Critical travelling waves of a vector-host disease model with spatio-temporal nonlocal effect

Abstract

This paper is concerned with the existence of travelling wave solution (TWS) with critical speed c∗ for a nonlocal reaction–diffusion vector-host disease model. When the basic reproduction ratio R0 at the disease-free equilibrium is greater than one, we adopt the limiting arguments and contradictory approach to show the existence of critical TWS. Furthermore, it is observed that R0 at the final size of susceptible hosts and vectors is less than one, which indicates that the disease will not eventually break out.