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

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 c* exists if a threshold R is greater than one. With the help of sub- and super-solutions, we find that the condition for the existence of TWS is R > 1 and wave speed c > c*. 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 R > 1 and 0 < c < c* or R <= 1.