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This study proposes a delay differential model for glucose-insulin endocrine and metabolic regulation. The model involves two time delays, \(\delta _g\) and \(\delta _\iota \) , 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.

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Modeling Glucose-Insulin Dynamics with Delay Differential Equations

  • 会议论文

  • 发表日期：

    2025年

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  • Fathalla A. Rihan,
  • K. Udhayakumar,
  • M-Naim Anwar,
  • Mutaz Mohammad

摘要

This study proposes a delay differential model for glucose-insulin endocrine and metabolic regulation. The model involves two time delays, \(\delta _g\) and \(\delta _\iota \) , 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.