Speed selection of traveling waves to an epidemic model

Abstract

This paper is devoted to investigating the selection mechanism of the minimal wave speed for traveling waves to an epidemic model. The determinacy of linear and nonlinear selections is further discussed by the upper–lower solutions and comparison principle. A threshold is defined by the eigenvalue problem of the linearized system. We show that the nonlinear determinacy is obtained as long as there exists a lower solution with a faster decay and a speed parameter that is larger than the threshold. When the speed parameter equals to the threshold, if there exists an upper solution satisfying proper limit behavior, then the linear selection is realized. For a special function of infection rate, we obtain a threshold parameter that determines the linear and nonlinear selections.