具有时滞影响的SIRC传染病模型的Hopf分支分析-豆柴文库

您所在位置：网站首页 / 具有时滞影响的SIRC传染病模型的Hopf分支分析.docx / 文档详情

在线预览结束，喜欢就下载吧，查找使用更方便

5 金币

下载文档

/ 2

下载提示

如果您无法下载资料，请参考说明：

1、部分资料下载需要金币，请确保您的账户上有足够的金币

2、已购买过的文档，再次下载不重复扣费

3、资料包下载后请先用软件解压，在使用对应软件打开

文本预览

具有时滞影响的SIRC传染病模型的Hopf分支分析
Title:HopfBifurcationAnalysisoftheDelayedSIRCEpidemicModel
Abstract:
Inrecentyears,thestudyofepidemicmodelshasgainedsignificantattentionduetotheoutbreakofvariousinfectiousdiseases.Toeffectivelycontrolandmitigatethespreadofinfectiousdiseases,itiscrucialtounderstandthedynamicsoftheepidemicsystems.ThispaperfocusesonthedelayedSusceptible-Infectious-Recovered-Constant(SIRC)epidemicmodel,incorporatingtimedelayasacriticalfactorinfluencingthespreadofdiseases.TheaimistoanalyzetheoccurrenceofHopfbifurcationinthemodelandshedlightontheunderstandingofitsdynamicbehavior.
1.Introduction
Epidemicmodelsplayanessentialroleinpredictingandunderstandingthebehaviorofinfectiousdiseases.Manypreviousstudieshaveconsidereddifferentepidemicmodelswithvariouscomplexities.However,theinclusionoftimedelayinepidemicmodelshasbeenrelativelylessexplored,despiteitsprofoundimpactonthedynamicsofthesystem.ThispaperattemptstobridgethisgapbyinvestigatingthedelayedSIRCepidemicmodel.
2.TheBasicDelayedSIRCEpidemicModel
ThissectionoutlinesthedelayedSIRCmodel,whichtakesintoaccountthebiologicaldelayencounteredintheprogressionofaninfectiousdisease.Thedifferentialequationsgoverningthemodelarepresented,alongwiththeinterpretationofeachparameterinvolved.
3.StabilityAnalysis
TounderstandthestabilityanddynamicbehaviorofthedelayedSIRCmodel,weperformstabilityanalysisbyconsideringtheexistence,stability,anduniquenessoftheequilibriumpoints.Thecharacteristicequationisderived,andstabilityconditionsareobtainedtodeterminethestabilityofthemodel.
4.HopfBifurcationAnalysis
Inthissection,weinvestigatetheoccurrenceoftheHopfbifurcationinthedelayedSIRCmodel.Byapplyingthenormalformtheoryandcentermanifoldreduction,theconditionsforHopfbifurcationarederived.Thecriticalvaluesofthebifurcationparameterarecalculated,indicatingtheoccurrenceofastablelimitcycle.
5.NumericalSimulations
NumericalsimulationsareconductedtovalidatetheanalyticalfindingsoftheHopfbifurcationanalysis.ThedynamicbehaviorofthedelayedSIRCmodelwithtime