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1、ARTICLEINPRESSJournalofTheoreticalBiology232(2005)587–604www.elsevier.com/locate/yjtbiAgeneralizedmodelofsocialandbiologicalcontagiona,b,cP.S.Dodds,D.J.WattsaInstituteforSocialandEconomicResearchandPolicy,ColumbiaUniversity,420West118thStreet,MC3355,NewYork,NY10027,USAbDep
2、artmentofSociology,ColumbiaUniversity,1180AmsterdamAvenue,NewYork,NY10027,USAcSantaFeInstitute,1399HydeParkRoad,SantaFe,NM87501,USAReceived27May2004;receivedinrevisedform15September2004;accepted15September2004Availableonline6November2004AbstractWepresentamodelofcontagiontha
3、tunifiesandgeneralizesexistingmodelsofthespreadofsocialinfluencesandmicroorganismalinfections.Ourmodelincorporatesindividualmemoryofexposuretoacontagiousentity(e.g.arumorordisease),variablemagnitudesofexposure(dosesizes),andheterogeneityinthesusceptibilityofindividuals.Throug
4、hanalysisandsimulation,weexamineindetailthecasewhereindividualsmayrecoverfromaninfectionandthenimmediatelybecomesusceptibleagain(analogoustotheso-calledSISmodel).Weidentifythreebasicclassesofcontagionmodelswhichwecallepidemicthreshold,vanishingcriticalmass,andcriticalmasscl
5、asses,whereeachclassofmodelscorrespondstodifferentstrategiesforpreventionorfacilitation.Wefindthattheconditionsforaparticularcontagionmodeltobelongtooneofthethesethreeclassesdependonlyonmemorylengthandtheprobabilitiesofbeinginfectedbyoneandtwoexposures,respectively.Thesepara
6、metersareinprinciplemeasurableforrealcontagiousinfluencesorentities,thusyieldingempiricalimplicationsforourmodel.Wealsostudythecasewhereindividualsattainpermanentimmunityoncerecovered,findingthatepidemicsinevitablydieoutbutmaybesurprisinglypersistentwhenindividualspossessmemo
7、ry.r2004ElsevierLtd.Allrightsreserved.Keywords:Contagion;Epidemic;Memory;Treshold;Doseresponse;Criticalmass;Universality;Bifuraction1.Introductionofwaysdependingontheapplicationathand,fallintooneofonlytwobroadcategories,wherethecriticalContagion,initsmostgeneralsense,isthes
8、preadingdistinctionbetweenthesecategoriescanbeexplainedinofanentityorinfluencebetwe
