一类具有垂直传染的随机SIS模型的稳定性

Stability of Stochastic SIS Model with Vertical Transmission

研究一类具有饱和发生率和垂直传染的随机SIS传染病模型,分别考虑外部环境对于易感者和染病者出生率、死亡率的扰动,证明了模型存在唯一的全局正解,通过构造Lyapunov函数证明了传染病的灭绝,得到疾病持久的充分条件。

A stochastic SIS epidemic model with saturation incidence and vertical transmission is investigated.Consider the noises of the external environment for the birth rate and mortality of susceptible and infective persons,respectively.There exists a unique global positive solution of the stochastic system.The extinction of epidemics was shown by using Lyapunov functions,the sufficient condition for persistence has been established in the mean of the disease.