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This paper is devoted to the investigation of the asymptotic behaviour for a reactiondiffusion model with a quiescent stage. We first establish the existence of the asymptotic speed of spread and show that it coincides with the minimal wave speed for monotone travelling waves. Then we obtain a threshold result on the global attractivity of either zero or positive steady state in the case where the spatial domain is bounded.doi:10.1098/rspa.2006.1806 fatcat:6ksskh5hazdzzlykdlzdwhe5sy