| 一类随机离散的SIR流行病模型解的稳定性分析 |
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| 引用本文： | 鲁银霞,廖新元,陈会利,李佳季.一类随机离散的SIR流行病模型解的稳定性分析[J].南华大学学报(自然科学版),2019,33(1):58-61. |
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| 作者姓名： | 鲁银霞 廖新元 陈会利 李佳季 |
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| 作者单位： | 南华大学 数理学院,湖南 衡阳 421001,南华大学 数理学院,湖南 衡阳 421001,南华大学 数理学院,湖南 衡阳 421001,南华大学 数理学院,湖南 衡阳 421001 |
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| 基金项目： | 南华大学研究生科学基金项目(2018KYY095) |
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| 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。
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| 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 |
| 收稿时间： | 2018/7/23 0:00:00 |
Analysis of Stability of Solutions for a Stochastic Discrete SIR Epidemic Model |
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| LU Yinxi,LIAO Xinyuan,CHEN Huili and LI Jiaji.Analysis of Stability of Solutions for a Stochastic Discrete SIR Epidemic Model[J].Journal of Nanhua University:Science and Technology,2019,33(1):58-61. |
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| Authors: | LU Yinxi LIAO Xinyuan CHEN Huili and LI Jiaji |
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| Institution: | School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China,School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China,School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China and School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China |
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| Abstract: | 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. |
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| Keywords: | stochastic discrete SIR epidemic model linearized method lyapunov functional asymptotic mean square stability |
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