MODELING & SIMULATION OF GLUCOSE – INSULIN DYNAMICS OF DIABETES

Abstract

Diabetes Mellitus is a persistent global health concern, impacting millions of individuals and standing as a prominent driver of illness and death due to its associated complications. Despite extensive research efforts spanning many years, the elusive quest for a definitive cure for diabetes persists. Management of the condition primarily revolves around the intricate task of blood sugar level control, achieved through a combination of dietary choices, physical activity, and pharmaceutical interventions. The field of mathematical modeling has surfaced as a promising avenue in this pursuit, but the accuracy of these models is closely linked to the effectiveness of the utilized machine learning techniques. In the current thesis, mathematical models have been used to explain many elements of glucose-insulin dynamics, their effects, and the maintenance of glucose levels and around the physiological range in diabetics. We have examined various mathematical models that satisfy the physiology underlying the mechanism involved in the dynamics of glucose and insulin in both type-1 and type-2 diabetics. We have looked at the details and causes of the persistently elevated glucose concentration levels in diabetics. Following the investigation of different systems, the outcomes of the dynamical analysis of the issues are explored. Every mathematical model has undergone a stability, positivity, and boundedness analysis. The primary tools used for analysis and simulation of mathematical models include local linearization, Routh-Hurwitz stability criterion, Lyapunov function, MATLAB 2012b (ode45, dde45) and Python 3.7. Two different types of mathematical models have been examined by us: the delay differential equations (DDE) model and the artificial intelligence (AI) model. The severity of the disease and, consequently, its treatment, are caused by delays in the dynamics of many occurrences. DDE model's significance in the advancement of an artificial pancreas cannot thus be understated. xiii Due to the robust data analysis capabilities of machine learning (ML), AI models based on supervised machine learning serve as highly effective tools for accurately predicting glucose levels in artificial pancreas systems. To enhance the efficiency of artificial pancreas functionality, models combining Delayed Differential Equations (DDE) and AI have been developed.