一类SIQS传染病随机离散模型的稳定性
Stability of a Class of Stochastic Discrete SIQS Epidemic Model
储家蕊 1廖新元1
作者信息
- 1. 南华大学 数理学院,湖南 衡阳 421001
- 折叠
摘要
本文考虑传染病模型SIQS系统,假设系统受到随机扰动的影响,基于该随机扰动与系统状态和平衡状态的偏差成正比的情况下,构建了随机离散SIQS传染病模型.利用Euler-Maruyama方法和Lyapunov泛函理论,结合MATLAB求解线性矩阵,推导出模型正平衡状态渐近均方稳定的充分条件,并通过数值模拟验证了其正确性.
Abstract
This paper considers the infectious disease model SIQS system,assuming that the system is affected by stochastic perturbations.A stochastic discrete SIRS epidemic model was constructed based on the assumption that the stochastic perturbation is proportional to the deviation between the system state and the equilibrium state.By using the Euler-Maruyama method and Lyapunov functional theory,in conjunction with MATLAB for solving linear matrix equations,we derive sufficient conditions for the asymptotic mean square stability of the model's positive equilibrium state.Numerical simulations are conducted to validate the correctness of these conditions.
关键词
随机离散SIQS传染病模型/渐近均方稳定/Lyapunov泛函Key words
stochastic discrete SIQS epidemic model/asymptotic mean square stability/Lyapunov functional引用本文复制引用
出版年
2024
NETL
NSTL
万方数据