Traveling wave solutions for a discrete diffusive epidemic model with asymptomatic carriers

Abstract

This paper mainly concerns about the traveling wave solution (TWS) for a discrete diffusive epidemic model with asymptomatic carriers. Analysis of the model shows that the minimum wave speed [Formula: see text] exists if a threshold [Formula: see text] is greater than one. With the help of sub- and super-solutions, we find that the condition for the existence of TWS is [Formula: see text] and wave speed [Formula: see text]. Further, we prove that the TWS connects two different boundary steady states. Through the arguments with Laplace transform, we show there is no TWS for the model if [Formula: see text] and [Formula: see text] or [Formula: see text].