ANALISIS KESTABILAN DAN SOLUSI NUMERIK PADA MODEL SEIR UNTUK PENYAKIT TUBERKULOSIS

Azkia Khairal Jamil; Yuni Yulida; Muhammad Ahsar Karim

doi:10.20527/epsilon.v17i1.6403

ANALISIS KESTABILAN DAN SOLUSI NUMERIK PADA MODEL SEIR UNTUK PENYAKIT TUBERKULOSIS

Azkia Khairal Jamil, Yuni Yulida, Muhammad Ahsar Karim

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.

Keywords

Tuberculosis, SEIR Model, Equilibrium, Stability analysis, Numerical simulation.

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DOI: https://doi.org/10.20527/epsilon.v17i1.6403