Traveling wave solutions of a diffusive SI model with strong Allee effect

We investigate a diffusive SI epidemic model with strong Allee effect. We establish the existence of traveling wave solutions connecting a disease-free equilibrium to the co-existence equilibrium for wave speed c>c∗c>c∗. A pair of upper–lower solutions are constructed delicately such that the application of Schauder fixed point theorem and iteration technique are available in a convex set restricted by the upper-lower solutions.