一类具有时滞的SIR传染病模型的稳定性与Hopf分支  

Stability and Hopf Bifurcation of SIR Infectious Disease Model with Time Delay

作　　者：李伟南 廖茂新[1] 李冰冰 LI Weinan;LIAO Maoxin;LI Bingbing(School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China)

机构地区：[1]南华大学数理学院,湖南衡阳421001

出　　处：《南华大学学报（自然科学版）》2023年第1期59-63,100,共6页Journal of University of South China：Science and Technology

基　　金：湖南省自然科学基金项目(2020JJ4516);湖南省研究生科研创新项目(CX20220980)。

摘　　要：本文研究了一类具有非线性发生率和恢复率的修正的SIR模型,考虑了疾病的潜伏期作为时滞因素,首先得到了模型的基本再生数R 0,然后运用时滞微分方程的稳定性和分支理论,分析了模型无病平衡点和地方病平衡点的稳定性,得到了在地方病平衡点Hopf分支存在的条件,最后用MATLAB数值模拟验证结果。In this paper,a modified SIR model with nonlinear incidence and recovery rate is studied.The latent period of the disease is considered as the delay factor.First the basic regeneration number R 0 of the model is obtained,then the stability of disease-free e quilibrium and endemic equilibrium is analyzed by using the stability and bifurcation theory of delay differential equation.The conditions of Hopf bifurcation at endemic equilibrium point were obtained,and the results were verified by MATLAB numerical simulation.

关 键 词：HOPF分支 时滞 平衡点 基本再生数 

分 类 号：O175[理学—数学]