| 若干具有非线性传染力的传染病模型的稳定性分析 |
| |
| 引用本文： | 陈军杰.若干具有非线性传染力的传染病模型的稳定性分析[J].生物数学学报,2005,20(3):286-296. |
| |
| 作者姓名： | 陈军杰 |
| |
| 作者单位： | 浙江大学,数学系,浙江,杭州,310029 |
| |
| 基金项目： | 浙江省教育厅科研项目资助 |
| |
| 摘 要： | 讨论了具有常数迁入和非线性传染力的三类传染病模型,即SIRI模型,SIRI框架下的DS模型及SIR框架下的DI模型。给出了它们基本再生数R0的表达式,证明了R0≤1时无病平衡点是全局稳定的,同时证明了如果地方病平衡点存在,则必是全局稳定的结果（从而必唯一）对第一和第三个模型还给出了R0＞1时地方病平衡点的存在唯一性。
|
| 关 键 词： | 传染病模型 非线性传染力 Liapunov函数 全局稳定性 |
| 文章编号： | 1001-9626（2005）03-0286-11 |
| 收稿时间： | 2003-09-02 |
| 修稿时间： | 2004-03-05 |
Stability Analysis for some Epidemic Models with Nonlinear Infectious Force |
| |
| CHEN Jun-jie.Stability Analysis for some Epidemic Models with Nonlinear Infectious Force[J].Journal of Biomathematics,2005,20(3):286-296. |
| |
| Authors: | CHEN Jun-jie |
| |
| Abstract: | This paper considers three epidemic models with constant immigration rate and nonlinear infectious force.They are SIRI model,differential susceptibility model of SIRI, and differential infectivity model of SIR.The basic reproduction numbers R_0 are identified.The disease-free equilibrium is globally stable if R_0<1 and endemic equilibrium is globally stable if it exists.For the first and the third model,it is also proved there exists an unique endemic equilibrium when R_0>1. |
| |
| Keywords: | Epidemic models Nonlinear infectious force Liapunov function Global stability |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
