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1、CommunNonlinearSciNumerSimulat16(2011)4438–4450ContentslistsavailableatScienceDirectCommunNonlinearSciNumerSimulatjournalhomepage:www.elsevier.com/locate/cnsnsAnalysisofstabilityandbifurcationforanSEIRepidemicmodelqwithsaturatedrecoveryratea,bc,⇑XueyongZhou,JinganCuiaSchoolofMathemati
2、calSciences,NanjingNormalUniversity,Nanjing210046,Jiangsu,PRChinabCollegeofMathematicsandInformationScience,XinyangNormalUniversity,Xinyang464000,Henan,PRChinacSchoolofScience,BeijingUniversityofCivilEngineeringandArchitecture,Beijing100044,PRChinaarticleinfoabstractArticlehistory:Int
3、hispaperwestudyanSEIRepidemicmodelwithsaturatedrecoveryrate.AbackwardReceived29November2010bifurcationleadingtobistabilitypossiblyoccurs,andglobaldynamicsareshownbycom-Receivedinrevisedform17March2011poundmatricesandgeometricapproaches.Numericalsimulationsarepresentedtoillus-Accepted1
4、8March2011tratetheresults.Availableonline24March2011Ó2011ElsevierB.V.Allrightsreserved.Keywords:SEIRepidemicmodelGlobalstabilityBackwardbifurcationSaturatedrecoveryrate1.IntroductionIn1760,DanielBernoulliformulatedandsolvedthefirstknowndifferentialequationtoevaluatetheeffectivenessofva
5、r-iolationofhealthypeoplewiththesmallpoxvirus.AndtheoreticalpapersoninfectiousdiseasemodelsbyKermackandMcKendrick[1–3]havehadamajorinfluenceinthedevelopmentofmathematicalepidemiologymodels.Afterthat,atre-mendousnumberofmodelshavebeenformulated,analyzedandappliedtoavarietyofinfectiousdi
6、seasesqualitativelyandquantitatively.Mathematicalmodelshavebecomeimportanttoolsinanalyzingthespreadandcontrolofinfectiousdiseases[4–6].Furthermore,mathematicalmodelshavebeenusedincomparing,planning,implementing,evaluating,andoptimizingvariousdetection,prevention,therapy,andcontrolprog
7、rams[7–9].LetusnowconsideranSEIRtypediseasewithsaturatedrecoveryrate.ThetotalpopulationsizeN(t)isdividedintofourdistinctepidemiologicalsubclassesofindividualswhicharesusceptible,exposed,infectious,andrecovered,withsizesde-notedbyS(t),E(t),I(t),andR(t),respectively.Oneassumesthatindivi
8、duals
