The SIR fuzzy epidemic model (Susceptible, Infected, Recovered) on spreading tuberculosis disease

This research aims to determine the mathematical modeling, stability analysis, and the result of a numerical simulation of the spread of tuberculosis disease in Indonesia in 2017. The stages performed were to form a fuzzy SIR epidemic model (Susceptible, Infected, Recovered), determine the equilibri...

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Bibliographic Details
Published in:AIP conference proceedings 2022-12, Vol.2575 (1)
Main Authors: Mawarni, Murtantina Dyahayu, Lestari, Dwi
Format: Article
Language:English
Subjects:
Asymptotic properties
Epidemics
Equilibrium
Mathematical models
Simulation
Stability analysis
Tuberculosis
Online Access:Get full text
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Summary:This research aims to determine the mathematical modeling, stability analysis, and the result of a numerical simulation of the spread of tuberculosis disease in Indonesia in 2017. The stages performed were to form a fuzzy SIR epidemic model (Susceptible, Infected, Recovered), determine the equilibrium point, determine the basic reproduction number, analyze the stability around the equilibrium point, and conduct a simulation using the Maple 18 software. The results of the study acquired two equilibrium points which were disease-free and endemic. The equilibrium point is free of local asymptotic stable disease when the basic reproduction number is worth less than one. It means for a long period of time tuberculosis disease will be reduced or disappear from the population. Meanwhile, the endemic equilibrium is locally asymptotically stable if the basic reproduction number is worth more than one. This means that tuberculosis disease will spread and be endemic to the disease. Based on the simulation established, the greater the rate of transmission, the more the disease will spread and the smaller the recovery rate, the more the disease will spread.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0108518