一类具有饱和发生率和复发的随机SIRI模型的稳定性  

Stability of a Stochastic SIRI Model with Saturated Incidence and Relapse

作　　者：穆宇光 徐瑞 MU Yuguang;XU Rui(Military and Political Basic Department, Army Engineering University, Shijiazhuang050003, China)

机构地区：[1]陆军工程大学石家庄校区军政基础系

出　　处：《应用数学》2019年第3期570-580,共11页Mathematica Applicata

基　　金：国家自然科学基金(11871316,11371368)

摘　　要：本文研究一类具有饱和发生率和复发的随机SIRI传染病模型.首先,我们证明随机系统存在唯一的全局正解.然后讨论无病平衡点的稳定性,并利用Lyapunov函数法证明流行病的灭绝.随后,我们得到疾病持久性的充分条件.最后,通过数值模拟说明结论的正确性.In this paper, a stochastic SIRI epidemiological model with saturation incidence and relapse is investigated. Firstly, we show that there exists a unique global positive solution of the stochastic system. Then we discuss the stability of the disease-free equilibrium state and show the extinction of epidemics by using Lyapunov functions. Subsequently, a sufficient condition for persistence has been established in the mean of the disease. Finally, some numerical simulations are carried out to confirm the analytical results.

关 键 词：随机SIRI传染病模型 复发 饱和发生率 灭绝性 持久性 

分 类 号：O175.1[理学—数学]