Existence and Stability of Traveling Wavefronts in a Diffusive Vector Disease Model With Nonlocal Distributed Delay

This article is concerned with the traveling wave front solutions of a vector disease model with a nonlocal distributed delay incorporated as an integral convolution over all past time and the whole one‐dimensional spatial domain . In the situation when the delay kernel is assumed to be the strong generic kernel and the kernel parameter is sufficiently small, the existence and the exponential stability of traveling wavefront solutions are separately established by using the linear chain techniques and the geometric singular perturbation theory, as well as the comparison principle and the weighted energy estimates in a suitable weighted space.