Traveling waves for epidemic models with nonlocal dispersal in time and space periodic habitats

This paper deals with the spatial spreading speed and traveling wave solutions of a general epidemic model with nonlocal dispersal in time and space periodic habitats. It should be mentioned that the existence of spreading speed and traveling wave solutions of nonlocal dispersal cooperative system in space-time periodic habitats have been established previously. In this paper, we further show that the epidemic system has a spreading speed c∗(ξ) and for any c>c∗(ξ), there exist a unique, continuous space-time periodic traveling wave solution (Φ1(x−ctξ,t,ctξ),Φ2(x−ctξ,t,ctξ)) of epidemic model in the direction of ξ with speed c, and there is no such solution for c