期刊论文

中文

南华大学学报(自然科学版)

1673-0062

2019

33

1

58-61

10.19431/j.cnki.1673-0062.2019.01.011

南华大学研究生科学基金项目(2018KYY095).

本校为第一机构

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...