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

Benoit Huard*, Jonathan Easton, Maia Angelova

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
9 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)211-222
Number of pages12
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number1-3
Early online date27 Feb 2015
Publication statusPublished - 1 Sept 2015


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