Traveling wave phenomena of a diffusive and vector-bias malaria model

Abstract

This paper is devoted to the study of a diffusive and vector-bias malaria model. We first analyze the well-posedness of the initial value problem of the model. Then, according to the basic reproduction ratio R0, we establish the existence and non-existence of traveling wave solutions for the model. The proof of the main theorems is based on Schauder fixed point theorem and the variation of constants formula of ODEs.