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From homogeneous eigenvalue problems to two-sex population dynamics.

Horst R Thieme1

  • 1School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287-1804, USA. hthieme@asu.edu.

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|March 10, 2017
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Summary
This summary is machine-generated.

Enclosure theorems provide bounds for operators in population dynamics. These methods are applied to a discrete-time two-sex model and reproduction numbers.

Keywords:
Enclosure theoremsHomogeneous order-preserving operatorsOrdered normed vector spacesPair formationSpectral radius

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Area of Science:

  • Mathematical Biology
  • Population Dynamics

Background:

  • Order-preserving operators are fundamental in mathematical analysis.
  • Karl-Peter Hadeler introduced pair-formation functions in population modeling.
  • Enclosure theorems offer a method for bounding operator behavior.

Purpose of the Study:

  • To derive and apply enclosure theorems for homogeneous bounded order-preserving operators.
  • To illustrate these theorems using operators with pair-formation functions.
  • To analyze a discrete-time two-sex population model and its key reproductive parameters.

Main Methods:

  • Derivation of enclosure theorems for specific operator classes.
  • Application of these theorems to operators involving pair-formation functions.
  • Analysis of a discrete-time two-sex population model.

Main Results:

  • Established enclosure theorems for homogeneous bounded order-preserving operators.
  • Demonstrated the utility of these theorems with Hadeler's pair-formation functions.
  • Provided insights into the relationship between turnover number and reproduction number in population models.

Conclusions:

  • Enclosure theorems are effective tools for analyzing population models.
  • The methods offer a rigorous approach to understanding population dynamics and reproductive numbers.