Stage-structured population systems with temporally periodic delay

For some ectotherms such as Ixodes scapularis, a vector of Lyme disease, changes in temperature are believed to affect the interstadial development time and hence give rise to a time-periodic delay due to seasonality in the population dynamics described by a stage-structured population growth model. Here, we develop a formulation linking the chronological delay with multiple stage-specific interstadial delays. We also present a definition for the basic reproductive ratio for such a system, develop a simple algorithm to compute it, and show that the results regarding the stability of the zero solution are consistent with those from computing the dominant Floquet multiplier. Numerical simulations also show that the threshold value for the population persistence or extinction depends not only on the mean but also on the amplitude and phase of the periodic development delays. Copyright (c) 2015John Wiley & Sons, Ltd.