Propagation dynamics of a nonlocal spatial Lyme disease model in a time–space periodic habitat

Abstract

This paper is concerned with the investigation of Lyme disease spread via a time–space periodic nonlocal spatial model in an unbounded domain. We first study the spatial periodic initial problem of the model system and discuss the existence of principal eigenvalue of a linear system with the spatial nonlocality induced by time delay under a smooth assumption. Then we establish the existence of the spreading speeds, and show its coincidence with the minimal wave speed. We further perform a perturbation argument to remove this aforementioned assumption and provide an estimation of the spreading speeds in terms of the spectral radius. Simulations are presented to illustrate our analytic results.