一类具有时滞的SIRS传染病模型的Hopf分岔分析  

Hopf Bifurcation Analysis of a Class of Delayed SIRS Epidemic Models

作　　者：李文娟[1] 牛潇萌 LI Wen-juan;NIU Xiao-meng(School of Mathematics and Statistics,Chifeng University,Chifeng 024000,China;Institute of Applied Mathematics,Chifeng University,Chifeng 024000,China)

机构地区：[1]赤峰学院数学与统计学院,内蒙古赤峰024000 [2]赤峰学院应用数学研究所,内蒙古赤峰024000

出　　处：《数学的实践与认识》2018年第22期278-282,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11761006);内蒙古自然科学基金项目(2017MS0113);内蒙古高校科研项目(NJZY17301)

摘　　要：研究了一类具有时滞的SIRS传染病模型。首先，利用特征值理论得到了模型的有病毒平衡点，然后通过分析在有病毒平衡点处的相应特征方程根的分布，得到有病毒平衡点处的局部渐近稳定和发生Hopf分岔的时滞临界点。以时滞为分岔参数，研究了SIRS传染病模型存在Hopf分岔的条件。We study a class of delayed SIRS epidemic models. Firstly, We obtain the viral equilibrium of the model with the eigenvalue theory. Then we acquire the local stability of the viral equilibrium and the delayed critical value of Hopf bifurcation by analyzing distribution of roots of the corresponding characteristic equation at the viral equilibrium. We study the existence condition of Hopf bifurcation of this SIRS epidemic model by taking delayed as bifurcation parameter.

关 键 词：SIRS传染病模型 时滞 稳定性 HOPF分岔 

分 类 号：O177.91[理学—数学]