Spatiotemporal Dynamics and Wave Propagation in the Diffusive Kermack-McKendrick Model

Abstract

We study the existence of traveling wave solutions for a diffusive Kermack–McKendrick SIR model with standard incidence. The three compartments—susceptible S, infected I, and recovered R—are all taken into account in the traveling waves analysis. We demonstrate that the minimum wave speed of traveling waves for this three-dimensional system can be obtained from the linearization around the initial disease-free equilibrium. The proof is based on Schauder’s fixed point theorem and the Arzelà-Ascoli theorem. This work offers a valuable approach for studying high-dimensional epidemic models.