Dynamics of a glucose-insulin model

Area of Science:

• Mathematical Biology
• Endocrinology
• Computational Medicine

Background:

• Diabetes mellitus is a global noncommunicable disease posing significant health risks.
• Understanding the complex glucose-insulin interplay is crucial for effective diabetes management.

Purpose of the Study:

• To develop a simplified mathematical model of glucose-insulin regulation.
• To investigate the pathogenic mechanisms of diabetes using a Michaelis-Menten insulin degradation function.
• To derive and validate treatment strategies for diabetes patients.

Main Methods:

• Theoretical analysis of a proposed glucose-insulin model.
• Incorporation of the Michaelis-Menten function to represent insulin degradation.
• Parameter sensitivity analysis to inform treatment strategies.
• Numerical simulations to support theoretical findings.

Main Results:

• The mathematical model demonstrates a unique, globally asymptotically stable positive equilibrium.
• Theoretical analysis confirms the stability of the glucose-insulin system under specific conditions.
• Numerical simulations validate the model's predictions and the efficacy of derived strategies.

Conclusions:

• The developed model accurately mimics diabetes pathogenesis.
• The study provides a theoretical basis for four distinct treatment strategies, including insulin therapy and medication.
• The findings offer insights into optimizing diabetes management through mathematical modeling.