  The aim of the current paper is to study the existence of traveling wave
solutions (TWS) for a vaccination epidemic model with bilinear incidence. The
existence result is determined by the basic reproduction number $\Re_0$. More
specifically, the system admits a nontrivial TWS when $\Re_0>1$ and $c \geq
c^*$, where $c^*$ is the critical wave speed. We also found that the TWS is
connecting two different equilibria by constructing Lyapunov functional.
Lastly, we give some biological explanations from the perspective of
epidemiology.
