Dynamics of a stochastic SIR epidemic model with saturated incidence

被引：25
作者：
Liu, Qun [1 ]
Chen, Qingmei [1 ]
机构：
[1] Yulin Normal Univ, Sch Math & Informat Sci, Guangxi Univ Key Lab Complex Syst Optimizat & Big, Yulin 537000, Guangxi, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2016年 / 282卷
关键词：
Persistence in the mean; Extinction; Stationary distribution; Ito's formula; Lyapunov functions; NONLINEAR INCIDENCE; GLOBAL STABILITY; STATIONARY DISTRIBUTION; PERTURBED SIR; EXTINCTION; BEHAVIOR; PERTURBATIONS; VACCINATION; THRESHOLD; SYSTEM;
D O I：
10.1016/j.amc.2016.02.022
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the dynamics of a stochastic SIR epidemic model with saturated incidence is investigated. Firstly, we prove that the system has a unique global positive solution with any positive initial value. Then we verify that random effect may lead the disease to extinction under a simple condition. Thirdly, we establish a sufficient condition for persistence in the mean of the disease. Moreover, we show that there is a stationary distribution to the stochastic system under certain parametric restrictions. Finally, some numerical simulations are carried out to confirm the analytical results. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码：155 / 166
页数：12
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