Exponential stability of traveling waves in a nonlocal dispersal epidemic model with delay

In this paper, we are concerned with the stability of traveling waves of a nonlocal dispersal epidemic model with delay. In the quasi-monotone case, we prove the exponential stability of traveling wavefronts by the weighted-energy method and the comparison principle, when the initial perturbation around the traveling wavefront decays exponentially as x→−∞, but can be arbitrarily large in other locations. In the non-quasi-monotone case, we investigate the exponential stability of traveling waves when the initial perturbation around the traveling wave is properly small in a weighted norm.