Exponential stability of traveling waves for a nonlocal dispersal SIR model with delay

Abstract This article is concerned with the nonlinear stability of traveling waves of a delayed susceptible-infective-removed (SIR) epidemic model with nonlocal dispersal, which can be seen as a continuity work of Li et al. [Traveling waves for a nonlocal dispersal SIR model with delay and external supplies, Appl. Math. Comput. 247 (2014), 723–740]. We prove that the traveling wave solution is exponentially stable when the initial perturbation around the traveling wave is relatively small in a weighted norm. The time decay rate is also obtained by weighted-energy estimates.