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 spatiallystratifed population with non-overlapping generations. We consider mean field equation of an endemic chain-binomial process and allow individuals to disperse in the spatial habitat. To be able to model the spatial movement, we used an averaging kernel. The existence of traveling waves for traveling wave speeds greater than a certain minimum is proved. In addition, an explicit formula for the critical wave speed is given in terms of the moment generating function of the dispersal kernel and the basic reproductive ratio of the infectives