糖尿病人群预测系统及Ⅰ型糖尿病患者血糖控制模型

发布时间：2018-05-23 21:47

本文选题：糖尿病 + 数学建模　；参考：《天津大学》2015年硕士论文

【摘要】：本文以糖尿病为研究对象,运用可靠性理论以及定向控制理论对两个系统进行了研究和分析。首先,我们讨论了糖尿病人群预测系统。在该系统中,所有的患者均为II型糖尿病患者,并且没有新的糖尿病患者出现,也不会出现糖尿病患者死亡的情况,然后根据糖尿病并发症的类别将系统分为4个状态。基于这些假设,我们得到了描述该系统的偏微分方程。进一步,运用线性算子半群理论以及线性算子谱理论得出该偏微分方程的适定性、动态解指数趋于稳态解,并且得到了系统的可靠性指数,用以研究糖尿病患者的健康指数。最后,根据康复率函数对整个系统的花费进行数值模拟,通过数值模拟的结果给糖尿病患者以警示:如果想要生活质量较高而且花费较少,需要遵从医嘱、了解更多有关糖尿病的知识、注意饮食和运动等来严格控制血糖。其次,我们研究了I型糖尿病患者血糖控制系统。在该系统中,针对I型糖尿病患者的生理特点,将热传导偏微分方程应用到血糖控制系统中,从定向控制的角度研究控制输入和控制目标输出的关系。最后运用Matlab编写程序进行数值模拟,得出控制输出目标(即,人体正常血糖浓度)所对应的精确控制输入,更好地保证糖尿病患者的身体健康,以免出现低血糖的情况。
[Abstract]:In this paper, the reliability theory and directional control theory are used to study and analyze diabetes mellitus. First, we discussed the diabetes prediction system. In this system, all patients were type II diabetics, and no new diabetes patients appeared, nor did they die, and then the system was divided into four states according to the type of diabetic complications. Based on these assumptions, we obtain partial differential equations describing the system. Furthermore, the theory of linear operator semigroup and the theory of linear operator spectrum are used to obtain the fitness of the partial differential equation, the dynamic solution exponent tends to the steady solution, and the reliability index of the system is obtained, which is used to study the health index of diabetic patients. Finally, the cost of the whole system is numerically simulated according to the rehabilitation rate function, and the results of the numerical simulation are used to warn diabetics that if they want a higher quality of life and less cost, they need to comply with the doctor's advice. Learn more about diabetes, pay attention to diet and exercise to strictly control blood sugar. Secondly, we studied the blood glucose control system in patients with type I diabetes. In this system, according to the physiological characteristics of patients with type I diabetes, the heat conduction partial differential equation is applied to the blood glucose control system, and the relationship between the control input and the control target output is studied from the point of view of directional control. Finally, the numerical simulation is made by using Matlab program, and the accurate control input corresponding to the control output target (that is, the normal blood glucose concentration of human body) is obtained, which can better ensure the health of the diabetic patients and avoid the occurrence of hypoglycemia.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：R587.1

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