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From homogeneous eigenvalue problems to two-sex population dynamics

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Abstract

Enclosure theorems are derived for homogeneous bounded order-preserving operators and illustrated for operators involving pair-formation functions introduced by Karl-Peter Hadeler in the late 1980s. They are applied to a basic discrete-time two-sex population model and to the relation between the basic turnover number and the basic reproduction number.

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Acknowledgements

I thank Jürgen Voigt for providing the breakthrough in the proof of Proposition 3.9. I thank Klaus Dietz and Birgitt Schönfisch for letting me use their collection of KP Hadeler’s publications and Mark Lewis and an anonymous referee for their comments.

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  1. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287-1804, USA

    Horst R. Thieme

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  1. Horst R. Thieme
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Correspondence to Horst R. Thieme.

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Dedicated to Karl-Peter Hadeler on the occasion of his 80th birthday (*Oct. 16, 1936) and in his remembrance ( $$\dag $$ † Feb. 3, 2017).

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Thieme, H.R. From homogeneous eigenvalue problems to two-sex population dynamics. J. Math. Biol. 75, 783–804 (2017). https://doi.org/10.1007/s00285-017-1114-9

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