Traveling waves for a nonlocal dispersal vaccination model with general incidence

This paper is concerned with the existence and asymptotic behavior of traveling wave solutions for a nonlocal dispersal vaccination model with general incidence. We first apply the Schauder’s fixed point theorem to prove the existence of traveling wave solutions when the wave speed is greater than a critical speed c^∗. Then we investigate the boundary asymptotic behaviour of traveling wave solutions at +∞ by using an appropriate Lyapunov function. Applying the method of two-sided Laplace transform, we further prove the non-existence of traveling wave solutions when the wave speed is smaller than c^∗. From our work, one can see that the diffusion rate and nonlocal dispersal distance of the infected individuals can increase the critical speed c^∗, while vaccination reduces the critical speed c^∗. In addition, two specific examples are provided to verify the validity of our theoretical results, which cover and improve some known results.