考虑信息变量Logistic自然增长的SIR传染病模型  

SIR Epidemic Model with Logistic Natural Growth of Information Variable

作　　者：原珊珊 张国洪[1] YUAN Shanshan;ZHANG Guohong(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《重庆理工大学学报（自然科学）》2020年第4期230-234,250,共6页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金项目(11701472);教育部基本科研项目(XDJK2017C055)。

摘　　要：讨论了一个信息变量按照Logistic自然增长的SIR传染病模型。得到了解的非负性和有界性,研究了无病平衡点和地方病平衡点存在性和稳定性的条件,并得到了在地方病平衡点处产生Hopf分支的条件,发现信息自然承载量的变化可能导致传染病呈周期震荡。最后用数值模拟验证了相关的结论。A SIR epidemic model with Logistic natural growth of information variables is discussed.The nonnegativityand boundedness of the solution are obtained.The conditions for the existence and stability of disease free equilibrium and endemic equilibrium are studied.We also obtain the conditions for Hopf bifurcation at endemic equilibrium.It is found that the change of natural capacity of information may leads to periodic oscillation of infectious diseases.Finally,the relevant conclusions are verified by numerical simulation.

关 键 词：信息 LOGISTIC增长 HOPF分支 稳定性 

分 类 号：O175[理学—数学]