Traveling wave solution for a diffusive simple epidemic model with a free boundary

In this paper, we proved existence and nonexistence of traveling wave solution for a diffusive simple epidemic model with a free boundary in the case where the diffusion coefficient \begin{document}$ d $\end{document} of susceptible population is zero and the basic reproduction number is greater than 1. We obtained a curve in the parameter plane which is the boundary between the regions of existence and nonexistence of traveling wave. We numerically observed that in the region where the traveling wave exists the disease successfully propagate like traveling wave but in the region of no traveling wave disease stops to invade. We also numerically observed that as \begin{document}$ d $\end{document} increases the speed of propagation slows down and the parameter region of propagation narrows down.