Abstract
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 \begin{document}$ c^* $\end{document} of traveling wave solutions is given. The existence of traveling semi-fronts with \begin{document}$ c>c^* $\end{document} is proved by Schauder's fixed-point theorem. The traveling semi-fronts are shown to be bounded by rescaling method and comparison principle. The existence of traveling semi-front with \begin{document}$ c = c^* $\end{document} is obtained by limit arguments. Finally, the traveling semi-fronts are shown to connect to the positive equilibrium by a Lyapunov function.
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