A DISCRETE TIME MODEL FOR EPIDEMIC SPREAD: TRAVELING WAVES AND SPREADING SPEEDS

Abstract

In this paper, we aim to study spread of an epidemic in a spatiallystratified population with non-overlapping generations. We consider mean fieldequation of an endemic chain-binomial process and allow individuals to dispersein the spatial habitat. To be able to model the spatial movement, we usedan averaging kernel. The existence of traveling waves for traveling wave speedsgreater than a certain minimum is proved. In addition, an explicit formula forthe critical wave speed is given in terms of the moment generating function ofthe dispersal kernel and the basic reproductive ratio of the infectives.