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All Journal Epsilon: Jurnal Matematika Murni dan Terapan
Azkia Khairal Jamil
Program Studi Matematika Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Lambung Mangkurat
Decision Sciences, Operations Research & Management Transportation

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Journal : Epsilon: Jurnal Matematika Murni dan Terapan

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ANALISIS KESTABILAN DAN SOLUSI NUMERIK PADA MODEL SEIR UNTUK PENYAKIT TUBERKULOSIS Azkia Khairal Jamil; Yuni Yulida; Muhammad Ahsar Karim
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 17, No 1 (2023)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v17i1.6403

Abstract

One of the infectious diseases that can be modelled into the SEIR model is Tuberculosis (TB), this is because TB has a bacterial incubation period, so it is at this time that a person enters the exposed subpopulation. TB is divided into two types, namely latent TB and active TB. This study aims to explain the formation of the SEIR Model for the Spread of Tuberculosis, determine the equilibrium point and Basic Reproductive Numbers on the SEIR Model for the Spread of Tuberculosis, analyze the stability of the SEIR Model for the spread of Tuberculosis at the equilibrium point, and make numerical simulations. The result of this research is the formation of a mathematical model on the spread of Tuberculosis, and from the model obtained two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. Then the basic reproduction number ( ) was found through the Next Generation Matrix. Furthermore, the stability analysis was carried out at the disease-free equilibrium point and it was found that the local asymptotic stable model with , while at the endemic equilibrium point it was found that the local asymptotic stable model with . Numerical simulations are presented to show numerical solutions and strengthen the explanation of the stability analysis of the model using the fourth-order Runge-Kutta method with parameters that meet the stability requirements.
Co-Authors Muhammad Ahsar Karim Yuni Yulida