关键词: 糖尿病, 血糖, 抽象发展方程, 渐进稳定性, 可靠性

Abstract:

The rapid development of diabetes has become a serious public health problem, diabetes can induce a variety of
chronic complications, and enormous economic burden to society and individuals. In this paper, we setup a mathematical warning model to study the development of diabetes and prove that a system exists non-negative
dynamic solution and steady-state solution  under the  assumption in the system model. We calculate dynamic solutions to  the probability of  time stages of diabetes, while the steady state solution can be the probability of diabetes stage when the time is full. Patients with diabetes in China are close to one hundred million people, nearly 150 million people in the pre-diabetes, diabetes is very serious form of development. The control of blood glucose is the key of the control of diabetes.  Through the different states of the blood sugar control  undervthe development of different states, this paper obtains steady-state solution validates the severe  form, and dynamic solutions  play a role in early warning to  the future development of the diabetes. Especially  the dynamic solution converges to  the steady-state  solution in the sense of norm. And the indices of the system determined by the steady-state solution are reliable.

Key words: Diabetes, Glucose, Abstract evolution equations,  Asymptotic stability, Reliability