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 R0$$ {\mathcal{R}}_0 $$ of virus infection and the antibody response reproduction number R1$$ {\mathcal{R}}_1 $$ but also by the critical wave speed c∗$$ {c}^{\ast } $$. More precisely, we obtain the existence of traveling wave solution connecting infection‐free equilibrium and antibody‐free infection equilibrium for R0>1,R1<1$$ {\mathcal{R}}_0>1,{\mathcal{R}}_1<1 $$, and c>c∗$$ c>{c}^{\ast } $$ and connecting infection‐free equilibrium and antibody‐present infection equilibrium for R0>1,R1>1$$ {\mathcal{R}}_0>1,{\mathcal{R}}_1>1 $$, and c>c∗$$ c>{c}^{\ast } $$. 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. [ABSTRACT FROM AUTHOR]