Statistical Insights into Stochastic Glucose-InsulinDynamics: Modeling Insulin Degradation with the Michaelis-Menten Function

Abstract

In this study, a glucose-insulin model with the Michaelis-Menten function as the rate of insulin degradation is analyzed using stochastic differential equations. Further, we solve the stochastic glucose-insulin model using the Milstein method, which is based on truncated Ito-Taylor expansions. Comparison of the approximation solution of a stochastic and deterministic model is illustrated by comparing the approximation solution with the deterministic model. A stochastic model allows random fluctuations in glucose-insulin diseases. Furthermore, the stochastic glucose-insulin model's numerical solution provides insight into its variability. The model predicts glucose-insulin dynamics accurately, which is a powerful tool for managing diabetes. Analytical and simulation results are consistent. Improved treatment strategies and personalized medical interventions could result. Treatments and insulin injections are sensitive to these parameters. Numerical simulation corroborates theoretical results.