Stability Analysis of Tuberculosis SITS Model
DOI:
https://doi.org/10.31605/jomta.v2i2.874Keywords:
tuberculosis, mathematical model, stability analysisAbstract
Tuberculosis (TB) is an infectious disease caused by mycobacterium tuberculosis. The purpose of this study is to investigate the dynamics of TB spread by using mathematical model. We develop SITS model which expressed as system of differential equations. The system has two equilibrium points, namely disease-free equilibrium point and endemic equilibrium point. The stability condition of the equilibrium points is proved. We perform several numerical simulations to support our theoretical results.
References
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[2] WHO, “WHO Global Tuberculosis Report,” World Health Organization, 2015.
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[7] P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Math. Biosci., vol. 180, no. 1–2, pp. 29–48, 2002, doi: 10.1016/S0025-5564(02)00108-6.
[8] B. K. Sahu, M. M. Gupta, and B. Subudhi, “Stability analysis of nonlinear systems using dynamic-Routh’s stability criterion: A new approach,” in 2013 International Conference on Advances in Computing, Communications and Informatics (ICACCI), 2013, pp. 1765–1769, doi: 10.1109/ICACCI.2013.6637448.
[2] WHO, “WHO Global Tuberculosis Report,” World Health Organization, 2015.
[3] DepKes, Profil Kesehatan Provinsi Sulawesi Barat. Mamuju: Dinas Kesehatan Provinsi Sulawesi Barat, 2007.
[4] U. Rafflesia, “Model Penyebaran Penyakit Tuberkulosis (TBC),” Gradien, vol. 10, no. 2, 2014.
[5] S. Side and W. Sanusi, Pemodelan Matematika Pada Penularan Penyakit Tuberkulosis. Makassar: Badan Penerbit UNM, 2016.
[6] N. Setiawan, “Analisis dan Simulasi Model SITR Pada Penyebaran Penyakit Tuberkulosis di Kota Makassar,” Universitas Negeri Makassar, 2017.
[7] P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Math. Biosci., vol. 180, no. 1–2, pp. 29–48, 2002, doi: 10.1016/S0025-5564(02)00108-6.
[8] B. K. Sahu, M. M. Gupta, and B. Subudhi, “Stability analysis of nonlinear systems using dynamic-Routh’s stability criterion: A new approach,” in 2013 International Conference on Advances in Computing, Communications and Informatics (ICACCI), 2013, pp. 1765–1769, doi: 10.1109/ICACCI.2013.6637448.
Published
2021-09-20
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