具有阶段结构的SEI传染病模型的全局分析

On Dynamic Behavior of an SEI Epidemic Model with Stage-Structure

建立和研究了一类具有幼年和成年两个阶段结构的SEI传染病模型,通过分析平衡点的特征方程,讨论了平衡点的局部稳定性.得到了基本再生数是传染病最终消除或成为地方病的阀值,当基本再生数小于1时,无病平衡点为全局稳定的,传染病最终消除,否则系统将一致持续生存.

In this paper,an SEI Epidemic Model with Stage-structure is established and studied,in which the population is divided into two stages:immature stage and mature stage.By discussing the eigenvalue equation of the equilibriums,locally asymptotic stability of the equilibriums are obtained.It is shown that the global dynamics is determined by the basic reproduction number,when the basic reproduction number is less than 1,the disease free equilibrium is globally asymptotically stable;otherwise the disease persists.