随机SIS流行病模型全局正解的渐近行为

Asymptotic Behavior of Global Positive Solution to a Stochastic SIS Epidemic Model

讨论了随机SIS流行病模型全局正解的渐近行为。首先证明了模型解的全局正性和有界性;其次建立Lyapunov函数,利用Ito’s公式和随机微分方程理论研究了当R_0<1时,该模型无病平衡点的随机稳定性,当R_0>1时,该模型的解在其确定性模型地方病平衡点处的渐近行为;最后给出数值仿真验证结论,揭示随机SIS流行病模型的现实意义。

Asymptotic behavior of global positive solution to a stochastic SIS epidemic model was discussed. At first, the global positive and boundness of the solution was proved. Then, we studied the stochastic stability of the disease-free equilibrium when R0<1 and the asymptotic behavior of the solution around the endemic equilibrium of the deterministic model when R0>1 by Lyapunov function ,Ito's formula and the theory of stochastic differential equations. Finally, numerical simulations were carried out to support our results and reveal the realistic meaning of the stochastic SIS epidemic model.