西北师范大学学报（自然科学版）2024，Vol.60Issue(1)：30-38,9.DOI:10.16783/j.cnki.nwnuz.2024.01.006
一类随机SIR传染病模型的非标准数值离散化
Nonstandard numerical discretization of a stochastic SIR epidemic model
摘要
Abstract
This paper studies the stability of a stochastic discrete SIR epidemic model with saturated incidence and vaccination rate.A deterministic SIR model with saturated incidence and vaccination rate is introduced.Considering the great influence of stochastic noise on disease transmission,the model is discretized by nonstandard finite difference(NSFD)method,and finally a stochastic discrete SIR epidemic model is obtained.This discretization method is to locally discretize the right side of the system to obtain the discrete model,and then use the generalized forward difference method to approximate the first derivative on the left side of the system,and select the appropriate denominator function.The sufficient conditions for the stability of the equilibrium solution of the system are given by using Lyapunov function method and matrix method,and the sufficient conditions for the probabilistic stability of nonlinear difference equations and the sufficient conditions for the asymptotic mean square stability of linear difference equations are also proposed.Finally,the conclusion is verified by numerical simulation.关键词
饱和发生率/随机离散模型/非标准有限差分方法/Lyapunov函数/渐近均方稳定Key words
saturation incidence/stochastic discrete model/nonstandard finite difference method/Lyapunov function/asymptotic mean square stability分类
数理科学引用本文复制引用
谭伟,刘茂省..一类随机SIR传染病模型的非标准数值离散化[J].西北师范大学学报（自然科学版）,2024,60(1):30-38,9.基金项目
国家自然科学基金资助项目(12071445,12001501) （12071445,12001501）
