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

Abstract

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 of virus infection and the antibody response reproduction number but also by the critical wave speed . More precisely, we obtain the existence of traveling wave solution connecting infection‐free equilibrium and antibody‐free infection equilibrium for , and and connecting infection‐free equilibrium and antibody‐present infection equilibrium for , and . 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.

Spreading speeds in an asymptotic autonomous system with application to an epidemic model

“…The main result is proved by using the known results for cooperative systems and constructing different auxiliary systems. Due to the special form of (), the study recipe is significantly different from many other epidemic models; see some recent results of propagation dynamics in SIR models [43–47]. Although we confirmed the leftward and rightward spreading speeds for this model under different conditions, the dynamics of () deserves further investigation since it may relate to some important models including ().…”