A Stage-Structured Population Model with Time-Dependent Delay in an Almost Periodic Environment

Abstract

In this paper, we derive and investigate a stage-structured population growth model with time-dependent maturation delays in an almost periodic environment. We introduce the basic reproduction ratio $$R_{0}$$ for this model and then obtain a threshold-type result on its global dynamics in terms of $$R_{0}$$. It is shown that the population tends to die out if $$R_{0} 1$$. In the monotone case and a specific non-monotone case, we also prove that there exists a globally stable almost periodic solution when $$R_{0}>1$$. For the Nicholson blowflies model, we further study the influence of time-dependent maturation delay on $$R_{0}$$ via numerical simulations.