两类易感者具垂直传染和预防接种的SIRS传染病模型  

THE TWO SIRS EPIDEMICAL MODELS WITH VERTICAL INFECTION AND VACCINATION IN THE EASILY INFECTED GROUPS

作　　者：付景超[1,2] 井元伟[2] 张中华[1] 张嗣瀛[1,2] 

机构地区：[1]东北电力大学理学院,吉林132012 [2]东北大学信息科学与工程学院,沈阳110004

出　　处：《系统科学与数学》2009年第4期502-511,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(62074009)资助课题.

摘　　要：讨论了具有连续预防接种和脉冲预防接种且具有垂直传染的双线性SIRS传染病模型,分别给出了SIRS传染病模型基本再生数.利用Liapunov函数方法和LaSalle不变原理证明了连续预防接种下无病平衡点和正平衡点的全局稳定性;利用脉冲微分方程的Floquet乘子理论和比较定理,证明了无病周期解的存在性和全局稳定性.The SIRS epidemical models with continuous and impulsive vaccinations are discussed. The reproduction numbers corresponding to those two models are given. A complete global analysis is given to the continuous vaccination models by using a Liapunov function and a Lasalle invariable theory. In the SIRS epidemical models with impulsive vaccinations, the existence and global stability of the disease-free periodic solution is proved by using a Floquet multiplication theory and a comparative theorem.

关 键 词：传染病模型 连续接种 脉冲接种 周期解 稳定性. 

分 类 号：R181.3[医药卫生—流行病学]