Traveling waves for a diffusive virus infection model with humoral immunity, cell-to-cell transmission, and nonlinear incidence

This paper is concerned with the existence and nonexistence of traveling waves of a virus infection model with humoral immunity, cell-to-cell transmission, and general nonlinear incidence. Our results show that the existence of traveling wave solutions is determined not only by the basic reproduction number R-0 of virus infection and the antibody response reproduction number R-1 but also by the critical wave speed c*. More precisely, we obtain the existence of traveling wave solution connecting infection-free equilibrium and antibody-free infection equilibrium for R-0 > 1, R-1 < 1, and c > c(*) and connecting infection-free equilibrium and antibody-present infection equilibrium for R-0 > 1, R-1 > 1, and c > c(*). The existence of traveling wave solution connecting infection-free equilibrium and antibody-present infection equilibrium is discussed. Some numerical simulations are carried out to illustrate our analytical results.