一类具有非线性感染率的随机SIQS传染病模型解的渐近行为

Asymptotic Behavior of the Solution of a Random SIQS Epidemic Model with Nonlinear Infection Rate

本文研究了一类带有非线性感染率的随机SIQS传染病模型。 首先证明了该随机SIQS传染病模型对正的初始条件存在着唯一的全局正解。 然后,通过构造适当的Lyapunov函数并结合伊藤公式的应用,对该随机SIQS传染病模型的解在无病平衡点以及地方病平衡点附近的渐进行为进行了分析讨论。

This paper studies a kind of random SIQS infectious disease model with nonlinear infection rate. First, it is proved that the random SIQS infectious disease model has a unique global positive solution to the initial conditions of the positive. Then, by constructing an appropriate Lyapunov Function and combined with the application of Ito’s formula, the gradual behavior of the solution of the random SIQS infectious disease model near the disease-free balance point and the endemic disease balance point is analyzed and discussed.