具有饱和发生率的随机SEIRS传染病模型的遍历性与灭绝性(英文)The Ergodicity and Extinction of Stochastically Perturbed SEIRS Epidemic Models with Saturated Incidence
热木孜亚·热布哈提,张学良,滕志东
摘要(Abstract):
文章研究了一类具有总人口数变化的且具有饱和发生率的随机SEIRS传染病模型,并且得到了该模型的灭绝性和存在独立的平稳分布的充分条件.
关键词(KeyWords): SEIRS传染病模型;Lyapunov函数;随机扰动;随机稳定性
基金项目(Foundation): supported by the(XJC2013234)
作者(Author): 热木孜亚·热布哈提,张学良,滕志东
DOI: 10.13568/j.cnki.651094.2017.02.004
参考文献(References):
- [1]Cooke K,van den Driessche P.Analysis of an SEIRS epidemic model with two delays[J].J Math Biol,1996,35:240-260.
- [2]Hethcote H W,van den Driessche P.An SIS epidemic model with variable population size and a delay[J].J Math Biol,1995,34:177-194.
- [3]Hethcote H W,van den Driessche P.Two SIS epidemiologic models with delays[J].J Math Biol,2000,40:3-26.
- [4]Li G,Jin Z.Global stability of an SEIR epidemic model with infectious force in latent,infected and immune period[J].Chaos Solitons Fractals,2005,25:1177-1184.
- [5]Gao S,Chen L,Teng Z.Pulse vaccination of an SEIR epidemic model with time delay[J].Nonlinear Anal Real World Appl,2008,9:599-607.
- [6]Van den Driessche P,Watmough J.Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J].Math Biosci,2002,180:29-48.
- [7]Korobeinikov A.Global properties of infectious disease models with nonlinear incidence[J].Bull Math Biol,2007,69:1871-1886.
- [8]Mao X.Stochastic Differential Equations and Applications[M].Horwood:Chichester,1997.
- [9]Lahrouz A.Stochastic Differential Equations:Theory and Applications[M].New York:Wiley,1972.
- [10]ksendal B.Stochastic differential equations:An introduction with application[M].New York:Springer Verlag,Heidelberg,2000.
- [11]Hasminskii R Z.Stochastic Stability of Differential Equations[M].The Netherlands:Sijthoff and Noordhoff,Alphen aan den Rijn,1980.