MATHEMATICAL MODELING OF DIABETES

Abstract

In the present thesis, various aspects of glucose - insulin dynamics, its consequences and maintenance of glucose level in and around physiological range in diabetics have been discussed through mathematical model. We have analyzed different mathematical models which satisfies the physiology behind the mechanism involved in glucose - insulin dynamics of both type 1 diabetics and type 2 diabetics. We have investigated the facts and reasons behind the consistently raised glucose concentration level in the people suffering from diabetes. After analyzing several systems, various results obtained by dynamical analysis of the problems are discussed. All mathematical models have been analyzed for stability, positiveness and boundedness. Local linearization, Routh-Hurwitz stability criterion, Lyapunov function, Runge-Kutta method, Matlab 2012b (ode45, dde45) are the main tools applied for analysis and simulation of mathematical models. We have studied two types of mathematical models : ordinary differential equations (ODE) model and delay differential equations (DDE) model. The delay occurred in the dynamics of different phenomena is responsible for the severity of the disease and hence in its treatment. Therefore, importance of DDE model can not be ignored in the development of artificial pancreas. DDE models have been developed for the better functioning of artificial pancreas.