传染病动力学建模研究进展

、。。R51A1674-9960201111-0828-06ResearchadvancesinmodelinginfectiousdiseaseXUZhi-jingZUZheng-huXUQingZHENGTao*InstituteofBiotechnologyAcademyofMilitaryMedicalSciencesBeijing100850China*[e-mail]odelsplayanimportantroleinunderstandingthetransmissionofinfectiousdiseasesandindevelopingeffectivepreventionandcontainmentstrategies．Thispaperreviewsseveralmajorepidemiologicalmodelswithabriefanalysisoftheirdifferenceandprovidesinsightintothecurrenttrendsofmathematicalmodels．Italsoconductsanin-vestigationonhowtochooseanappropriatemodelduringresearch．Keywordscommunicablediseasescomputersimulationbiosecurity705731207077311890924019“”2008ZX10403“”06J022“”2008-ZD-03。[e-mail][e-mail]1。、、。。、、、、、、、。20039200696852。。3。。20702。。。。。“”compartmentmodel、net-workmodel、individual-basedmodelmetapopulationmodel。1“”1926KermackMcKendrick1665～8282011113511MilMedSciVol35No11Nov201116661906SIRsusceptiblein-fectiousandrecovered4。1932SIS“”5。SEIR。。“”。2。SI、SISSIR1、SEIR。1SIR6SIR6S、IR。SIR3dS/dt=－βSI①dI/dt=βSI－γI②dR/dt=γI③S、I、RS+I+R=1βγ1/γ。dI/dt=βS－γIS0＜γ/βdI/dt＜07R0R0=β/γS0＜γ/β=1/R0S0=1R0＞1。①/③dS/dR=－βS/γ=－R0SSt=S0e－RtR0④R0=0e－RR0＞0St＞0。8～10。Eichner11InfluSim。InfluSim。。HIV、12。2HIV、12。Grassberger13。。。。。14。。3、15。102。t=0a。eijijjrij。t=τeRae=1－1－raeτ。eaeef、g、h。。。2。9282011113511MilMedSciVol35No11Nov201116～17。Moore18Kuperman19Pastor-Satorras20。。。16。Rozenfeld2122、23、2425。。3、、26。WooldridgeJennings27、、。3。。5transmission、recovery、birth、deathmovement。jiλi=β∑jinfectiousKTdijdijijKTjGi=γ2。3、。。Grimm28。。2930。transportationanalysisandsimulationsystemTRAN-SIMSEpiSimSBisset31EpiFast。EpiSimS。Eubank32EpiSimS。440382011113511MilMedSciVol35No11Nov2011。。Hanski334。4Levins3435、。206036。37。2。、、38。“”。2P1P2S1=S2=1ρijijρii=1ρij1。P1P1P2。dI2/dt=β2ρ21I1+β2I2－γ2I2⑤βγI2t=∫t0β2ρ21I1sexpβ2－γβsds⑥⑥P1P2P1P2。Pepidemic=∑Nn=1Pcasesin1causencasesinP2×Pninitialcasesleadtoamajorepidemic=∑Nn=1exp－β2ρ21∫∞0I1sdsβ2ρ21∫∞0I1sdsnn×1－γβ2n=1－exp－β2ρ211－γβ2∫∞0I1sds⑦＜1－exp－β2ρ21/γ⑦ρ21P239。“”。3。VandenBroeck40GLEaM-viz2009H1N1。5。。。5．1、3。31。。。1“”。“”→→→。。。1382011113511MilMedSciVol35No11Nov20111“”。199541SARS42。43。。。。。Kermack44。。5．2。、。5。5、。。。。。。【】1．M．20083－99．2WorldHealthOrganization．TheWorldHealthreport2007asa-ferfutureglobalpublichealthsecurityinthe21stCenturyR．GenevaWorldHealthOrganization20079－12．3．M．2005268－272．4KermackWOMcKendrickAG．Acontributiontothemathemati-caltheoryofepidemicsJ．ProcRSocLondA1927115772700－721．5KermackWOMcKendrickAG．Contributionstothemathemati-2382011113511MilMedSciVol35No11Nov2011caltheoryofepidemics-Ⅱ．TheproblemofendemicityJ．ProcRSocLondA193213883455－83．6KeelingMJRohaniP．ModelinginfectiousdiseasesinhumansandanimalsM．NewJerseyPrincetonUniversityPress200815－288．7HeesterbeekJ．AbriefhistoryofR0andarecipeforitscalcula-tionJ．ActaBiotheor2002503189－204．8EarnDJDRohaniPBolkerBMetal．Asimplemodelforcom-plexdynamicaltransitionsinepidemicsJ．Science20002875453667－670．9DyeCGayN．ModelingtheSARSepidemicJ．Science200330056271884－1885．10MillsCERobinsJMLipsitchM．Transmissibilityof1918pan-demicinfluenzaJ．Nature20044327019904－906．11EichnerMSchwehmMDuerrHPetal．Theinfluenzapan-demicpreparednessplanningtoolInfluSimJ．BMCInfectDis20077117－30．12MossARBacchettiP．NaturalhistoryofHIVinfectionJ．Aids19893255－61．13GrassbergerP．OnthecriticalbehaviorofthegeneralepidemicprocessanddynamicalpercolationJ．MathBiosci1983632157－172．14MeyersLA．Contactnetworkepidemiologybondpercolationap-pliedtoinfectiousdiseasepredictionandcontrolJ．BullAmMathSoc200744163－86．15SanderLWarrenCSokolovIetal．Percolationonheteroge-neousnetworksasamodelforepidemicsJ．MathBiosci20021801－2293－305．16etal．J．JSystEng2010256742－754．17BorgattiSPMehraABrassDJetal．NetworkanalysisinthesocialsciencesJ．Science20093235916892－895．18MooreCNewmanMEJ．Epidemicsandpercolationinsmall-worldnetworksJ．PhysRevE20006155678－5682．19KupermanMAbramsonG．Smallworldeffectinanepidemio-logicalmodelJ．PhysRevLett200186132909－2912．20Pastor-SatorrasRVespignaniA．Epidemicspreadinginscale-freenetworksJ．PhysRevLett200186143200－3203．21RozenfeldAFCohenRBen-AvrahamDetal．Scale-freenet-worksonlatticesJ．PhysRevLett20028921218701－218705．22LiXChenGR．Alocal-worldevolvingnetworkmodelJ．PhysA200617121815－1822．23LiCMainiPK．AnevolvingnetworkmodelwithcommunitystructureJ．JPhysA200538459741－9749．24WangLNGuoJLYangHXetal．Localpreferentialattach-mentmodelforhierarchicalnetworksJ．PhysA200938881713－1720．25MannaSSSenP．Modulatedscale-freenetworkinEuclideanspaceJ．PhysRevEStatNonlinSoftMatterPhys2002666pt2066114－066118．26RailsbackSF．Conceptsfromcomplexadaptivesystemsasaframe-workforindividual-basedmodellingJ．EcolModell2001139147－62．27WooldridgeMJenningsNR．Intelligentagentstheoryandprac-ticeJ．KnowEngRev1995102115－152．28GrimmVBergerUBastiansenFetal．Astandardprotocolfordescribingindividual-basedandagent-basedmodelsJ．EcolModell20061981－2115－126．29YangYSugimotoJDHalloranMEetal．ThetransmissibilityandcontrolofpandemicinfluenzaAH1N1virusJ．Science20093265953729－733．30EpsteinJM．Modellingtocontainpan