Traveling Waves for a Spatial SIRI Epidemic Model

Abstract

The aim of this paper is to study the traveling waves in a spatial SIRI epidemic model arising from herpes viral infection. We obtain the complete information about the existence and non-existence of traveling waves in the model. Namely, we prove that when the basic reproduction number $\mathcal{R}_0 \gt 1$, there exists a critical wave speed $c^* \gt 0$ such that for each $c \gt c^*$, the model admits positive traveling waves; and for $c \lt c^*$, the model has no non-negative and bounded traveling wave. We also give some numerical simulations to illustrate our analytic results.