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

Abstract

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 R0 is calculated, when R0≤1 the global asymptotical stability of the infection-free steady state is established, and when R0>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 R1 is calculated, by using the Lyapunov functions method and the persistence theory of dynamical systems we obtain that when R0>1 and R1≤1 the antibody-free infection equilibrium is globally asymptotically stable, and when R0>1 and R1>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.