一类具有时滞效应的SIS传染病模型  

An SIS Epidemic Model with Delay Effect

作　　者：汪雨琴 谢景力[1] 赵佳璐 李嘉隆 WANG Yuqin;XIE Jingli;ZHAO Jialu;LI Jialong(College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

机构地区：[1]吉首大学数学与统计学院,湖南吉首416000

出　　处：《吉首大学学报(自然科学版)》2025年第1期12-17,共6页Journal of Jishou University(Natural Sciences Edition)

基　　金：湖南省教育厅科学研究重点项目(22A0368)。

摘　　要：研究了一类具有时滞效应和logistic增长的SIS传染病模型的动力学性质.运用泛函微分方程基本理论和常数变易法证明了模型解的非负性和有界性,结合特征方程得到了各平衡点局部稳定的条件.以时滞τ为分支参数,通过Hopf分支理论,获得了地方病平衡点在不稳定时发生Hopf分支的条件.The dynamical properties of a class of SIS infectious disease models with time delay effects and logistic growth are investigated.The non-negativity and boundedness of the model solutions are proved by using the basic theory of functional differential equations and the constant variational method,and the conditions for the local stability of the equilibrium points are obtained by combining with the characteristic equations.Taking the time delayτas the branching parameter,the conditions for Hopf branching of the endemic equilibrium points when they are unstable are obtained by Hopf branching theory.

关 键 词：SIS传染病模型 LOGISTIC增长 时滞效应 HOPF分支 稳定性 

分 类 号：O175[理学—数学]