Optimal control and stability analysis of a glucose-insulin-FFA dynamic model with GLP-1 incretin effects

作者：Salma M. Al-Tuwairqi, Khlood Al Amer, Hunida M. Malaikah · 发表于：Mathematical Modelling and Analysis · 年份：2026 · DOI：10.3846/mma.2026.24231

Obesity and its associated metabolic dysregulations, particularly Type 2 Diabetes Mellitus (T2DM), constitute a global health crisis. Understanding the intricate interplay of key metabolic components is crucial for effective management strategies. This study presents a novel mathematical model capturing the dynamic interactions among plasma glucose, insulin, and free fatty acids (FFAs), critically integrating the regulatory influence of Glucagon-Like Peptide-1 (GLP-1). Through qualitative analysis, we established the model’s physiological relevance and demonstrated the existence of a stable equilibrium point, confirmed by numerical simulations across various initial conditions. Sensitivity analysis revealed that FFA-related parameters (e.g., lipolysis rates and FFA-induced insulin impairment) and insulin secretion/clearance rates profoundly affect glucose homeostasis, underscoring the detrimental role of elevated FFAs in hyperglycemia. Furthermore, we applied optimal control theory, using Pontryagin’s Maximum Principle, to design GLP-1 receptor agonist intervention strategies. We evaluated two scenarios that balance the cost of intervention with the effectiveness of glucose regulation. Results show that GLP-1 agonism effectively lowers glucose and FFA levels, with greater glucose reduction achieved when control cost and glucose deviation are equally weighted. This research provides a comprehensive mathematical framework for analyzing complex glucose-insulin-FFA-GLP-1 dynamics...