On uniqueness of traveling waves for a reaction diffusion equation with spatio-temporal delay

This paper is devoted to study the uniqueness (up to translation) of traveling wave solutions for a general reaction-diffusion equation with spatio-temporal delay. It is shown that the traveling wave solutions with any given admissible speed (including the minimal wave speed) of this general equation are unique up to translation under certain assumptions. The main result helps us to solve some open problems on the uniqueness of traveling wave solutions of a few well-known models such as the diffusive Nicholson's blowflies model, the diffusive Mackey-Glass' hematopoiesis model, an age-structured population model, an epidemic model and a reaction-diffusion model with a quiescent stage. (c) 2021 Elsevier Inc. All rights reserved.