本文選題：糖尿病 + 數(shù)學(xué)建模　； 參考：《天津大學(xué)》2015年碩士論文

【摘要】：本文以糖尿病為研究對象,運(yùn)用可靠性理論以及定向控制理論對兩個系統(tǒng)進(jìn)行了研究和分析。首先,我們討論了糖尿病人群預(yù)測系統(tǒng)。在該系統(tǒng)中,所有的患者均為II型糖尿病患者,并且沒有新的糖尿病患者出現(xiàn),也不會出現(xiàn)糖尿病患者死亡的情況,然后根據(jù)糖尿病并發(fā)癥的類別將系統(tǒng)分為4個狀態(tài)�；谶@些假設(shè),我們得到了描述該系統(tǒng)的偏微分方程。進(jìn)一步,運(yùn)用線性算子半群理論以及線性算子譜理論得出該偏微分方程的適定性、動態(tài)解指數(shù)趨于穩(wěn)態(tài)解,并且得到了系統(tǒng)的可靠性指數(shù),用以研究糖尿病患者的健康指數(shù)。最后,根據(jù)康復(fù)率函數(shù)對整個系統(tǒng)的花費(fèi)進(jìn)行數(shù)值模擬,通過數(shù)值模擬的結(jié)果給糖尿病患者以警示:如果想要生活質(zhì)量較高而且花費(fèi)較少,需要遵從醫(yī)囑、了解更多有關(guān)糖尿病的知識、注意飲食和運(yùn)動等來嚴(yán)格控制血糖。其次,我們研究了I型糖尿病患者血糖控制系統(tǒng)。在該系統(tǒng)中,針對I型糖尿病患者的生理特點(diǎn),將熱傳導(dǎo)偏微分方程應(yīng)用到血糖控制系統(tǒng)中,從定向控制的角度研究控制輸入和控制目標(biāo)輸出的關(guān)系。最后運(yùn)用Matlab編寫程序進(jìn)行數(shù)值模擬,得出控制輸出目標(biāo)(即,人體正常血糖濃度)所對應(yīng)的精確控制輸入,更好地保證糖尿病患者的身體健康,以免出現(xiàn)低血糖的情況。
[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.
【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：R587.1

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