Analysis of a diffusive virus infection model with humoral immunity, cell-to-cell transmission and nonlinear incidence

Abstract

In this paper, we investigate a reaction–diffusion virus infection model with humoral immunity and nonlinear incidence in heterogeneous and homogenous environments. The model includes simultaneously the virus-to-cell and cell-to-cell transmissions of the infection. The well-posedness of solutions, including the existence of global solutions and the ultimate boundedness, is established. The virus infection reproduction number R0 is calculated. When R0≤1, it is proved that the infection-free steady state is globally asymptotically stable. Otherwise, when R0>1 then the infection with antibody-free response is uniformly persistent. Furthermore, the antibody-free infection equilibrium is also globally asymptotically stable in spatially homogeneous case. In order to investigate the effect of humoral immunity, the virus infection with antibody response model in the spatially homogeneous environment is considered. The antibody response reproduction number R1 is calculated. The threshold criteria on the uniform persistence of total model and the global asymptotic stability of the antibody-response infection equilibrium are established. Finally, the numerical examples are presented to illustrate the theoretical results and verify the conjectures.