Traveling waves of the spread of avian influenza

Abstract

This paper gives a proof for the existence and nonexistence of traveling wave solutions of a reaction-convection epidemic model for the spatial spread of H5N1 avian influenza involving a wide range of bird species and environmental contamination. The threshold condition for the existence of traveling waves coincides with the basic reproduction number exceeding one. The existence of wave solutions is obtained by constructing an invariant cone of initial functions defined on a large spatial domain, applying a fixed point theorem on this cone and then a limiting argument. The invariant cone is based on the information of initial growth pattern of the epidemic and the final size estimation during the entire course of the outbreak.