Stability Analysis of Type 2 Diabetes Mellitus Prognosis Model with Obesity as A Trigger Factor and Metabolic Syndrome as A Risk Factor

摘要

Obesity is found in 90% of the world's patients with a type 2 diabetes mellitus (DM) diagnosis. If it is not being treatment, the disease advances to a metabolic syndrome related to some atherosclerotic cardiovascular diseases. In this study, a mathematical model was constructed that represent the prognosis of type 2 DM. The prognosis is started from the transition of vulnerable people to overweight and obese. The advanced prognosis makes the type 2 DM sufferer become a metabolic syndrome. The model has no disease-free critical point, while the implicit endemic critical point is guaranteed for some requirements. The analysis of the critical point stability, by Jacobian matrix and Routh Hurwitz criteria, requires a parameter interval that identified from the characteristic polynomial. The requirements show that we have to pay attention to the transition rate of overweight to obese, more over the transition rate of obese to type 2 DM. The simulations show that the unstable condition of type 2 DM is easier to achieve because of the tightness of the parameter stability interval.