THRESHOLD DYNAMICS IN A STOCHASTIC SIRS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATE

被引：0

作者：

Zhao, Yanan ^{[1
,2
]}

Zhang, Xiaoying ^{[2
]}

O'Regan, Donal ^{[3
]}

机构：

[1] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China

[2] Changchun Univ, Sch Sci, Changchun 130021, Jilin, Peoples R China

[3] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2019年 / 9卷 / 06期

基金：

中国博士后科学基金; 美国国家科学基金会; 中国国家自然科学基金;

关键词：

SIRS epidemic model; nonlinear incidence rate; extinction; persistence; threshold; GLOBAL STABILITY; EXTINCTION; BEHAVIOR; VACCINATION; PERSISTENCE; EQUATION;

D O I：

10.11948/20180041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss the dynamic of a stochastic Susceptible-InfectiousRecovered-Susceptible (SIRS) epidemic model with nonlinear incidence rate.The crucial threshold (R) over tilde (0) is identified and this will determine the extinction and persistence of the epidemic when the noise is small. We also discuss the asymptotic behavior of the stochastic model around the endemic equilibrium of the corresponding deterministic system. When the noise is large, we find that a large noise intensity has the effect of suppressing the epidemic, so that it dies out. Finally, these results are illustrated by computer simulations.

引用

页码：2096 / 2110

页数：15

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