Wave propagation for a discrete diffusive vaccination epidemic model with bilinear incidence

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 ${\mathrm{\Re }}_0$. More specifically, the system admits a nontrivial TWS when ${\mathrm{\Re }}_0>1$ 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.