一类具有进化效应的时滞SIR模型的动力学分析  

Dynamic Analysis of an Evolutionary SIR Model with Time Delay

作　　者：袁海龙 李一多 张嘉祥 YUAN Hailong;LI Yiduo;ZHANG Jiaxiang(School of Mathematics&Data Science,Shaanxi University of Science&Technology,Xi’an 710021,China)

机构地区：[1]陕西科技大学数学与数据科学学院,陕西西安710021

出　　处：《应用数学》2024年第3期749-764,共16页Mathematica Applicata

基　　金：国家自然科学基金资助项目(11901370);陕西省自然科学基础研究计划资助项目(2019JQ-516);陕西省教育厅专项科研计划资助项目(19JK0142);陕西省科协人才托举项目(20200508)。

摘　　要：主要研究具有进化效应和受时滞影响的SIR传染病模型的动力学行为.首先,将时滞参数作为分支参数,在常微分和偏微分系统中研究带时滞因素的SIR模型的正平衡点稳定性,并得到在健康个体的防御能力和已感染个体的感染能力相互作用的情况下产生Hopf分支的条件;其次,利用规范型理论和中心流形定理,判断Hopf分支方向及分支周期解的稳定性;最后,通过MATLAB进行数值模拟以验证理论结果的正确性.In this paper,we mainly study the dynamic behavior of the SIR epidemic model with evolutionary effect and time delay.Firstly,the delay parameter is taken as the bifurcation parameter,the positive equilibrium stability of SIR model with delay is studied in ordinary differential and partial differential systems,and the conditions for Hopf bifurcation are obtained in the case of the interaction between the defensive ability of healthy individuals and the infectious ability of infected individuals.Secondly,the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem.Finally,numerical simulation was carried out by MATLAB to verify the correctness of the theoretical results.

关 键 词：时滞 SIR模型 稳定性 HOPF分支 

分 类 号：O175[理学—数学]