APPLICATION OF CONTROLLER IN MATHEMATICAL MODELING FOR THE MANAGEMENT OF DIABETES

Abstract

Diabetes Mellitus is a chronic disease that affects millions of people worldwide, with its complications being a leading cause of morbidity and mortality. Despite decades of research, a cure for diabetes remains elusive, and the management of the disease relies heavily on controlling blood sugar levels through a combination of diet, exercise, and medication. Mathematical modelling has proven to be an effective tool in this regard, but the accuracy of the models depends on the effectiveness of the controller used. The aim of the present thesis is to discuss the factors controlling the glucose level through ordinary and delayed mathematical models of glucose in sulin system to manage the glucose level. The goal of regulated blood glucose level has been achieved by application of mathematical models and applying controller on these models for the management of both the types of diabetes, Type 1 and Type 2. The thesis consists of seven chapters, in which first chapter is introductory in na ture. Second chapter devotes to the effect of physical activity on blood glucose is intro duced through a mathematical model that compares normal, non-insulin dependent and insulin dependent diabetes. The third chapter examines the influence of vitamin D on glucose-insulin dynamics in healthy and diabetic individuals. It investigates the role of vitamin D in maintaining glucose concentration, which is critical but challenging for diabetics. we introduced factors related to the impact of vitamin D into a mathemat ical model and used numerical simulations to explore how vitamin D affects glucose insulin regulation in diabetics. Fourth chapter aims to evaluate the effectiveness of diabetes awareness campaigns in prevention. A fuzzy logic controller was designed to lower the diabetic population, with positive and bounded solutions. Fifth chap ter focuses on developing a fuzzy logic closed-loop insulin therapy recommendation system for people with type 1 diabetes with delays in insulin production, absorption, and action are addressed with a non-linear delay mechanism in the glucose-insulin model. The controller has been used to regulate glucose concentration in response to changes in delay parameters. The model was tested in four different scenarios includ xiii ing skipping a meal, multiple meals, unusual meals, and uncertainty in parameters. Sixth chapter presents a new automatic insulin delivery system called a proportional integral derivative-fuzzy logic controller (PID-FLC) for patients with Type 1 diabetes. Seventh chapter is devoted to describe the conclusion and future work.