The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with saturated incidence

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:388

Article

Yang, Qingshan¹  Jiang, Daqing¹  Shi, Ningzhong¹  Ji, Chunyan¹ 

[1] NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China

关键词: SIR epidemic model;    SEIR epidemic model;    Ito's formula;    Stochastic Lyapunov function;    Exponential stability;    Ergodic property;   

DOI  :  10.1016/j.jmaa.2011.11.072

来源: Elsevier

【 摘 要 】

In this paper, we include stochastic perturbations into SIR and SEIR epidemic models with saturated incidence and investigate their dynamics according to the basic reproduction number R-0. The long time behavior of the two stochastic systems is studied. Mainly, we utilize stochastic Lyapunov functions to show under some conditions, the solution has the ergodic property as R-0 > 1, while exponential stability as R-0 <= 1. At last, we make simulations to conform our analytical results. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free