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Stage‐structured population systems with temporally periodic delay
Author(s) -
Wu Xiaotian,
Magpantay Felicia Maria G.,
Wu Jianhong,
Zou Xingfu
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3424
Subject(s) - mathematics , floquet theory , population , population model , stadial , extinction (optical mineralogy) , ectotherm , multiplier (economics) , hopf bifurcation , control theory (sociology) , demography , computer science , bifurcation , control (management) , artificial intelligence , physics , nonlinear system , ecology , biology , paleontology , macroeconomics , quantum mechanics , sociology , optics , economics , pleistocene
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 © 2015 John Wiley & Sons, Ltd.