A PERIODIC REACTION-DIFFUSION MODEL WITH A QUIESCENT STAGE

In this paper, we investigate the asymptotic behaviour for a periodic reaction-diffusion model with a quiescent stage. By appealing to the theory of asymptotic speeds of spread and traveling waves for monotone periodic semiflow, we establish the existence of the spreading speed and show that it coincides with the minimal wave speed for monotone periodic traveling waves. Finally, we consider the case where the spatial domain is bounded. A threshold result on the global attractivity of either zero or a positive periodic solution are established.