Asymptotic speed of propagation and traveling wavefronts for a lattice vector disease model

In this paper, we study a lattice vector disease model with infinite delay and global spatial interaction. We obtain the existence of solutions of the initial value problem, the asymptotic speed of propagation and the strictly monotonic traveling waves for the system. We also confirm that the asymptotic speed of propagation coincides with the minimal wave speed for traveling wavefronts. Furthermore, some asymptotic behaviors for the traveling waves as ξ=n+ct→−∞ξ=n+ct→−∞ are described.