具有时滞效应的SIS模型的动力学分析  

Dynamics Analysis of SIS Model with Time Delay Effect

作　　者：刘志华 曹慧[1] 徐河苗[2] LIU Zhihua;CAO Hui;XU Hemiao(School of Mathematics and Data Science,Shaanxi University of Science and Technology,Xi'an 710029,China;Department of Mathematics,Changzhi University,Changzhi Shanxi 046011,China)

机构地区：[1]陕西科技大学数学与数据科学学院,西安710029 [2]长治学院数学系,山西长治046011

出　　处：《西南师范大学学报（自然科学版）》2022年第9期37-47,共11页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(12071268,11971281)。

摘　　要：研究了一类具有媒体报道引起的时滞效应的SIS传染病模型的动力学性态.给出了模型的基本再生数,分析了无病平衡点和地方病平衡点的存在性、稳定性,讨论了地方病平衡点不稳定时可能发生的全局Hopf分支,并通过数值模拟展示了所得到的理论结果和模型的复杂动力学性态.In this paper,a SIS epidemic model with delay effect has been studied to elaborate the media impact on the dynamics of infectious diseases.The basic reproduction number of the model has been given.The existence and stability of disease-free equilibrium and endemic equilibrium has been analyzed.The global Hopf bifurcation that may occur when the endemic equilibrium is unstable has been discussed.Numerical simulations show the theoretical results and the complex dynamic behavior of the model.

关 键 词：SIS模型 媒体报道 时滞效应 稳定性 HOPF分支 

分 类 号：O175.14[理学—数学]