ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Mathematical Biology
Volume 11 - 2025 | doi: 10.3389/fams.2025.1562636
This article is part of the Research TopicAdvances in Mathematical Biology and Medicine: Modeling, Analysis, and Numerical SolutionsView all 8 articles
Sensitivity Analysis for a Delay Mathematical Model: The Glucose-Insulin Model
Provisionally accepted
- Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia
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We analyse insulin-glucose regulation with delay differential equations posed in Sobolev spaces.Extending the minimal Bergman-Cobelli model by incorporating physiologically motivated time delays, we formulate the system within a semigroup framework that guarantees well-posedness.Parameter influence is quantified through a sensitivity analysis based on Fr échet derivatives, while optimal-design criteria derived from the Fisher Information Matrix refine parameter estimation.The results illustrate how Sobolev-space and semigroup techniques provide a rigorous and flexible foundation for modelling delayed physiological processes.
Keywords: Least squares inverse problems, Sensitivity functions, Fisher Information Matrix, Retarded functional differential equations, Approximation, Splines
Received: 17 Jan 2025; Accepted: 24 Jul 2025.
Copyright: © 2025 Bachar. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Mostafa Bachar, Department of Mathematics, College of Science, King Saud University, Riyadh, 11451, Saudi Arabia
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