一类随机离散的SIR流行病模型解的稳定性分析  

Analysis of Stability of Solutions for a Stochastic Discrete SIR Epidemic Model

作　　者：鲁银霞 廖新元[1] 陈会利 李佳季 LU Yinxia;LIAO Xinyuan;CHEN Huili;LI Jiaji(School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China)

机构地区：[1]南华大学数理学院,湖南衡阳421001

出　　处：《南华大学学报（自然科学版）》2019年第1期58-61,共4页Journal of University of South China：Science and Technology

基　　金：南华大学研究生科学基金项目(2018KYY095)

摘　　要：引进一个确定的用微分方程表示的SIR流行病模型,考虑到随机因素的扰动,并用Euler-Milstein法将模型进行离散化,得到了随机离散的SIR流行病模型。然后利用线性化、Lyapunov函数法,得到该模型平衡解的渐近均方稳定性的充分条件,并用数值仿真说明了所得结论的正确性。The study derives a deterministic SIR model described by ordinary differential equation.Taking the stochastic perturbation into consideration and using the Euler-Milstein discretization method,it obtains a stochastic discrete SIR epidemic model.Some sufficient conditions for the asymptotic mean square stability of the positive equilibrium state are established by linearized and Lyapunov functional method.The correctness of the conclusion is showed by numerical simulation.

关 键 词：随机离散SIR流行病模型 线性化 LYAPUNOV函数 渐进均方稳定 

分 类 号：O174[理学—数学]