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Numerical bifurcation analysis of delay differential equations arising from physiological modeling
K Engelborghs1, V Lemaire, J Bélair
1Department of Computer Science, Katholieke Universiteit Leuven, Belgium. Koen.Engelborghs@cs.kuleuven.ac.be
Journal of Mathematical Biology
|May 26, 2001
Summary
This study introduces numerical methods for analyzing delay differential equations in biological systems. These methods reveal distinct patient categories for external system efficiency in diabetes management.
Area of Science:
- Mathematical Biology
- Computational Science
- Systems Biology
Background:
- Biological systems often involve time delays impacting regulatory dynamics.
- Understanding these delays is crucial for modeling complex physiological processes like glucose-insulin regulation.
Purpose of the Study:
- To present numerical methods for analyzing steady-state and periodic solutions in delay differential equations.
- To apply these methods to a diabetic patient model with technological and physiological delays.
Main Methods:
- Continuation and bifurcation analysis of delay differential equations.
- Modeling of plasma glucose and insulin concentrations with two distinct time delays.
- Stability analysis of steady-state and periodic solutions.
Main Results:
- The study computes stability of the steady-state solution concerning two parameters.
- Multiple branches of periodic solutions and their stability are calculated.
- Numerical results differentiate patient responses to external assistance systems.
Conclusions:
- The developed numerical methods are effective for analyzing complex biological regulatory systems with time delays.
- The findings suggest distinct patient classifications based on external system efficiency in diabetes management.