| Abstract: |
Diabetes mellitus is one of the fastest-growing non-communicable diseases globally, with India currently holding the second-largest diabetic population in the world, estimated at 101 million adults in 2024. This study presents a systematic analytical investigation of diabetes dynamics through differential equation-based mathematical modelling, with specific focus on the Bergman minimal model framework and its extended variants. The primary objectives are: (i) to simulate plasma glucose and insulin dynamics using Ordinary Differential Equations (ODEs) under normal and Type 2 diabetic physiological parameter sets, and (ii) to assess equilibrium stability as a function of declining insulin sensitivity. A numerical-analytical methodology is adopted, integrating parameter estimation, equilibrium analysis, and stability assessment using clinically validated datasets. The core hypothesis posits that diminished insulin sensitivity (SI) and elevated basal glucose concentrations are sufficient conditions to shift the ODE system toward a persistent hyperglycaemic equilibrium characteristic of Type 2 diabetes. Simulation results reveal clear divergence in post-IVGTT glucose and insulin trajectories between normal and diabetic parameter conditions. Equilibrium analysis confirms that below a critical SI threshold, physiological glucose restoration fails entirely. These findings validate differential equation-based frameworks as robust predictive tools for understanding diabetes progression and designing targeted interventions in the Indian public health context. |
