Optimal control of glucose-insulin dynamics via delay differential model with fractional-order

Abstract

This paper proposes a delay differential model with fractional order for glucose-insulin endocrine, metabolic regulation model, incorporating beta-cell dynamics to regulate and maintain bloodstream insulin concentration. In the model, two time delays are involved, namely δg and δι, which represent delayed insulin secretion and delayed glucose reduction. A moderate hyperglycemia results in beta-cell growth (negative feedback), while a severe hyperglycemia results in beta-cell reduction (positive feedback). When a time delay passes a bifurcation point, Hopf bifurcation occurs. It is evident from biological findings that the model exhibits periodic oscillations. Furthermore, we present an optimal control problem for external insulin infusions to minimize prolonged high blood sugar levels. Numerical simulations have validated the theoretical results.

Keywords

• Delay differential equations
• Optimal control
• Glucose-insulin
• Stability
• Chaos behavior
• Hopf bifurcation