Traveling waves for a nonlocal dispersal vaccination model with general incidence

Abstract

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 \begin{document}$ c^* $\end{document} . Then we investigate the boundary asymptotic behaviour of traveling wave solutions at \begin{document}$ +\infty $\end{document} by using an appropriate Lyapunov function. Applying the method of two-sided Laplace transform, we further prove the non-existence of traveling wave solutions when the wave speed is smaller than \begin{document}$ c^* $\end{document} . From our work, one can see that the diffusion rate and nonlocal dispersal distance of the infected individuals can increase the critical speed \begin{document}$ c^* $\end{document} , while vaccination reduces the critical speed \begin{document}$ c^* $\end{document} . In addition, two specific examples are provided to verify the validity of our theoretical results, which cover and improve some known results.