Hopf Bifurcation Analysis for a Delayed SIRS Epidemic Model with a Nonlinear Incidence Rate

被引：0

作者：

张子振 ^{[1
,2
]}

杨慧中 ^{[1
]}

机构：

[1] Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education),Jiangnan University

[2] School of Management Science and Engineering,Anhui University of Finance and Economics

来源：

Journal of Donghua University(English Edition) | 2014年 / 31卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Hopf bifurcation; delay; SIRS model; stability; periodic solution;

D O I：

10.19884/j.1672-5220.2014.02.024

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

This paper is concerned with a delayed SIRS epidemic model with a nonlinear incidence rate. The main results are given in terms of local stability and Hopf bifurcation. Sufficient conditions for the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained by regarding the time delay as the bifurcation parameter. Further,the properties of Hopf bifurcation such as the direction and stability are investigated by using the normal form theory and center manifold argument. Finally,some numerical simulations are presented to verify the theoretical analysis.

引用

页码：201 / 206

页数：6

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