ANALISIS STABILITAS MODEL SIRS PADA PENYEBARAN PENYAKIT TUBERCULOSIS (TB)

Bukit, Jovi Big Lucky (2021) ANALISIS STABILITAS MODEL SIRS PADA PENYEBARAN PENYAKIT TUBERCULOSIS (TB). Undergraduate thesis, UNIMED.

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Abstract

Tuberkulosis (TB) adalah suatu penyakit menular yang disebabkan oleh bakteri Mycobacterium tuberculosis(Mtb) yang menyebar melalui udara. Penyakit TB merupakan penyebab kematian nomor tiga di dunia. Oleh karena itu perlu dilakukan analisis yang dapat diterima secara ilmiah terhadap peristiwa penyebaran penyakit TB. Salah satu yang dapat di pandang adalah peodelan matematika yaitu membentuk model dari penyebaran penyakit TB. Model yang dibentuk perlu dianalisis dengan mencari titik kesetimbangan, nilai Reproduksi dasar (R0) dan nilai eigen untuk menganalisis kestabilan titik kesetimbangan. Kemudian dilakukan simulasi dengan menggunakan metode Runge-Kutta orde 4. Hasil analisi diperoleh dua titik kesetimbangan yaitu titik kesetimbanga bebas penyakit dan endemik. Titik kesetimbangan bebas penyakit stabil asimtotik untuk R0 < 1 dan titik kesetimbangan endemik stabil untuk R0 > 1. Berdasarkan simulasi yang dilakukan diperoleh nilai parameter yang paling berpengaruh adalah laju penularan dan laju kesembuhan. Dengan demikian penyebaran tuberkulosis dapat diminimalkan dengan menurunkan laju penularan dan meningkatkan laju kesembuhan.

Item Type: Thesis (Undergraduate)
Contributors:
ContributionNameNIDN/NIDK
Thesis advisorHutapea, Tri Andri198104192006041001
Call Number: SK-2021 MAT 261
Keywords: Model matematika; Tuberkulosis; Runge-Kutta; Sistem persamaan diferensial
Subjects: Q Science > QA Mathematics
R Medicine > RC Internal medicine > RC581 Specialties of internal medicine > RC705 Diseases of the respiratory system
Divisions: Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika
Depositing User: Mrs Harly Christy Siagian
Date Deposited: 14 Dec 2021 08:03
URI: http://digilib.unimed.ac.id/id/eprint/44061

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