Modeling Glucose-Insulin Dynamics with Delay Differential Equations

Fathalla A. Rihan; K. Udhayakumar; Mohamed Naim Anwar; Mutaz Mohammad

doi:10.1007/978-3-031-94039-2_2

Modeling Glucose-Insulin Dynamics with Delay Differential Equations

Fathalla A. Rihan
, K. Udhayakumar
, Mohamed Naim Anwar
, Mutaz Mohammad

Department of Mathematical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

This study proposes a delay differential model for glucose-insulin endocrine and metabolic regulation. The model involves two time delays, δ_g and δ_ι, which represent delayed insulin secretion and delayed glucose reduction. Moderate hyperglycemia results in beta-cell growth (negative feedback), whereas severe hyperglycemia results in beta-cell reduction (positive feedback). Hopf bifurcation occurs when a time delay passes bifurcation points. Based on biological findings, the model exhibits periodic oscillations. Diabetes and pre-diabetes may be characterized by chaotic glucose-insulin dynamics, which makes blood sugar levels unpredictable and difficult to control. The theoretical results have been validated by numerical simulations.

Original language	English
Title of host publication	Bioinformatics and Computational Biology - 17th International Conference, BICOB 2025, Proceedings
Editors	Tamer Aldwairi, Hisham Al-Mubaid, Oliver Eulenstein
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	12-25
Number of pages	14
ISBN (Print)	9783031940385
DOIs	https://doi.org/10.1007/978-3-031-94039-2_2
Publication status	Published - 2025
Event	17th International Conference on Bioinformatics and Computational Biology, BICOB 2025 - San Francisco, United States Duration: Mar 17 2025 → Mar 17 2025

Publication series

Name	Communications in Computer and Information Science
Volume	2535 CCIS
ISSN (Print)	1865-0929
ISSN (Electronic)	1865-0937

Conference

Conference	17th International Conference on Bioinformatics and Computational Biology, BICOB 2025
Country/Territory	United States
City	San Francisco
Period	3/17/25 → 3/17/25

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Chaos behavior
Delay differential equations
Glucose-insulin
Hopf bifurcation
Stability

ASJC Scopus subject areas

General Computer Science
General Mathematics

Access to Document

10.1007/978-3-031-94039-2_2

Cite this

Rihan, F. A., Udhayakumar, K., Anwar, M. N., & Mohammad, M. (2025). Modeling Glucose-Insulin Dynamics with Delay Differential Equations. In T. Aldwairi, H. Al-Mubaid, & O. Eulenstein (Eds.), Bioinformatics and Computational Biology - 17th International Conference, BICOB 2025, Proceedings (pp. 12-25). (Communications in Computer and Information Science; Vol. 2535 CCIS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-94039-2_2

Modeling Glucose-Insulin Dynamics with Delay Differential Equations. / Rihan, Fathalla A.; Udhayakumar, K.; Anwar, Mohamed Naim et al.
Bioinformatics and Computational Biology - 17th International Conference, BICOB 2025, Proceedings. ed. / Tamer Aldwairi; Hisham Al-Mubaid; Oliver Eulenstein. Springer Science and Business Media Deutschland GmbH, 2025. p. 12-25 (Communications in Computer and Information Science; Vol. 2535 CCIS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Rihan, FA, Udhayakumar, K, Anwar, MN & Mohammad, M 2025, Modeling Glucose-Insulin Dynamics with Delay Differential Equations. in T Aldwairi, H Al-Mubaid & O Eulenstein (eds), Bioinformatics and Computational Biology - 17th International Conference, BICOB 2025, Proceedings. Communications in Computer and Information Science, vol. 2535 CCIS, Springer Science and Business Media Deutschland GmbH, pp. 12-25, 17th International Conference on Bioinformatics and Computational Biology, BICOB 2025, San Francisco, United States, 3/17/25. https://doi.org/10.1007/978-3-031-94039-2_2

Rihan FA, Udhayakumar K, Anwar MN, Mohammad M. Modeling Glucose-Insulin Dynamics with Delay Differential Equations. In Aldwairi T, Al-Mubaid H, Eulenstein O, editors, Bioinformatics and Computational Biology - 17th International Conference, BICOB 2025, Proceedings. Springer Science and Business Media Deutschland GmbH. 2025. p. 12-25. (Communications in Computer and Information Science). doi: 10.1007/978-3-031-94039-2_2

Rihan, Fathalla A. ; Udhayakumar, K. ; Anwar, Mohamed Naim et al. / Modeling Glucose-Insulin Dynamics with Delay Differential Equations. Bioinformatics and Computational Biology - 17th International Conference, BICOB 2025, Proceedings. editor / Tamer Aldwairi ; Hisham Al-Mubaid ; Oliver Eulenstein. Springer Science and Business Media Deutschland GmbH, 2025. pp. 12-25 (Communications in Computer and Information Science).

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