具有常数输入的SEIR模型的稳定性分析  

Stable Analysis of SEIR Epidemic Model with Constant Recruitment

作　　者：王莲花[1] 刚毅[1] 张凤琴[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18期208-214,共7页Mathematics in Practice and Theory

基　　金：山西省自然科学基金(20051010);山西省重点扶持学科项目;山西省教育厅科技开发项目(2007151);运城学院院级科研项目(20060217)

摘　　要：讨论了易感者类和潜伏者类均为常数输入,潜伏期、染病期和恢复期均具有传染力,且传染率为一般传染率的SEIR传染病模型.利用Hurwitz判据证明了地方病平衡点的局部渐近稳定性,进一步利用复合矩阵理论得到了地方病平衡点全局渐近稳定的充分条件.We consider an SEIR epidemic model with the general contact rate that susceptible and exposed individuals have constant recruitment. In the model, the latent, infected and recovered period are also infective. The local asymptotical stable results of the epidemic equilibrium is proved by Hurwitz criterion. Furthermore, using the compound matrix theory we obtain sufficient conditions for the global asymptotical stable of the unique endemic equilibrium.

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[理学—数学]