Propagation Dynamics in a Time Periodic Nonlocal Dispersal Model with Stage Structure

This paper is devoted to the study of propagation dynamics for a time periodic nonlocal dispersal model with stage structure. In the case where the birth rate function is monotone, we establish the existence of the spreading speed and its coincidence with the minimal wave speed for monotone periodic traveling waves by appealing to the theory developed for monotone semiflows. In the case where the birth rate function is non-monotone, we first obtain the spreading properties by the squeezing technique combined with some known results for the monotone case, and then investigate the existence of periodic traveling waves by using the asymptotic fixed point theorem due to the lack of parabolic estimates and compactness. Finally, we apply the general results to the Nicholson's blowflies model for its spatial dynamics.