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Long-term behavior of a stochastic HBV model with logistic hepatocyte growth and log-normal Ornstein–Uhlenbeck process

Author

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  • Tao, Hong
  • Zu, Li
  • Jiang, Daqing

Abstract

In this paper, we propose a stochastic HBV epidemic model with logistic hepatocyte growth and log-normal Ornstein–Uhlenbeck process. In deterministic systems, local asymptotic stability of the disease-free equilibrium is determined via the Routh–Hurwitz criterion; the endemic equilibrium’s stability is verified by proving global stability of its corresponding linearized system. For stochastic system, we first analyze the existence and uniqueness of globally positive solution through construct a nonnegative Lyapunov function. Subsequently, the stationary distribution of the system is confirmed by developing a complex Lyapunov function. Notably, the exact expression of probability density function near the epidemic equilibrium is derived by solving the associated four-dimensional Fokker–Planck equation. In addition, a sufficient condition for disease eradication is established via constructing a suitable Lyapunov function. In the end, we introduce numerical simulations to authenticate the theoretical outcomes, thereby ensuring that the theoretical deductions hold true in practical applications.

Suggested Citation

  • Tao, Hong & Zu, Li & Jiang, Daqing, 2026. "Long-term behavior of a stochastic HBV model with logistic hepatocyte growth and log-normal Ornstein–Uhlenbeck process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 247(C), pages 266-285.
    • Handle: RePEc:eee:matcom:v:247:y:2026:i:c:p:266-285
    DOI: 10.1016/j.matcom.2026.02.035
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    References listed on IDEAS

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    1. Liu, Qun & Jiang, Daqing, 2023. "Stationary distribution and probability density for a stochastic SEIR-type model of coronavirus (COVID-19) with asymptomatic carriers," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Hussain, Ghulam & Khan, Amir & Zahri, Mostafa & Zaman, Gul, 2022. "Ergodic stationary distribution of stochastic epidemic model for HBV with double saturated incidence rates and vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
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    4. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Periodic solution for a stochastic nonautonomous SIR epidemic model with logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 816-826.
    5. Xie, Falan & Shan, Meijing & Lian, Xinze & Wang, Weiming, 2017. "Periodic solution of a stochastic HBV infection model with logistic hepatocyte growth," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 630-641.
    6. Su, Xinxin & Zhang, Xinhong & Jiang, Daqing, 2024. "Dynamics of a stochastic HBV infection model with general incidence rate, cell-to-cell transmission, immune response and Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    7. Shenxing Li & Wenhe Li, 2024. "Dynamical behaviors of a stochastic SIVS epidemic model with the Ornstein-Uhlenbeck process and vaccination of newborns," PLOS ONE, Public Library of Science, vol. 19(10), pages 1-26, October.
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