Sensitivity analysis for a delay mathematical model: the glucose-insulin model

We investigate glucose-insulin regulation through a delay differential equation model formulated in Sobolev spaces. A physiologically motivated time delay is incorporated into an advanced modeling framework that builds upon the classical ordinary differential equation based model proposed by Bergman...

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Main Author: Mostafa Bachar
Format: Article
Language:English
Published: Frontiers Media S.A. 2025-08-01
Series:Frontiers in Applied Mathematics and Statistics
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Online Access:https://www.frontiersin.org/articles/10.3389/fams.2025.1562636/full
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author Mostafa Bachar
author_facet Mostafa Bachar
author_sort Mostafa Bachar
collection DOAJ
description We investigate glucose-insulin regulation through a delay differential equation model formulated in Sobolev spaces. A physiologically motivated time delay is incorporated into an advanced modeling framework that builds upon the classical ordinary differential equation based model proposed by Bergman and Cobelli. The resulting system is formulated within a semigroup-theoretical setting that ensures well-posedness. Sensitivity analysis based on Fréchet derivatives is employed to quantify parameter influence, while optimal design criteria derived from the Fisher Information Matrix are used to improve parameter estimation. The findings highlight the effectiveness of Sobolev-space and semigroup techniques in providing a rigorous and adaptable foundation for modeling delayed physiological processes.
format Article
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spelling doaj-art-998c54316f4d4da486e057ae552452bd2025-08-20T03:07:12ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872025-08-011110.3389/fams.2025.15626361562636Sensitivity analysis for a delay mathematical model: the glucose-insulin modelMostafa BacharWe investigate glucose-insulin regulation through a delay differential equation model formulated in Sobolev spaces. A physiologically motivated time delay is incorporated into an advanced modeling framework that builds upon the classical ordinary differential equation based model proposed by Bergman and Cobelli. The resulting system is formulated within a semigroup-theoretical setting that ensures well-posedness. Sensitivity analysis based on Fréchet derivatives is employed to quantify parameter influence, while optimal design criteria derived from the Fisher Information Matrix are used to improve parameter estimation. The findings highlight the effectiveness of Sobolev-space and semigroup techniques in providing a rigorous and adaptable foundation for modeling delayed physiological processes.https://www.frontiersin.org/articles/10.3389/fams.2025.1562636/fullleast squaresinverse problemssensitivity functionsfisher information matrixretarded functional differential equationsapproximation
spellingShingle Mostafa Bachar
Sensitivity analysis for a delay mathematical model: the glucose-insulin model
Frontiers in Applied Mathematics and Statistics
least squares
inverse problems
sensitivity functions
fisher information matrix
retarded functional differential equations
approximation
title Sensitivity analysis for a delay mathematical model: the glucose-insulin model
title_full Sensitivity analysis for a delay mathematical model: the glucose-insulin model
title_fullStr Sensitivity analysis for a delay mathematical model: the glucose-insulin model
title_full_unstemmed Sensitivity analysis for a delay mathematical model: the glucose-insulin model
title_short Sensitivity analysis for a delay mathematical model: the glucose-insulin model
title_sort sensitivity analysis for a delay mathematical model the glucose insulin model
topic least squares
inverse problems
sensitivity functions
fisher information matrix
retarded functional differential equations
approximation
url https://www.frontiersin.org/articles/10.3389/fams.2025.1562636/full
work_keys_str_mv AT mostafabachar sensitivityanalysisforadelaymathematicalmodeltheglucoseinsulinmodel