Mathematical modeling of pathophysiology of Type 2 Diabetes

The following research of Type-2 Diabetes is modeled using a system of non-linear deterministic differential equations. The model variables include: the quantity of glucose in the blood plasma, the quantity of glycogen in the liver/tissue, the concentration of the hormone glucagon, and the concentration of insulin in the blood plasma. The appropriate interaction constants are used to depict the physiology of Type-2 Diabetes. The non-linear equations are analyzed using the principles of the Hartman-Grobman Theory. In particular, the principles of Linearized Stability are used to compute the criteria under which hypoglycemia and hyperglycemia occur. The effect of the gluconeogenesis and glycogenolysis on the plasma glucose concentration and on the morbidity of Type-2 Diabetes is demonstrated by theorems. The results of this research will provide quantitative information on Type-2 Diabetes which will enable the design of equipment to monitor the disease