Existence of travelling waves in a diffusive vector disease model with distributed delay

Abstract

This paper is concerned with a diffusive vector disease model with distributed delay. The existence of travelling wave front solutions connecting the zero equilibrium and the positive equilibrium is established by using an iterative technique and a nonstandard ordering for the set of profiles of the corresponding wave system recently developed by Wang, Li and Ruan (Travelling wave fronts in reactiondiffusion systems with spatio-temporal delays. J. Differential Equations 222 (2006), 185---232). The existence of travelling front solutions shows that there is a moving zone of transition from the disease free state to the infective state.