一类具有Logistic增长和病程的SIR模型  

A Class SIR Epidemic Model with Logistic Growth and Infection Age

作　　者：杨俊元[1,2] 郑福[3] 王晓燕[2] 张凤琴[2] 

机构地区：[1]北京信息与控制研究所,北京100037 [2]运城学院数学系,山西运城044000 [3]渤海大学数学系,辽宁锦州211016

出　　处：《数学的实践与认识》2009年第11期120-124,共5页Mathematics in Practice and Theory

基　　金：山西省科技开发项目(20081045);运城学院院级科研项目(20060218)

摘　　要：研究具有Logistic增长和病程的SIR流行病模型.运用微分、积分方程理论,得到再生数R0<1时,无病平衡点E0是全局渐近稳定的;而当R0>1时,地方病平衡点E*是局部渐近稳定的.It is diseussed a SIR epidemic model with Logistic growth and infection age. The disease-free equilibrium E0 is globally asymptotically stable if R0 〈 1, and also the endemic equilibrium E^＊ is locally asymptotically stable if R0 〉 1, by using the theory of differential and integral equation.

关 键 词：数学模型 LOGISTIC增长 再生数 平衡点 稳定性 

分 类 号：R181.3[医药卫生—流行病学] O175[医药卫生—公共卫生与预防医学]