Global dynamics of a reaction-diffusion virus infection model with humoral immunity and nonlinear incidence

In this paper, we propose and investigate a reaction-diffusion virus infection model with humoral immunity and nonlinear incidence. In spatially heterogeneous case, the basic reproduction number of virus infection R-0 is calculated, when R-0 <= 1 the global asymptotical stability of the infection-free steady state is established, and when R-0 > 1 the uniform persistence of infected cells and viruses, as well as the existence of antibody free infection steady state are also obtained. In spatially homogeneous case, the antibody response basic reproduction number R-1 is calculated, by using the Lyapunov functions method and the persistence theory of dynamical systems we obtain that when R-0 > 1 and R-1 <= 1 the antibody-free infection equilibrium is globally asymptotically stable, and when R-0 > 1 and R-1 > 1 the model is uniformly persistent and the infection equilibrium exists and is also globally asymptotically stable. Finally, the numerical examples are presented in order to verify the validity of our theoretical results. (C) 2019 Elsevier Ltd. All rights reserved.