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Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 4, 2007

A net reproductive number for periodic matrix models.

J M Cushing¹, A S Ackleh

¹Department of Mathematics, Interdisciplinary Program in Applied Mathematics, University of Arizona, Tucson, AZ, 85721-0089, USA. cushing@math.arizona.edu

Journal of Biological Dynamics

|August 10, 2012

Summary

This study defines a new net reproductive number (R0) for structured populations with periodic parameters. This R0 value determines population extinction or persistence, offering a generalized method for population dynamics analysis.

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Area of Science:

Population Dynamics
Mathematical Biology
Ecology

Background:

Periodic matrix models are crucial for understanding structured populations with time-varying parameters.
Existing definitions of net reproductive number (R0) may not fully capture dynamics in periodic models.
Generalizing R0 is essential for accurate population viability assessments.

Purpose of the Study:

To define and validate a net reproductive number (R0) for periodic matrix population models.
To provide a generalized framework for R0 applicable to structured populations with periodic dynamics.
To establish R0 as a determinant of population extinction or persistence.

Main Methods:

Developed a definition of R0 based on the composite of a periodic map.
Utilized additive decomposition of the composite map.
Extended the Cushing-Zhou definition of R0 for autonomous models.

Main Results:

The defined R0 accurately predicts population extinction (R0 < 1) or persistence (R0 > 1).
Derived specific formulas for R0 in scalar periodic maps and period 2 Leslie models.
Demonstrated the definition's utility through examples and literature case studies.

Conclusions:

The new R0 definition provides a robust measure for periodic population models.
This generalized R0 enhances the analysis of population persistence and extinction risks.
The study offers a valuable tool for ecological and demographic research.