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
  • [41] A Stochastic Model for Transmission Dynamics of AIDS with Protection Consciousness and Log-normal Ornstein-Uhlenbeck Process
    Jiao, Xue
    Zhang, Xinhong
    Jiang, Daqing
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2024, 23 (SUPPL 1)
  • [42] Stationary distribution and extinction of a stochastic HLIV model with viral production and Ornstein-Uhlenbeck process
    Liu, Qun
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2023, 119
  • [43] Stationary distribution and extinction of a stochastic SVEIS epidemic model incorporating Ornstein-Uhlenbeck process
    Song, Yunquan
    Zhang, Xinhong
    APPLIED MATHEMATICS LETTERS, 2022, 133
  • [44] Analysis of a stochastic HIV/AIDS model with commercial heterosexual activity and Ornstein-Uhlenbeck process
    Hao, Yicheng
    Luo, Yantao
    Huang, Jianhua
    Zhang, Long
    Teng, Zhidong
    MATHEMATICS AND COMPUTERS IN SIMULATION, 2025, 234 : 50 - 72
  • [45] Dynamics of a stochastic predator-prey model with disease in predators and Ornstein-Uhlenbeck process
    Yuan, Meng
    Ning, Wenxu
    Zhao, Chenxia
    Zhang, Tonghua
    Yuan, Sanling
    INTERNATIONAL JOURNAL OF BIOMATHEMATICS, 2024,
  • [46] Dynamics of a stochastic reaction-diffusion Kawasaki disease model with Ornstein-Uhlenbeck process
    Hao, Yicheng
    Luo, Yantao
    Huang, Jianhua
    Zhang, Long
    Teng, Zhidong
    NONLINEAR DYNAMICS, 2025, : 15619 - 15643
  • [47] Stationary distribution and extinction of a stochastic generalized SEI epidemic model with Ornstein-Uhlenbeck process
    Su, Tan
    Zhang, Xinhong
    APPLIED MATHEMATICS LETTERS, 2023, 143
  • [48] A STOCHASTIC EXAMINATION OF THE SIRI EPIDEMIC MODEL INCLUDING NONLINEAR RELAPSE AND THE ORNSTEIN-UHLENBECK PROCESS
    El Haitami, Adil
    COMMUNICATIONS IN MATHEMATICAL BIOLOGY AND NEUROSCIENCE, 2024,
  • [49] Asymptotic Properties of a Stochastic SIR Model With Regime Switching and Mean-Reverting Ornstein-Uhlenbeck Process
    Wei, Wei
    Xu, Wei
    Wang, Deli
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2025,
  • [50] Stationary distribution analysis of a stochastic SIAM epidemic model with Ornstein-Uhlenbeck process and media coverage
    Tian, Yilin
    Liu, Chao
    Cheung, Lora
    APPLIED MATHEMATICS LETTERS, 2024, 153