奥恩斯坦-乌伦贝克过程
数学
随机微分方程
独特性
李雅普诺夫函数
应用数学
概率密度函数
流行病模型
时滞微分方程
指数函数
考克斯-英格索尔-罗斯模型
统计物理学
随机过程
微分方程
数学分析
统计
物理
非线性系统
人口
人口学
量子力学
社会学
货币经济学
经济
利率
作者
Zhenfeng Shi,Daqing Jiang
摘要
This paper considers a stochastic hybrid differential infectivity epidemic model with standard incidence perturbed by mean‐reverting Ornstein–Uhlenbeck process. Applying Lyapunov method, we first show existence and uniqueness of the global solution. Then sufficient conditions for persistence in the mean and exponential extinction of the infectious disease are obtained. Furthermore, by solving the corresponding Fokker–Planck equation, we derive that the global solution around the endemic equilibrium follows a unique probability density function. Finally, numerical simulations are employed to demonstrate the analytical results.
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