Investigation of stability in a two-delay model of the ultradian oscillations in glucose-insulin regulation

Huard, Benoit, Easton, Jonathan and Angelova, Maia (2015) Investigation of stability in a two-delay model of the ultradian oscillations in glucose-insulin regulation. Communications in Nonlinear Science and Numerical Simulation, 26 (1-3). pp. 211-222. ISSN 1007-5704

PDF (Full text)
glucose-insulin_regulation.pdf - Published Version
Available under License Creative Commons Attribution 4.0.

Download (2MB) | Preview
Official URL:


In this paper, a two-delay model for the ultradian oscillatory behaviour of the glucose-insulin regulation system is studied. Hill functions are introduced to model nonlinear physiological interactions within this system and ranges on parameters reproducing biological oscillations are determined on the basis of analytical and numerical considerations. Local and global stability are investigated and delay-dependent conditions are obtained through the construction of Lyapunov-Krasovskii functionals. The effect of Hill parameters on these conditions, as well as the boundary of the stability region in the delay domain, are established for the first time. Numerical simulations demonstrate that the model with Hill functions represents well the oscillatory behaviour of the system with the advantage of incorporating new meaningful parameters. The influence of the time delays on the period of oscillations and the sensitivity of the latter to model parameters, in particular glucose infusion, are investigated. The model can contribute to the better understanding and treatment of diabetes.

Item Type: Article
Uncontrolled Keywords: Glucose-insulin regulation; Differential delay equations; Stability analysis; Hill functions
Subjects: B100 Anatomy, Physiology and Pathology
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Dr Benoit Huard
Date Deposited: 03 Mar 2015 10:58
Last Modified: 31 Jul 2021 10:51

Actions (login required)

View Item View Item


Downloads per month over past year

View more statistics