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Updated: Jul 22, 2025
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Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli
Published on: August 18, 2023
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Growth bound and threshold dynamic for nonautonomous nondensely defined evolution problems.
Ramsès Djidjou-Demasse1,2, Ibou Goudiaby3, Ousmane Seydi4
1MIVEGEC, CNRS, IRD, University of Montpellier, Montpellier, France.
Journal of Mathematical Biology
|July 21, 2023
Summary
This study introduces a novel framework to determine population growth thresholds and bounds using Hille-Yosida operators. The method is applied to diverse models, including age-structured, delay differential, and malaria dynamics.
Area of Science:
- Mathematical Biology
- Dynamical Systems
- Functional Analysis
Background:
- Population dynamics modeling often requires understanding growth thresholds and bounds.
- Evolution families generated by linear operators are crucial for analyzing differential equations.
- Periodic forcing and operator properties complicate the analysis of population growth.
Purpose of the Study:
- To develop a unified framework for calculating population growth thresholds.
- To determine the sign of the growth bound for evolution families.
- To apply this framework to various population models.
Main Methods:
- Utilizing Hille-Yosida linear operators (potentially unbounded and non-densely defined) on Banach spaces.
- Analyzing p-periodic and continuous maps in the operator norm topology.
- Developing a general method for simultaneous calculation of threshold values and growth bound signs.
Main Results:
- A general framework for analyzing population growth thresholds and bounds is established.
- The approach is successfully applied to age-structured models and delay differential systems.
- The framework is also demonstrated for nonlocal population genetics and structured human-vector malaria models.
Conclusions:
- The proposed framework provides a robust method for analyzing population dynamics.
- It offers a unified approach applicable to a wide range of structured population models.
- This work advances the mathematical understanding of population growth in complex systems.
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