Minimal wave speed in a diffusive epidemic model with temporal delay

Abstract

Taking incubation period into account, we modify Capasso et al.’s epidemic model and consider a reaction-diffusion system with time delay. By the method of upper and lower solutions to a related second-order ordinary differential equation with infinite time delay, we establish the existence of the minimal wave speed for the modified epidemic model, and show that incubation period reduces the minimal wave speed of epidemic model indeed.