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 Omega subset of R-n. Then, we define the basic reproduction number R-0 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 R-0 > 1, and there do not exist traveling wave solutions connecting the uninfected steady state itself when R-0 < 1. Numerical simulations are provided to illustrate the main results. Crown Copyright (C) 2013 Published by Elsevier Ltd. All rights reserved.