Bivariate Stochastic Modelling of Glucose and Insulin Regulatory System among Type -2 Diabetes Mellitus Patients Kiran Kumar Paidipati 1 and Tirupathi Rao Padi 2 Dept. of Statistics, Pondicherry University, Puducherry -605014, India. 1 kirankumarpaidipati@gmail.com, 2 drtrpadi@gmail.com Key Words: Stochastic Model, Glucose-Insulin Regulatory System, Simultaneous Linear Differential Equations 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. 1. Introduction 1.1. Importance of the study: Glucose metabolism is the main source of getting energy to living cells. Normal and healthy human body has proper metabolism where the level of glucose shall be in the range of 70 to 110 mg/dl in the blood plasma. The changing patterns of glucose consumption in human body are observed due to several factors like sedentary life styles, obesity, ageing, etc. According to the studies of International Diabetes Federation, the most diabetic prone nations are china and India. Predictions of study speculate that India is going to occupy the first position with a prevalence of around 75.9 million people by 2035 (IDF Atlas 6 th Edition). The system of Endocrine is playing a vital role in conversion of glucose into energy, which is normally referred as glucose metabolism. It includes a chemical reaction in the inner part of the cell with the combination of glucose, oxygen and water to release energy (ATP, Adenosine tri- phosphate), carbon-dioxide and water. The mechanism of synchronized endocrine and digestive systems is to maintain the plasma glucose levels in the normal range. If the glucose levels of plasma in fasting is more than 110 mg/dl then the problem is called hyperglycemia where as if it is less than 70 mg/dl then the problem is referred as hypoglycemia. The person who is in either state is considered to be diabetic. It is cleared that the key role of insulin is to orderly maintenance of glucose levels in the blood plasma. Some organs are having the cells of nature that they require insulin to get the glucose through infusion technique. However, some organs of the body may utilize the glucose without involvement of insulin. Glucose transporters are of two types, namely insulin independent and insulin dependent. Except brain and genital organs, all the other parts of the body require insulin to make use of glucose for getting energy to the cell. Among the healthy individuals, the minimum needed quantity of insulin will be produced by pancreas for glucose metabolism. However, insulin secretion depends on mass of beta cells in pancreas. The inferior functioning of pancreas and low quantum of insulin secretion are influenced by increased age, genetical history of diabetes, Sullen and sedentary life styles. Low levels of insulin causes to accumulation of glucose levels in the plasma and further leads to many health complications. The Bulletin of Mathematical Science and Applications Vol. 11 (2015) pp 30-43 Online: 2015-02-02 © (2015) SciPress Ltd., Switzerland doi:10.18052/www.scipress.com/BMSA.11.30 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of SciPress Ltd., www.scipress.com. (ID: 210.212.230.197-12/07/15,18:05:48)