Model Matematika Interaksi Glukosa-Insulin Dalam Tubuh Penderita Diabetes Tipe 1

Nurma Yenni - Universitas Negeri Padang
Muhammad Subhan - Universitas Negeri Padang

Abstract


Diabetes Mellitus (DM) is a metabolic disease caused by a lack of the hormone insulin. This disease is a non-communicable disease that causes death. Diabetes control measures are needed, especially trying to keep blood sugar levels as close to normal as possible. This research is a basic or theoretical research. This study begins by determining the variables, assumptions, and parameters related to the problem so that a mathematical model of the glucose-insulin interaction in the body of type 1 diabetes patients can be formed. one equilibrium point. Then the stability of the equilibrium point is seen based on the eigenvalues of the Jacobi matrix, which shows that all the eigenvalues are negative, so that the equilibrium point of the mathematical model of glucose-insulin interaction in the body of type 1 diabetics is asymotic stable. This shows that diabetes will not disappear from the sufferer's body. The results of the numerical simulation also strengthen the analysis that has been carried out.

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References


Wahyuni, Khurin In. (2019). Diabetes Mellitus. Surabaya: Jakad Media Publishing.

Ardiansah, N dan Kharis, M. (2012). Model Matematika Untuk Penyakit Diabetes Tanpa Faktor Genetik. Jurnal MIPA 35 (1).

Lanywati, Endang. (2001). Diabetes Mellitus: Penyakit Kencing Manis. Yogyakarta:Kanisius (Anggota IKAPI).

Srinivas, P dan Rao, P Durgan Prasada. (2012). Closed Loop Model For Glucose Insulin Regulation System Usinglabview. International Journal of Instrumentation and Control Systems (IJICS). Vol. 2, No. 4.

Arisman. (2010). Buku ajar ilmu gizi obesitas, diabetes melitus, dan dislipidemia. Jakarta: EGC.

Sustrani, Lanny., Alam, Syamsir dan Hadibroto, Iwan. (2005). Diabetes. Jakarta: PT. Gramedia Pustaka Utama.

Ndii, Meksianis Zadrak. (2018). Pemodelan Matematika Dinamika Populasi dan Penyebaran Penyakit. Yogyakarta: CV BUDI UTAMA.

Li, J., Kuang, Y. dan Mason, C. (2006). Modeling the glucose–insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays. Journal of Theoretical Biology, 242, 722-735.

Wang, Haiyan., Li, Jiaxu dan Kuang, Yang. (2009). Enhanced modelling of the glucose-insulin system and its applications in insulin therapies. J. of Biological Systems, 3, 22–38.

Afifah. (2011). Model Matematika Glukosa Dan Insulin Pada Penyakit Diabetes Mellitus. Skripsi. Malang: UIN Maulana Malik Ibrahim Malang.

Akter, Sonia., Islam, Md. Majid., Biswas, Md. Haider Ali dan Mandul, Sajib. (2020). Mathematical Model Applied to Monitoring the Glucose-Insulin Interaction inside the Body of Diabetes Patients. J. Bangladesh Math. Soc. 40.1 (2020) 1-12.




DOI: http://dx.doi.org/10.24036/unpjomath.v7i3.12905