一类基于心理作用的SIRS传染病模型  

A Class of SIRS Epidemic Model Based on Psychology Effect

作　　者：李文轩 李辉来[1] 赵彦军[2] LI Wenxuan;LI Huilai;ZHAO Yanjun(College of Mathematics,Jilin University,Changchun 130012,China;College of Humanities and Sciences of Northeast Normal University,Changchun 130117,China)

机构地区：[1]吉林大学数学学院,长春130012 [2]东北师范大学人文学院,长春130117

出　　处：《吉林大学学报（理学版）》2020年第3期513-517,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11271154).

摘　　要：根据传染病动力学原理建立一类基于心理作用的SIRS传染病模型.先通过构造Lyapunov函数,利用常微分方程稳定性和极限系统理论,分别获得该模型在无病平衡点和地方病平衡点全局渐近稳定性的充分条件,再通过数值仿真验证所得结论.数值模拟结果表明,心理作用的积极影响在一定程度上能控制传染病的传播与流行.According to the principle of epidemic dynamics,we established a class of SIRS epidemic model based on psychology effect.The sufficient conditions for the global asymptotic stability of the model at the disease-free equilibrium point and endemic disease equilibrium point were obtained by constructing Lyapunov function,using the stability of ordinary differential equation and the theory of limit system,and then the results were verified by numerical simulation.The results of numerical simulation show that the positive influence of psychology effects can control the spread and prevalence of infectious diseases to a certain extent.

关 键 词：SIRS传染病模型 LYAPUNOV函数 心理作用 全局渐近稳定性 

分 类 号：O175.1[理学—数学]