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

被引：170
|
作者：
Yang, Qingshan [1 ]
Jiang, Daqing [1 ]
Shi, Ningzhong [1 ]
Ji, Chunyan [1 ]
机构：
[1] NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 388卷 / 01期
关键词：
SIR epidemic model; SEIR epidemic model; Ito's formula; Stochastic Lyapunov function; Exponential stability; Ergodic property; HIV EPIDEMIC; GLOBAL STABILITY; HOMOSEXUAL POPULATIONS; NUMERICAL-SIMULATION; PULSE VACCINATION; MARRIED-COUPLES; TRANSMISSION; PERSISTENCE; PROSTITUTES;
D O I：
10.1016/j.jmaa.2011.11.072
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
引用
收藏
页码：248 / 271
页数：24
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