Traveling Waves for a Reaction-Diffusion Model with a Cyclic Structure

In this paper, a reaction-diffusion model with a cyclic structure is studied, which includes the SIS disease-transmission model and the nutrient-phytoplankton model. The minimal wave speed c* of traveling wave solu- tions is given. The existence of traveling semi-fronts with c > c* is proved by Schauder's fixed-point theorem. The traveling semi-fronts are shown to be bounded by rescaling method and comparison principle. The existence of traveling semi-front with c = c* is obtained by limit arguments. Finally, the traveling semi-fronts are shown to connect to the positive equilibrium by a Lyapunov function.