Traveling waves for SVIR epidemic model with nonlocal dispersal

In this paper, we studied an SVIR epidemic model with nonlocal dispersal and delay, and we find that the existence of traveling wave is determined by the basic reproduction number $\Re_0$ and minimal wave speed $c^*$. By applying Schauder's fixed point theorem and Lyapunov functional, the existence and boundary asymptotic behaviour of traveling wave solutions is investigated for $\Re_0>1$ and $c>c^*$. The existence of traveling waves is obtained for $\Re_0>1$ and $c=c^*$ by employing a limiting argument. We also show that the nonexistence of traveling wave solutions by Laplace transform. Our results imply that (i) the diffusion and infection ability of infected individuals can accelerate the wave speed; (ii) the latent period and successful rate of vaccination can slow down the wave speed.