Existence of Travelling Waves with Strong Generic Kernel in a Vector-Disease Model

In this paper,traveling wave solutions for a vector-disease model incorporating time delay and diffusion have been studied.The existence of traveling wave solutions for the sufficiently small delays has been proved.In order to solve these problems,we are able to deal with travelling wave solutions using dynamical systems techniques,invariant manifold theory,together with linear chain techniques and the geometric singular perturbation theory.For the strong generic delay kernel,traveling wave solutions exist while the delay is sufficiently small,using the methods above.