The Traveling Wave Solutions in a Mixed-Diffusion Epidemic Model

Abstract

In this paper, we study the traveling wave solution of an epidemic model with mixed diffusion. First, we give two definitions of the minimum wave speeds and prove that they are equivalent. Second, the existence, decaying behavior, and uniqueness of traveling wave fronts are obtained. Third, the signs of minimum wave speeds are studied, and further, in two specific cases of the dispersal kernel, we show how to identify the signs of minimum wave speeds.

Keywords

• traveling wave solutions
• epidemic model
• mixed-diffusion
• nonlocal dispersal
• minimum wave speeds