Dynamics of a diffusive HBV model with delayed Beddington–DeAngelis response

The purpose of this paper is to study the dynamics of a diffusive HBV model with delayed Beddington–DeAngelis response. First, we analyze the well-posedness of the initial value problem of the model in the bounded domain Ω⊆RnΩ⊆Rn. Then, we define the basic reproduction number R0R0 which serves as a threshold to predict whether epidemics will spread, and by analyzing the corresponding characteristic equations of the uninfected steady state and infected steady state, respectively, we discuss the local stability of them. Moreover, by employing two Lyapunov functionals, we investigate the global stability of the two steady states. Finally, applying a known result, we show that there exist traveling wave solutions connecting the two steady states when R0>1R0>1, and there do not exist traveling wave solutions connecting the uninfected steady state itself when R0<1R0<1. Numerical simulations are provided to illustrate the main results.