Abstract
In this paper, we establish the theory of basic reproduction ratio \(R_0\) for a large class of time-delayed compartmental population models in a periodic environment. It is proved that \(R_0\) serves as a threshold value for the stability of the zero solution of the associated periodic linear systems. As an illustrative example, we also apply the developed theory to a periodic SEIR model with an incubation period and obtain a threshold result on its global dynamics in terms of \(R_0\).
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The author is very grateful to the anonymous referee for careful reading and valuable comments which led to important improvements of the original manuscript. This research was supported in part by the NSERC of Canada.
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Zhao, XQ. Basic Reproduction Ratios for Periodic Compartmental Models with Time Delay. J Dyn Diff Equat 29, 67–82 (2017). https://doi.org/10.1007/s10884-015-9425-2
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DOI: https://doi.org/10.1007/s10884-015-9425-2