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一类具有人口流动的SEIR传染病模型的全局稳定性分析.docx

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一类具有人口流动的SEIR传染病模型的全局稳定性分析 Title:GlobalStabilityAnalysisofanSEIREpidemicModelwithPopulationMobility Abstract: Theunderstandingandcontrolofinfectiousdiseaseshavealwaysbeencrucial.Inrecenttimes,populationmobilityhasplayedasignificantroleinthespreadofinfectiousdiseases,makingitimperativetostudyepidemicmodelsthatincorporatethisaspect.ThispaperaimstoanalyzetheglobalstabilityofaspecificclassofepidemicmodelsknownasSEIRmodels,whichincludepopulationmobility.SEIRmodelsarewidelyusedtodescribethespreadandcontrolofinfectiousdiseases. Introduction: Infectiousdiseasesspreadrapidlyinaglobalizedworldduetoincreasedtravelandpopulationmobility.Studyingepidemicmodelsthatincorporatethesefactorsiscrucialforunderstandingthedynamicsofdiseasetransmission.TheSEIRmodeliswidelyusedtosimulatethespreadofinfectiousdiseases,incorporatingsusceptible(S),exposed(E),infected(I),andrecoveredorimmune(R)individuals.However,toaccuratelycapturetheimpactofpopulationmobility,weneedtoextendtheclassicalSEIRmodelbyincorporatingmigrationanddemographiceffects. Methods: ThisstudyadoptsapopulationmobilityextensiontotheclassicalSEIRmodelbyconsideringmigrationrates,birth,anddeathrates.Themodelincludesequationsthatdescribethemovementofindividualsbetweenregionsorsubpopulations,consideringbothincomingandoutgoingmigrationrates.Moreover,themodelincorporatesbirthanddeathratestoaccountfortheoverallpopulationdynamics. Acriticalaspectofanalyzingtheglobalstabilityofepidemicmodelsisdeterminingtheexistenceandpropertiesofthedisease-freeequilibriumandendemicequilibrium.Thedisease-freeequilibriumrepresentsthestateinwhichthediseaseiseliminated,whiletheendemicequilibriumrepresentsthepersistentpresenceofthedisease.Linearstabilityanalysiswillbeemployedtoinvestigatethestabilityoftheseequilibria. Further,thebasicreproductionnumber(R0)willbecomputedasathresholdparametertodeterminewhetherthediseasespreadsordiesout.R0providesvitalinsightsintotheepidemicdynamicsandcontrolmeasuresrequired.Moreover,theeffectsofpopulationmobilityontheR0valuewill