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ANALISIS MODEL MATEMATIKA KADAR GLUKOSA DAN INSULIN PADA DIABETES MELLITUS DENGAN MENGGUNAKAN PROGRAM MAPLE 13

Anisa, Defi (2012) ANALISIS MODEL MATEMATIKA KADAR GLUKOSA DAN INSULIN PADA DIABETES MELLITUS DENGAN MENGGUNAKAN PROGRAM MAPLE 13. Other thesis, University of Muhammadiyah Malang.

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Abstract

Event in real life can be analyzed using a variety of viewpoints. One of these events there can be seen in the form of mathematical models. This means that these events can be formulated in the form of equestions or mathematical functions. The equestion is made in the mathematical model is an approximation to a physical phenomenon. One phenomenon that can be modeled, namely glucose and insulin levels in diabetes mellitus. Glucose level is the level or amount of glucose in the blood whereas, insulin level is the level or amount of insulin in the blood. High levels of glucose in the blood are influenced by food and glycolysis. Increased glucose levels if it is not offset by the insulin levels will lead to diabetes mellitus. Based on the above problems then this analysis aims to analyze the critical point or fixed point and stability of critical points of a mathematical model of glucose and insulin levels in diabetes mellitus. This analysis uses maple 13 program, the result of a literature review and researchers think about problem of models without and with the input of glucose and insulin in the blood. The results obtained by analyzing the model dG/dt= 〖-K〗_1 GI-K_2 G+ M_1 (t) and dI/dt= 〖-K〗_4 I+ K_5 G+ M_2 (t) has two fixed points are not all stable. Analysis without the input of glucose and insulin produced a 2 point remains that the first fixed point (G,I)=(0,0) and a second fixed point (G,I)= ((〖-K〗_4 K_2)/(K_5 K_1 ) , -K_2/K_1 ) but the stable fixed point only the first. While the mechanism of glucose and insulin input produces two fixed points is the first fixed point (G,I)=(371,0365710,120.415086) and the second fixed point (G,I)=(-393.12233721,-124,9335932) but only a point the first remains stable. By using maple 13 program stability is shown clearly by the curves representing the glucose and insulin levels. The first fixed point on the mechanism of glucose and insulin without a stable input to the minutes to 8000 while the input mechanisms of glucose and insulin levels stable fixed point first at minute 150.

Item Type: Thesis (Other)
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Teacher Training and Education > Department of Mathematics Education (84202)
Depositing User: Gusti Vani Putri Cahya
Date Deposited: 02 Feb 2015 04:31
Last Modified: 02 Feb 2015 04:31
URI : http://eprints.umm.ac.id/id/eprint/15516

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