Traveling Waves in a Kermack-McKendric Epidemic Model

Abstract

This study explores the existence of traveling wave solutions in the classical Kermack-McKendrick epidemic model with local diffusive. The findings highlight the critical role of the basic reproduction number R0 in shaping wave dynamics. Traveling wave solutions are shown to exist for wave speeds c ≥ c* when R0 > 1, with c* denoting the minimal wave speed. Conversely, no traveling waves are observed for c < c* or R0 < 1. Numerical simulations are employed to validate the theoretical results, demonstrating the presence of traveling waves for a range of nonlinear incidence functions and offering insights into the spatial spread.