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.
引用
收藏
页数:20
相关论文
共 50 条
  • [11] Dynamic properties for a stochastic SEIR model with Ornstein-Uhlenbeck process
    Lu, Chun
    Xu, Chuanlong
    MATHEMATICS AND COMPUTERS IN SIMULATION, 2024, 216 (288-300) : 288 - 300
  • [12] Dynamical Analysis and Numerical Simulation of a Stochastic Influenza Transmission Model with Human Mobility and Ornstein-Uhlenbeck Process
    Su, Tan
    Zhang, Xinhong
    Kao, Yonggui
    Jiang, Daqing
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2025, 24 (02)
  • [13] Threshold behaviors and density function of a stochastic parasite-host epidemic model with Ornstein-Uhlenbeck process
    Zhang, Xiaoshan
    Zhang, Xinhong
    APPLIED MATHEMATICS LETTERS, 2024, 153
  • [14] Dynamical behavior and numerical simulation of a stochastic eco-epidemiological model with Ornstein-Uhlenbeck process
    Zhang, Xinhong
    Yang, Qing
    Su, Tan
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2023, 123
  • [15] Susceptible-infected-recovered model with stochastic transmission
    Gourieroux, Christian
    Lu, Yang
    CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, 2025,
  • [16] Dynamical Properties of a Chemostat Model with Log-Normal Ornstein-Uhlenbeck Process and Distributed Delay
    Gao, Miaomiao
    Jiang, Daqing
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2025, 24 (02)
  • [17] Dynamical Behaviors of a Stochastic Food Chain System with Ornstein–Uhlenbeck Process
    Qing Yang
    Xinhong Zhang
    Daqing Jiang
    Journal of Nonlinear Science, 2022, 32
  • [18] The dynamics and density function of a stochastic SEIW brucellosis model with Ornstein-Uhlenbeck process
    Wen, Buyu
    Teng, Zhidong
    Nie, Linfei
    Li, Zhiming
    Cao, Hong
    INTERNATIONAL JOURNAL OF BIOMATHEMATICS, 2025,
  • [19] A stochastic turbidostat model with Ornstein-Uhlenbeck process: dynamics analysis and numerical simulations
    Mu, Xiaojie
    Jiang, Daqing
    Hayat, Tasawar
    Alsaedi, Ahmed
    Liao, Yunhui
    NONLINEAR DYNAMICS, 2022, 107 (03) : 2805 - 2817
  • [20] A stochastic turbidostat model with Ornstein-Uhlenbeck process: dynamics analysis and numerical simulations
    Xiaojie Mu
    Daqing Jiang
    Tasawar Hayat
    Ahmed Alsaedi
    Yunhui Liao
    Nonlinear Dynamics, 2022, 107 : 2805 - 2817