Dynamics of a stochastic HBV infection model with general incidence rate, cell-to-cell transmission, immune response and Ornstein–Uhlenbeck process

In this paper, a stochastic HBV infection model with virus-to-cell infection, cell-to-cell transmission and CTL immune response is proposed. The model has a general form of infection rate, in which the contact rate is governed by the log-normal Ornstein–Uhlenbeck process. First, it is proved that the stochastic model has a unique positive global solution. The dynamic properties of the solutions around the equilibrium points are also analysed. It further follows that the disease-free equilibrium is globally asymptotically stable if R0<1, while the endemic equilibrium is globally asymptotically stable if R0>1. Then, we establish sufficient conditions for the stationary distribution and extinction of the model by constructing suitable Lyapunov functions, respectively. After that, we calculate the exact analytical expression for the probability density function of stationary distribution near the quasi-endemic equilibrium. Finally, the effect of the Ornstein–Uhlenbeck process on the dynamical behaviour of the model is verified by numerical simulations. One of the most interesting findings is that larger regression speeds and smaller volatility intensities can significantly reduce major outbreaks of HBV infection within the host, which may have important implications for future HBV therapeutic regimens.