Traveling wavefronts in a bistable reaction diffusion system with spatio-temporal delay

This paper is concerned with a reaction–diffusion system with spatio-temporal delay. Under the bistable assumptions, the existence of traveling wavefronts is established by transforming the system with spatio-temporal delay to a three-dimensional reaction–diffusion system without delay. The uniqueness (up to a translation) of the traveling wavefronts is also proved by using upper and lower solutions technique. From the point of view of epidemiology, the result implies that the spatio-temporal delay appeared in the interaction term is not sensitive to the moving zone for the transition from the disease-free state to the infective state.