Analisis Model Matematika Virus Covid-19 Pada Manusia Dengan Subjek Manusia Sehat Dan Penderita Diabetes Tipe 2

Hasanah, Amaliyatul (2022) Analisis Model Matematika Virus Covid-19 Pada Manusia Dengan Subjek Manusia Sehat Dan Penderita Diabetes Tipe 2. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Penyakit virus corona (COVID-19) adalah penyakit menular yang disebabkan oleh virus SARS-CoV-2 yang menginfeksi sistem pernapasan. Virus COVID-19 dapat menginvasi banyak organ di dalam tubuh penderitanya, bahkan virus COVID-19 dapat masuk ke pankreas. Penelitian ini membahas tentang analisis model matematika COVID-19 pada manusia dengan subjek manusia sehat dan penderita diabetes tipe 2. Model matematika virus COVID-19 pada manusia diperoleh dengan mengkontruksi model matematika virus COVID-19 yang masuk dan menginfeksi organ paru-paru dan pankreas. Kemudian dilakukan analisis pada model dengan menentukan titik kesetimbangan, kestabilan dan analisis Bifurkasi Hopf. Adapun simulasi yang dilakukan menggunakan metode Runge-Kutta orde empat. Hasil analisis menunjukkan bahwa Titik setimbang bebas penyakit ( ) stabil asimtotis lokal jika . Hal ini merepresentasikan bahwa tidak terjadi infeksi virus COVID-19 pada sel epitel paru, sel endotel paru, sel endokrin dan sel eksokrin. Titik setimbang endemik ( ) stabil asimtotis lokal jika . Hal ini merepresentasikan bahwa infeksi virus COVID-19 menyebar pada sel epitel paru, sel endotel paru, sel endokrin dan sel eksokrin. Berdasarkan simulasi, virus COVID-19 yang menginfeksi dan sel yang terinfeksi lebih besar pada penderita diabetes tipe 2 dari pada manusia sehat dan Bifurkasi Hopf tidak terjadi pada titik kesetimbangan endemik.
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Coronavirus disease (COVID-19) is an infectious disease caused by the SARS-CoV-2 virus that infects the respiratory system. The COVID-19 virus can invade many organs in the sufferer's body, and even the COVID-19 virus can enter the pancreas. This study discusses the analysis of the mathematical model of COVID-19 in humans for healthy and type 2 diabetic subjects. The mathematical model of COVID-19 in humans for healthy and type 2 diabetic subjects was obtained by constructing a mathematical model of the COVID-19 virus that enters and infects the lung and pancreatic organs. Then an analysis is carried out on the model by determining the equilibrium point, stability and Hopf Bifurcation analysis. The simulation is carried out using the fourth-order Runge-Kutta method. The results of the analysis showed that the disease-free equilibrium point ( ) is locally asymptotic stable if . This represents that there is no infection with the COVID-19 virus in pulmonary epithelial cells, vascular endothelial cells, endocrine cells and exocrine cells. Endemic equilibrium point ( ) is locally asymptotic stable if . This represents that the COVID-19 virus infection spreads to pulmonary epithelial cells, vascular endothelial cells, endocrine cells and exocrine cells. The infecting COVID-19 virus and infected cells are greater in people with type 2 diabetes than in healthy and Hopf Bifurcation does not occur at the endemic equilibrium point.

Item Type:	Thesis (Masters)
Additional Information:	RTMa 511.8 Has a-1 2022
Uncontrolled Keywords:	COVID-19, Diabetes Melitus Tipe 2, Model Matematika, Kestabilan, Bifurkasi Hopf, Metode Runge-Kutta, Diabetes Mellitus, Mathematical Model, Stability, Hopf Bifurcation, Runge-Kutta Method.
Subjects:	H Social Sciences > HG Finance > HG4012 Mathematical models
Divisions:	Faculty of Mathematics, Computation, and Data Science > Mathematics > 44101-(S2) Master Thesis
Depositing User:	Mr. Marsudiyana -
Date Deposited:	27 Apr 2026 07:19
Last Modified:	27 Apr 2026 07:19
URI:	http://repository.its.ac.id/id/eprint/132919

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