具有饱和发生率的随机SIRI传染病模型

A Stochastic SIRS Epidemic Model with Saturated Incidence

研究了具有饱和发生率和复发的随机传染病模型。首先证明了随机系统正解的存在唯一性,其次利用李雅普诺夫函数和伊藤公式讨论了随机模型的解在相应确定模型的无病平衡点和地方平衡点附近波动时所需要满足的条件,最后通过数值模拟证实了这些分析结果。

In this paper, we investigate a stochastic infectious disease model with saturated incidence and relapse. First, we prove the existential uniqueness of global positivity of solutions. Using Lyapunov function and Ito formula, we discuss the conditions to be satisfied when the solution of stochastic model fluctuates around the disease-free equilibrium point and the positive equilibrium point of the corresponding deterministic model. Finally, these results are verified by numerical simulation.