Bivariate Stochastic Modelling of Glucose and Insulin Regulatory System among Type -2 Diabetes Mellitus Patients

Abstract

In this paper, a bivariate stochastic model for glucose and insulin regulatory system is developed. Difference Differential equations are derived from the processes of arrival and consumption of glucose molecules and insulin granules in blood plasma. Probability generating functions and linear differential equations are obtained, through which statistical measures on glucose and insulin levels are derived. Numerical illustrations are provided with suitable sensitivity analysis. Model behaviour is analyzed while using the derived measures. Indicators on health care and management of Type-2 Diabetes can be obtained with this study.