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Mathematical Studies Of The Glucose-Insulin Regulatory System Models., Minghu Wang

Electronic Theses and Dissertations

Three dynamic models are proposed to study the mechanism of glucose-insulin regulatory system and the possible causes of diabetes mellitus. The progression of diabetes comes along with the apoptosis of pancreatic beta-cells. A dynamical system model is formulated based on physiology and studied by geometric singular perturbation theory. The analytical studies reveal rich analytical features, such as persistence of solutions, Hopf bifurcation and backward bifurcation, while numerical studies successfully fit available longitudinal T2DM data of Pima Indian tribe. These studies together not only validate our model, but also point out key intrinsic factors leading to the development of T2DM. We …