Dynamics of the deterministic and stochastic SIQS epidemic model with non-linear incidence

被引：63
|
作者：
Zhang, Xiao-Bing [1 ,2 ]
Huo, Hai-Feng [1 ,2 ]
Xiang, Hong [2 ]
Meng, Xin-You [2 ]
机构：
[1] Lanzhou Univ Technol, Coll Elect & Informat Engn, Lanzhou 730050, Gansu, Peoples R China
[2] Lanzhou Univ Technol, Dept Appl Math, Lanzhou 730050, Gansu, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 243卷
关键词：
Lyapunov function; Random perturbations; Non-linear incidence; It(o)over-cap's formula; Stationary distribution; NONAUTONOMOUS LOGISTIC EQUATION; STATIONARY DISTRIBUTION; GLOBAL STABILITY; EXTINCTION; BEHAVIOR; ERGODICITY; SIR; DIFFUSION; SYSTEMS; SEIR;
D O I：
10.1016/j.amc.2014.05.136
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The deterministic and stochastic SIQS models with non-linear incidence are introduced. For deterministic model, the basic reproductive rate R-0 is derived. Moreover, if R-0 <= 1, the disease-free equilibrium is globally asymptotically stable and if R-0 > 1, there exists a unique endemic equilibrium which is globally asymptotically stable. For stochastic model, sufficient condition for extinction of the disease that is regardless of the value of R-0 is presented. In addition, if the intensities of the white noises are sufficiently small and R-0 > 1, then there exists a unique stationary distribution to stochastic model. Numerical simulations are also carried out to confirm the analytical results. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：546 / 558
页数：13
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