Stochastic dynamics of glucose–insulin regulation with impulsive drug interventions

Type 2 diabetes arises from coupled glucose–insulin dysregulation and obesity-driven insulin resistance. We develop a stochastic impulsive differential equation model that integrates an anti-obesity drug compartment into a glucose–insulin–β-cell–adipose system, where discrete impulses represent periodic insulin and anti-obesity dosing and multiplicative noise captures intrinsic metabolic variability. We establish the existence, uniqueness, positivity, and boundedness of solutions, and derive explicit threshold criteria that separate adipose extinction, non-persistence, weak persistence, and stochastic persistence. The results of numerical experiments show that stochastic fluctuations can result in adipose extinction, while sufficiently strong and timely impulsive therapies suppress adipose growth and stabilize glucose–insulin dynamics over time. A qualitative comparison with continuous glucose monitoring data from Type 2 diabetic participants indicates that the model reproduces clinically observed patterns of glucose fluctuations.