Exercise is beneficial for all individuals; it lowers blood pressure, keeps the heart healthy and increases insulin sensitivity. Recent studies have shown the power that regular exercise has to improve metabolic health, which in turn works to prevent and to reverse the onset of the widespread epidemics of type 2 diabetes (T2DM).
However, diabetics taking insulin are required to meticulously plan exercise around meals and intake of insulin as they face an increased risk of hypoglycaemia from physical activity, which can discourage them from taking part.
This thesis describes the use of systems of ordinary differential equations to model the effects of exercise on the glucose regulatory system, for both healthy and diabetic individuals. A particular focus is given to the role of glucagon, whose role is often neglected in glucoregulatory models, and its ability to enhance hepatic glucose production and so to prevent hypoglycaemia. Models of glucose-insulin-glucagon dynamics are first developed to describe an Intravenous glucose tolerance test (IVGTT), as the processes involved are simpler than in exercise and already widely modelled for glucose and insulin, thus is a good basis for validating the incorporation of glucagon.
Mathematical models are used as tools within biological applications as they allow for an investigation into the dynamics that are involved in complex regulatory processes. The mathematical models in this thesis serve as accurate tools to predict blood glucose levels during exercise for both a non-diabetic and type 1 diabetic individual (T1DM) and emphasise exercise as a key element in the prevention of T2DM. By mathematically modelling the system and the mechanisms that occur to maintain glucose homeostasis an insight is gained into what the principal factors are for the greatest increase in insulin sensitivity and for the reduction in the likelihood of either hypoglycaemic or hyperglycaemic episodes. This may lead to recommendations for exercise plans which not only provide the greatest benefits for everyday health ant to assist with preventing the onset of diabetes but also to offer safer regimes for individuals with T1DM
