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一类SIRS传染病模型的稳定性分析

发表时间:2018-08-15  浏览量:156  下载量:40
全部作者: 吴长青,朱长荣
作者单位: 重庆大学数学与统计学院;重庆市育才中学
摘 要: 以非线性发生率为条件,选择在总人口不为常数的情况下,研究一类SIRS传染病模型的解的有界性和平衡点稳定性,包括无病平衡点的稳定性和地方病平衡点的局部稳定性。运用微分动力系统理论证明了无病平衡点在不同条件下是稳定结点、鞍点和退化平衡点。最后使用Matlab给出了系统在两个平衡点的主要相图,从而进一步验证了本文理论的正确性。
关 键 词: 生物数学;传染病模型;局部稳定性;退化平衡点;Matlab
Title: Stability analysis of a class of SIRS epidemic model
Author: WU Changqing, ZHU Changrong
Organization: College of Mathematics and Statistics, Chongqing University; Chongqing Yucai Secondary School
Abstract: Under the condition of nonlinear incidence and with the situation that the total population is not constant, the boundedness and equilibrium stability of the solution of an SIRS epidemic model are studied, including the stability of disease-free equilibrium and the local stability of endemic disease equilibrium. Using the theory of differential dynamic system, it is proved that the disease-free equilibrium can be the stable, saddle, and degenerate equilibrium node. Finally, the main phase diagram of the system in the two equilibriums is obtained by Matlab, furthermore the correctness of the theory is verified.
Key words: biomathematics; epidemic model; local stability; degenerate equilibrium; Matlab
发表期数: 2018年8月第15期
引用格式: 吴长青,朱长荣. 一类SIRS传染病模型的稳定性分析[J]. 中国科技论文在线精品论文,2018,11(15):1514-1519.
 
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