一类总人口变动的SIR和SIS组合传染病模型  

Class of the Combined SIR and SIS Contagion Model for Population with Varying Size

作　　者：兰晓晶[1] 杨海霞[1] 孙志强[1] 

机构地区：[1]兰州交通大学数理与软件工程学院,兰州730070

出　　处：《重庆工学院学报》2007年第11期40-42,共3页Journal of Chongqing Institute of Technology

基　　金：国家自然科学基金资助项目(604730304);兰州交通大学"青蓝"人才工程基金资助项目(QL-05-18A)

摘　　要：在考虑因病死亡因素的情况下,建立了一类具有常数输入的总人口变动的SIR和SIS组合传染病模型,利用微分方程稳定性理论和方法证明了无病平衡点和地方病平衡点的存在性及全局渐近稳定性,并且得到了决定疾病绝灭或持续生存的基本再生数.This paper establishes a class of combined SIR and SIS contagion model for varying-size population with constant immigration under the condition of taking death factor into consideration. By the means of the stable theory and method of differential equation, this paper proves the existence and global asymptotical stability of the disease-free equilibrium and the endemic equilibrium, and obtains the basic reproductive number which determines whether the disease dies out or remains.

关 键 词：传染病模型 平衡点 基本再生数 全局渐近稳定性 

分 类 号：O175.1[理学—数学]