具有非单调发生率的随机离散SIR传染病模型的稳定性  

Stability of stochastic discrete SIR epidemic model with nonmonotonic incidence rate

作　　者：谭伟 刘茂省[1] Tan Wei;Liu Maoxing(College of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学理学院,太原030051

出　　处：《河南师范大学学报（自然科学版）》2023年第3期56-65,共10页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(12071445,12001501).

摘　　要：研究了一个具有非单调发生率的随机离散SIR传染病模型在平衡点上的稳定性.基于具有随机噪声扰动和非单调发生率的连续SIR传染病模型,用Euler-Marryama方法对其进行离散化,得到了一个随机离散的SIR模型.利用Lyapunov函数证明了系统在平衡点处稳定的充分条件,提出了非线性差分方程在零解处概率稳定的充分条件,以及线性差分方程在零解处均方稳定的充分条件.然后证明了系统在正平衡点和边界平衡点处的稳定性.最后,对于所得到的结论运用数值仿真进行了验证,并证明了系统中随机扰动的影响.The stability of a stochastic discrete SIR epidemic model with nonmonotonic incidence rate at equilibrium point is studied.Based on a continuous SIR epidemic model with noise disturbance and nonmonotonic incidence rate,discretized by Euler-Marryama method,and a stochastic discrete SIR model is obtained.Using Lyapunov function,we prove the sufficient conditions for the stability of the system at the equilibrium point,and propose the sufficient conditions for the probability stability of nonlinear difference equations at the zero solution and the sufficient conditions for the mean square stability of linear difference equations at the zero solution.Then we prove the stability of the system at the positive equilibrium point and the boundary equilibrium point.Finally,The conclusion is verified by numerical simulation,and the influence of stochastic disturbance in the system is proved.

关 键 词：随机离散 非单调发生率 Euler-Marryama方法 均方稳定 数值仿真 

分 类 号：O175.7[理学—数学]