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

Hong Tao, Li Zu and Daqing Jiang

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 247, issue C, 266-285

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.

Keywords: Local stability; Stationary distribution; Probability density function; Extinction; Stochastic HBV model (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:247:y:2026:i:c:p:266-285

DOI: 10.1016/j.matcom.2026.02.035

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