糖尿病人群发展状况预警建模研究  

Study on the Diabetic Population Development of Early Warning Modeling

作　　者：刘丹红[1] 许跟起[1] 

机构地区：[1]天津大学数学系,天津300072

出　　处：《数学物理学报（A辑）》2014年第3期495-511,共17页Acta Mathematica Scientia

基　　金：国家自然科学基金(61174080)资助

摘　　要：糖尿病发展迅速,已成为严重的公共健康问题,糖尿病能够诱发多种并发症,给社会和个人带来巨大的经济负担,该文通过建立数学预警模型来研究糖尿病的发展状况,在系统模型的假定下,证明了系统存在非负的动态解和稳态解,计算动态解得到了某一时间糖尿病人在不同阶段的概率,而稳态解可以研究时间充分大时糖尿病人在不同阶段的概率.目前,我国糖尿病患者接近一亿人,接近1.5亿人处于糖尿病前期,糖尿病发展形式非常严峻,控制血糖是控制糖尿病发展的关键,该文通过糖尿病不同阶段的血糖控制不同状态,得到的稳态解不仅验证了这一严峻形式,而且动态解对糖尿病未来发展起到预警作用,特别是在范数意义下动态解收敛到稳态解,从而由系统稳态解得到系统指标是可靠的.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 so- ciety 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 so- lutions 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.

关 键 词：糖尿病 血糖 抽象发展方程 渐进稳定性 可靠性 

分 类 号：O211.4[理学—概率论与数理统计]