Modeling Glucose-Insulin Dynamics with Delay Differential Equations

Author First name, Last name, Institution

Fathalla A. Rihan, United Arab Emirates University
K. Udhayakumar, United Arab Emirates University
M. Naim Anwar, Faculty of Engineering
Mutaz Mohammad, Zayed University

Document Type

Conference Proceeding

Source of Publication

Communications in Computer and Information Science

Publication Date

7-24-2025

Abstract

This study proposes a delay differential model for glucose-insulin endocrine and metabolic regulation. The model involves two time delays, δg and δι, 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.

DOI Link

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

ISBN

[9783031940385]

ISSN

1865-0929

Publisher

Springer Nature Switzerland

Volume

2535 CCIS

First Page

12

Last Page

25

Disciplines

Life Sciences | Mathematics

Keywords

Chaos behavior, Delay differential equations, Glucose-insulin, Hopf bifurcation, Stability

Scopus ID

105012422683

Recommended Citation

Rihan, Fathalla A.; Udhayakumar, K.; Anwar, M. Naim; and Mohammad, Mutaz, "Modeling Glucose-Insulin Dynamics with Delay Differential Equations" (2025). All Works. 7374.
https://zuscholars.zu.ac.ae/works/7374

Indexed in Scopus

yes

Open Access

no