The Hidden Geometry of Complex, Network-Driven Contagion Phe(4)

SCIENCE

separatedfromthepointcloud.Symbolsizequantifiestotaltrafficpernode.(D)Alongthesamelinesasin(C),thepanelsdepictdatapairs(mF,sF)forallcountriesasoutbreakcandidatesfortheH1N1pandemicduringfourdifferentweeksofthepandemic.Asdescribedinthetext,weusedacourse-grained,country-resolutionglobalmobilitynetwork(GMNc).Althoughtheactualoutbreaklocationdoesnotseparatefromthemainpointcloudasmuchasinthesimulatedscenario,theactualoutbreaklocationisnever-thelessidentifiedasthepointwithminimumcombined(mF,sF),exceptforthelasttimeframewheretheapproachwouldidentifytheUnitedStatesasthesource.(E)Outbreakreconstructionforthe2011EHEC-HUSoutbreak,usingamodelanddataforfooddistributionamong412districtsinGermanyastheunderlyingnetwork.TheactualdistrictUelzeniscorrectlyidentifiedinallbutthelasttimewindows.Foralltimes,however,someotherlocationspossesscomparativelylowvaluesof(mF,sF)aswell.Althoughthismakesdefinitesourceidentificationdifficult,itsubstantiallyreducesthenumberofpotentialoutbreaklocations.VOL342

13DECEMBER2013

1341

RESEARCHARTICLE

Asexpected,thisisthecasefortheH1N1andSARSdatasets(Fig.4,AandB).However,thisapproachrequiresknowledgeoftheentiretimecourseoftheepidemic,e.g.,arrivaltimesatalllocations,whichistypicallynotavailableinrealsituations.Therefore,weusedanalter-nativeapproach,mathematicallysimilartosur-faceroughnesscharacterization(35),thatonlyrequiresdynamicinformationinasmalltimewindow,e.g.,onesnapshotofthespreadingpat-tern.Foreachofthepotentialcandidateoutbreaklocations,wecomputedtheeffectivedistancetothesubsetofnodeswithprevalenceaboveacertainthreshold,e.g.,theredsymbolsinthepatternsofFig.3AorFig.1B.Onthebasisofthissetofeffectivedistances(denotedbyF),wecomputethemeanmF(Deff)andstandardde-viationsF(Deff).Concentricityincreaseswithacombinedminimizationofmeanandstandarddeviation(supplementarytext).Figure4Cde-pictsthedistributionofensemble-normalizedpairs[mF(Deff),sF(Deff)]forasimulatedscenarioatfourdifferenttimes.Foralltimepoints,theactualoutbreaklocationiswellseparatedfromtheremainingpointcloudandclosesttotheorigin.Thisshowsthattheeffectivedistanceperspectiveisuniquefromtheactualoutbreaklocationandthatknowledgeofatemporalsnap-shotofthespreadingstatecombinedwithknowl-edgeoftheunderlyingmobilitynetworkisapowerfultoolforoutbreakreconstruction.Althoughourmethodworkswellforsimulation-generateddata(i.e.,diseasedynamicsgeneratedbyEq.3),realdataposeadditionalchallenges:(i)Dataaresubjecttoinaccuraciesandincomplete-nessinprevalencecounts;(ii)fluctuations,notcapturedexplicitlybyourmodel,mayplayapar-ticularroleduringtheonsetofanepidemic;and(iii)responseandmitigationmeasuresthatcanchangethetimecourseofdiseasedynamicsarenotaccountedforbyourmodel.Therefore,toassesstheapplicabilityofourapproachinarealisticcon-text,wevalidatedtheeffectivedistancemethodusingdataonthe2009H1N1pandemicandthe2011outbreakoffood-borneenterohemorrhagicEscherichiacoli(EHEC)O104:H4/HUSinGermanywith~4000casesand53deaths.AlthoughtheapplicationtotheH1N1pandemicisaproof-of-conceptapplication,asfindingthespatialoriginonacountryresolutionwasactuallynottheprob-lemthatweinvestigatedhere,reconstructingthespatialoutbreakoriginduringtheEHEC-HUSepi-demic(districtUelzeninNorthernGermany)wasnotoriouslydifficultbecauseofthespatialinco-herenceofreportedcases.FortheapplicationtoH1N1,weuseddataoftheworldwideprevalencecountbycountryinweeks14to30of2009(36).ForEHEC-HUS,weconstructedanetworkoffooddistributioninGermanyusingagravitymodelfortransportationnetworks(37).Forthespatialprevalence,weuseddataoncasecountsperdis-trictinGermany(38).

Figure4DillustratestheresultsforH1N1.InanalogytoFig.4C,weusefourdistincttimewindows(weeks24,26,27,and29).Themethod

successfullyidentifiesMexicoasthesourceofthisevent,eventhoughthetimewindowscovera2-monthperiodwhenthepandemic’speakprev-alencehadalreadyreachedabroadgeographicaldistribution(fig.S16).Onlyaslateasweek29,anothercountry(theUnitedStates)isincorrectlyidentifiedasthelikelyoutbreaklocation.

Figure4Edepictstheanalogousresultsforthe2011EHEC-HUSepidemic,wherediseasespreadingwaspromotednotbyairtransporta-tion,butbyfoodtransport.Thenodesinthenet-workare412administrativedistrictsinGermany,coupledbythefoodsupplynetworkofthecoun-try.Astimewindows,wechoseweeks3to6afteronset.Forthisepidemic,alocalfarminBienenbüttel,districtUelzen,waslateridenti-fiedasthesourceofcontaminatedsprouts(38).Onthebasisofprevalencedistributionintheentirecountry,theeffectivedistancemethodcor-rectlyidentifiesdistrictUelzenasthemostlike-lygeographicsource.However,inthiscase,theseparationinthemean/standarddeviationdia-gramisnotaspronouncedasfordiseasespreadbyairpassengerflows.Nevertheless,althoughthemethodcannotidentifytheOLwithfullreli-abilityhere,itdramaticallyreducesthesetofpotentialoriginlocations.

Inbothreal-worldscenarios—the2011EHEC/HUSepidemicandthe2009H1N1pandemic—theOLreconstructionworkssurprisinglywell,despitetheintrinsicfluctuationsandthelow-incidenceregime.Theunexpecteddegreeofpre-dictabilityindicatesthatthesetoflinksinthenetworkcontributingtheshortestpathsaccumu-latesasubstantialfractionoftheoveralltransmis-sionprobability(andthatthissetisalmostidenticalfromtheperspectiveofallnodes;fig.S20).Discussion

Insummary,theanalysisofglobaldiseasedy-namicsintheframeworkofeffectivedistancesenablesresearcherstounderstandcomplexcon-tagiondynamicsinmultiscalenetworkswithsimplereaction-diffusionmodels.Givenfixedvaluesforepidemicparameters,ouranalysisshowsthatnetworkandfluxinformationaresufficienttopredictthedynamicsandarrivaltimes.Themethodisapromisingstartingpointformoredetailedinvestigations,includingthefunctionaldependenciesofkeyepidemicvariablessuchasthespreadingspeedandrelatedmacro-scopicquantitiesonepidemiologicalparameters.Thesuccessfulapplicationtorealepidemicdatasuggeststhatourmethodisalsoofpracticaluse.Finally,itseemspromisingtogeneralizetheef-fectivedistancemethodtoothercontagionphenom-ena,suchashuman-mediatedbioinvasionandthespreadofrumorsorviolence,asubjectofever-moreimpor …… 此处隐藏：5986字，全部文档内容请下载后查看。喜欢就下载吧 ……