Stability of traveling wave solutions for a spatially discrete SIS epidemic model

This paper is concerned with the stability of traveling wave solutions for a spatially discrete SIS epidemic model. We investigate the problem by using the weighted energy method and comparison principles for the Cauchy problem and initial-boundary value problem of the lattice differential equations. Our main results show that any solution of the Cauchy problem for the SIS model converges exponentially to the traveling wave solution provided that the initial perturbation around the traveling wave solution belongs to a suitable weighted Banach space.