Dynamics of a time-periodic and delayed reaction-diffusion model with a quiescent stage

In this paper, we study a time-periodic and delayed reaction-diffusion system with quiescent stage in both unbounded and bounded habitat domains. In unbounded habitat domain R, we first prove the existence of the asymptotic spreading speed and then show that it coincides with the minimal wave speed for monotone periodic traveling waves. In a bounded habitat domain Omega subset of R-N (N >= 1), we obtain the threshold result on the global attractivity of either the zero solution or the unique positive time-periodic solution of the system.