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一类具有时滞和非连续治愈的脉冲SEIR模型分析.docx

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一类具有时滞和非连续治愈的脉冲SEIR模型分析 Title:AnalysisofaPulseSEIRModelwithTimeDelayandNon-ContinuousTreatment Abstract: Inthispaper,weinvestigateapulseSEIR(Susceptible-Exposed-Infected-Removed)modelwithtimedelayandnon-continuoustreatment.Theincorporationoftimedelayandnon-continuoustreatmentallowsustostudytheimpactofthesefactorsondiseasetransmissiondynamics.Weproposeamathematicalmodeltodescribethespreadofinfectiousdiseases,takingintoaccountthetimedelayinthetransitionbetweendifferentcompartmentsandtheintermittentnatureofthetreatment.Throughstabilityanalysisandnumericalsimulations,weexploretheeffectsoftimedelayandnon-continuoustreatmentontheexistenceandpersistenceoftheinfection.Theresultsshedlightontheimportanceofthesefactorsindevisingeffectivestrategiestocontrolandpreventthespreadofinfectiousdiseases. Introduction: Inrecentyears,themodelingandanalysisofdiseasespreadhavebecomeincreasinglyimportanttounderstandandmitigatetheimpactofinfectiousdiseases.Variousmathematicalmodelshavebeenproposedtodescribeepidemicdynamicsandevaluatecontrolstrategies.TheSEIRmodelisawidelyusedframeworkthatdividesthepopulationintofourcompartments:susceptible(S),exposed(E),infected(I),andremoved(R).However,traditionalSEIRmodelsoftenneglectimportantfactorssuchastimedelayandthenon-continuousnatureoftreatment,whichcansignificantlyaffectthedynamicsofdiseasetransmission.Therefore,itiscrucialtoincorporatethesefactorsintothemodelingframeworktoobtainamorerealisticrepresentationofdiseasespreaddynamics. ModelDescription: WeconsiderapulseSEIRmodelwithtimedelayandnon-continuoustreatmenttocapturetheimpactofthesetwofactorsondiseasetransmissiondynamics.Themodelisdescribedbyasystemofdelaydifferentialequations,whichaccountforthetransitionsbetweendifferentcompartmentsandthetimedelayinthesetransitions.Thenon-continuoustreatmentisrepresentedasintermittentpulses,wherethetreatmentintensitychangesperiodically.Theparametersofthemodelareadjustedtoreflectthecharacteristicsofthespecificdiseaseunderconsideration. StabilityAnalysis: Toanal