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Vol 14 No 3 (2020): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Articles

MODEL MATEMATIKA PENYEBARAN PENYAKIT PULMONARY TUBERCULOSIS DENGAN PENGGUNAAN MASKER MEDIS

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  • Nur Inayah,
  • Muhammad Manaqib,
  • Nina Fitriyati,
  • Ikhwal Yupinto
Nur Inayah
Universitas Islam Negri Syarif Hidayatullah Jakarta
Muhammad Manaqib
UIN Syarif Hidayatullah Jakarta
Nina Fitriyati
Universitas Islam Negri Syarif Hidayatullah Jakarta
Ikhwal Yupinto
Universitas Islam Negri Syarif Hidayatullah Jakarta
DOI: https://doi.org/10.30598/barekengvol14iss3pp459-472
Published October 12, 2020
Keywords
  • Tuberculosis,
  • Equilibrium Point Stability,
  • Basic Reproduction Number
How to Cite
[1]
N. Inayah, M. Manaqib, N. Fitriyati, and I. Yupinto, “MODEL MATEMATIKA PENYEBARAN PENYAKIT PULMONARY TUBERCULOSIS DENGAN PENGGUNAAN MASKER MEDIS”, BAREKENG: J. Math. & App., vol. 14, no. 3, pp. 459-472, Oct. 2020.
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Abstract

This research developed a model of tuberculosis disease spread using the SIR model with addition of the medical mask usage factor. First, we create a diagram of the tuberculosis disease spread compartment through contact between individuals with medical mask usage. After that, we construct a system of nonlinear differential equations  based on the compartment diagram and then find the disease-free equilibrium point, the endemic equilibrium point, and the initial reproduction number . We use linearization to analyze of the disease-free equilibrium point. The disease-free equilibrium point obtained is asymptotically stable at .  The simulation result shows that the value of  . It means that tuberculosis disease in the future will disappear. But if we reduce the value of medical mask usage and increase the value of tuberculosis disease spread, the value . It means that tuberculosis diseases can become an outbreak.

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