Periodic traveling waves of a SIR model with renewal and delay in one-dimensional lattice

This paper is primarily addressed to the (non)existence and asymptotic behaviors of periodic traveling waves for a SIR model with renewal and delay in one-dimensional lattice, which generalizes the conclusions of SIR models in one-dimensional continuous space. Especially, the challenge of establishing the asymptotic behaviors of periodic traveling waves when periodicity arises is solved by integral and analytic techniques. Moreover, the spreading speed is equal to the minimal wave speed can be obtained by our results.