Traveling Wave Phenomena in a Kermack–McKendrick SIR Model

We study the existence and nonexistence of traveling waves of general diffusive KermackMcKendrick SIR models with standard incidence where the total population is not constant. The three classes, susceptible S, infected I and removed R, are all involved in the traveling wave solutions. We show that the minimum speed for the existence of traveling waves for this three-dimensional non-monotonic system can be derived from its linearizaion at the initial disease-free equilibrium The proof in this paper is based on Schauder fixed point theorem and Laplace transform and provides a promising method to deal with high dimensional epidemic models.