Traveling wave solutions for a diffusive sis epidemic model

Abstract

In this paper, we study the traveling wave solutions of an SIS reaction-diffusion epidemic model. The techniques of qualitative analysis has been developed which enable us to show the existence of traveling wave solutions connecting the disease-free equilibrium point and an endemic equilibrium point. In addition, we also find the precise value of the minimum speed that is significant to study the spreading speed of the population towards to the endemic steady state.