Modeling the Glucose-Insulin-Glucagon Interactions

Abstract

This research presents a mathematical model that investigates the regulation of glucose levels in the human body through interactions with insulin and glucagon. The model accounts for the action of incretin hormones in the intestine, which stimulates the release of insulin. The study uniquely combines sensitivity analysis and equilibrium stability analysis to provide a comprehensive understanding of these interactions. A system of nonlinear ordinary differential equations is formulated to describe the model’s dynamics. Qualitative analysis ensures the positivity and boundedness of state variables, identifies a unique steady-state solution, and establishes its local and global asymptotic stability. Sensitivity analysis further elucidates the complicated relationships between glucose, insulin, and glucagon, highlighting the impact of key parameters on glucose equilibrium levels. Numerical simulations validate the theoretical findings, demonstrating the model’s robustness and reliability. The study’s findings have significant implications in the real world, particularly in the advancement of clinical and therapeutic strategies for managing diabetes. By offering insights into the mechanisms of glucose regulation, the model provides a valuable framework for optimizing treatments and developing targeted interventions for metabolic disorders.