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Updated: Dec 16, 2025
06:44
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
389
A Lyapunov-Schmidt method for detecting backward bifurcation in age-structured population models
Maia Martcheva1, Hisashi Inaba2
1Department of Mathematics, University of Florida, Gainesville, FL, USA.
Journal of Biological Dynamics
|July 4, 2020
Summary
This study extends the center manifold method to analyze backward bifurcation in partial differential equation models. The research provides a new theorem and applies it to infectious disease models, offering crucial insights for disease dynamics.
Area of Science:
- Mathematical Biology
- Epidemiology
- Dynamical Systems
Background:
- Backward bifurcation is a critical phenomenon in infectious disease modeling, influencing disease persistence.
- The center manifold method, previously developed for Ordinary Differential Equations (ODEs), is effective for detecting backward bifurcation.
Purpose of the Study:
- To extend the center manifold method for detecting backward bifurcation in partial differential equation (PDE) systems.
- To establish a theoretical framework for analyzing backward bifurcation in more complex epidemiological models.
Main Methods:
- Development of a novel theorem for applying the center manifold method to PDEs.
- Application of the extended method to age-structured Susceptible-Infected-Susceptible (SIS), HIV/AIDS, and cholera models.
Main Results:
- The study successfully extends the center manifold method to the analysis of PDEs.
- The method's applicability is demonstrated on diverse epidemiological models, including those with age structure and vaccination.
Conclusions:
- The extended center manifold method provides a robust tool for analyzing backward bifurcation in PDE-based infectious disease models.
- This work enhances the understanding of disease dynamics and persistence in structured populations.
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