Dynamics of a nonlocal multi-type SIS epidemic model with seasonality

In this paper, we propose and study a multi-type SIS nonlocal epidemic model with seasonality. We first establish the existence of the spreading speed c⁎ and the non-existence of periodic traveling waves with wave speed cc⁎. Finally, the existence of the critical periodic traveling wave fronts is established by using a limiting argument. To overcome the difficulty of lack of compactness of solution maps of the nonlocal system with respect to compact open topology, we show that the solution sequence is pre-compact in Lloc(R2,Rm).