Monotonicity and uniqueness of traveling waves for a reaction–diffusion model with a quiescent stage

This paper is concerned with the monotonicity and uniqueness of traveling waves for a reaction–diffusion model with quiescent stage. We first obtain the exponential decay rate of wave profiles, and then we show that any profile is strictly monotone by using the strong comparison principle. Furthermore, we prove the uniqueness (up to translation) of all traveling waves including even the waves with minimal speed.