潜伏期和染病期均具有康复的年龄结构MSEIS流行病模型的稳定性

Stability of an Age-structured MSEIS Epidemic Model with Recovery both in Latent Period and in Infectious Period

本文建立和研究了潜伏期和染病期均具有康复的年龄结构MSEIS流行病模型.在总人口规模不变的假设下,得到了决定疾病消亡与否的基本再生数R0的表达式,证明了当R0<1时,无病平衡点是局部和全局渐近稳定的,此时疾病消失;当R0>1时,无病平衡点不稳定,此时系统至少存在一个地方病平衡点,并在一定条件下证明了地方病平衡点的局部渐近稳定性.

An age-structured MSEIS epidemic model with recovery both in latent period and in infectious period is studied. By using the theory and methods in differential and integral equation, the explicit expression of the basic reproductive number was first obtained,it is showed that the disease-free equilibrium is locally and globally asymptotically stable if 〈1 , at least one endemic equilibrium exists if 〉 1, the stability conditions of the endemic equilibrium are also given.