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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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2025-08-01
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| 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 |
| id | doaj-art-998c54316f4d4da486e057ae552452bd |
| institution | DOAJ |
| issn | 2297-4687 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| 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 |