一类带有潜伏期和部分免疫的传染病模型的全局分析  

Global Analysis of an Epidemic Model with Latent Period and Partial Immunity

作　　者：王文娟[1] 辛京奇[1] 

机构地区：[1]运城学院应用数学系,山西运城044000

出　　处：《数学的实践与认识》2009年第17期97-103,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10471040);山西省自然科学基金(2009011005-3);山西省重点扶持学科项目

摘　　要：通过假设被接种者具有部分免疫,建立了一类具有潜伏期和接种的SEIR传染病模型,借助再生矩阵得到了确定此接种模型动力学行为的基本再生数.当基本再生数小于1时,模型只有无病平衡点;当基本再生数大于1时,除无病平衡点外,模型还有唯一的地方病平衡点.借助Liapunov函数,证明了无病平衡点和地方病平衡点的全局稳定性.Under the assumption that the vaccinated individuals have partial immunity, an SEIR epidemic model with Latent period and vaccination was established, and the basic productive number determining the dynamics of the model was obtained. When the basic productive number is less than 1, the model only has the disease-free equilibrium; when the basic productive number is greater than 1, in addition to the disease-free equilibrium, the model also has a unique endemic equilibrium. By means of Liapunov function, the global stability of the disease-free equilibrium and endemic equilibrium was proved.

关 键 词：传染病模型 部分免疫 平衡点 全局稳定性 

分 类 号：O175[理学—数学]