateenough(Loverdo et al., 2012).To do this, there is an important needfor highly resolvedempiricaldataaboutthedynamicsofcellular-scale pro-cesses.

Somemodelsinvolvingmore thantwoscalesexist(Metzger etal.,2011), butthis areais quiteunderdeveloped.Akey chal-lenge,incommontoanyothercaseofdramaticincreaseinmodel complexity,istounderstandwhentheinclusionofanotherscale isrelevantingainingmoreinsightorismotivatedbyasufﬁcient increaseinmodelaccuracy.Theanswertosuchaquestionisof coursedependentonthepathogenunderconsideration,thedata available,andtheparticularquestionathand.

7. Approachestolinkingprocessesacrossscales

Ingeneralwecannot(ordonotwishto)modelmulti-scale pro-cessesinfullmechanisticdetail,andevensimulatingsuchmodels

becomescomputationallyintractable.Canwecomeupwithways

ofextractingtheessenceoflower-scalemodelssothattheycan beembeddedintohigher-scale modelsefﬁciently (Mideo etal., 2008)?Whenaretheseapproachessafetouse,inthattheygive representativeresults?

One approach that has yielded success is separation of

timescales, where essentiallyseparatemodels maybe usedfor

differentscales.Forexample,embeddinga Markovchainmodel

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48 J.R.Gogetal./Epidemics10(2015)45–48

between-hosttransmissioncanhelpcaptureevolutionary dynam-icsofpathogens(Parketal.,2013):heretheseparationoftimescales isthatthefateofeachnewmutationisdeterminedbeforethenext mutationarises.Anotherexampleofawithin-andbetween-host dual-scalemodelistheapplicationtoimmunewaningand vacci-nationinmeasles(HeffernanandKeeling,2009):herethesmaller scalemodelissimpliﬁedtomakethedual-scalemodeltractable.

The challenge is to develop better methods for

incorporat-ingtwo ormorescalesintoasingleframework.Wemightlook

topopulation-level epidemiology, for example the approach of

embeddingafullsolutionforasingleseason’sinﬂuenzaepidemic intoamulti-annualmodelforpopulationdynamicsandviral evo-lution(Bonietal.,2004;AndreasenandSasaki,2006).Orwemaybe abletoadaptapproachesfromotherareasofbiologicalmodeling, forexamplecreatinga“look-up”directoryforthesmallscale

inter-actionsbetweensmallswimmingorganismstocomputationally

modelalargepopulation(Ishikawaetal.,2006).Theremaywellbe otherapproachesfromcompletelydifferentscientiﬁcareas, partic-ularlythosewhichalsohaveanextensivehistoryofmathematical modelingandalsosharetheneedtoworkwithmultiplescales, forexampleclimateandmeteorologicaldynamics.Cross-seeding acrossareasshouldyieldvaluablenewdirectionsformulti-scale modelingofwithin-hostpathogendynamics.

Summary

Clearly it is possible to incorporate more scales and ﬁner detailregardingtransmissionbottlenecks,geography,celltypes,

immunodynamics,anddemographicswithinhost.Thelargeopen

challengeistodosoinawaythatis(a)shapedbyempiricaldata,(b) consistentwithcurrentbiologicalknowledge,(c)mathematically and/orcomputationallytractable,and(d)appropriatein complex-ityforthequestionsunderinvestigation.

Acknowledgments

WewishtothankNicoleMideoforhelpfulcommentsonthis manuscript.JLS,JRGandJLNWaresupportedbytheRAPIDD

pro-gramof theScienceandTechnologyDirectorate,Departmentof

HomelandSecurityandtheFogartyInternationalCenter,National InstitutesofHealth.JLNWisalsosupportedbytheAlboradaTrust. LPissupportedbytheEngineeringandPhysicalSciencesResearch CouncilandJLSbytheNationalScienceFoundation(EF-0928690) andtheDeLogiChairinBiologicalSciences.

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