Dynamical Behaviors of a Stochastic Susceptible-Infected-Treated-Recovered-Susceptible Cholera Model with Ornstein-Uhlenbeck Process

被引:0
|
作者
Li, Shenxing [1 ]
Li, Wenhe [1 ]
机构
[1] Northeast Petr Univ, Sch Math & Stat, Daqing 163318, Peoples R China
基金
中国国家自然科学基金;
关键词
cholera; Ornstein-Uhlenbeck process; stochastic model; density function; EPIDEMIC MODEL; SYSTEMS; HOST;
D O I
10.3390/math12142163
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this study, a cholera infection model with a bilinear infection rate is developed by considering the perturbation of the infection rate by the mean-reverting process. First of all, we give the existence of a globally unique positive solution for a stochastic system at an arbitrary initial value. On this basis, the sufficient condition for the model to have an ergodic stationary distribution is given by constructing proper Lyapunov functions and tight sets. This indicates in a biological sense the long-term persistence of cholera infection. Furthermore, after transforming the stochastic model to a relevant linearized system, an accurate expression for the probability density function of the stochastic model around a quasi-endemic equilibrium is derived. Subsequently, the sufficient condition to make the disease extinct is also derived. Eventually, the theoretical findings are shown by numerical simulations. Numerical simulations show the impact of regression speed and fluctuation intensity on stochastic systems.
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页数:20
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