Analisis Model Epidemi Penyebaran Tuberkulosis Dengan Struktur Umur

Erna Sari, Asrul Sani, Muh. Kabil Djafar

Abstract


Tuberculosis (TBC) is a contagious disease caused by infection with the bacterium Mycobacterium tuberculosis (Mtb), which attacks the lungs. taking into account the laten period of individuals infected with tuberculosis, this study uses the SEIRS model. The total population is grouped into two age groups, group child and group adult . The purpose of this research is to determine SEIRS model of the spread tuberculosis disease with age structure and its completion behavior. The steps in analyzing of the model can be done by determining the equilibrium point, the results are obtained two equilibrium points, namely disease-free equilibrium points and endemic equilibrium points. Determine basic reproduction number and stability analysis at the equilibrium point. Analysis of the stability of the disease-free equilibrium point is carried out to find the stability of the model using linearization around the equilibrium point. The simulation result are disease-free equilibrium point is the asymptotic stable if the basic reproduction number is less than one, and it means that the disease will disappear over time, and the endemic equilibrium point is stable if the basic reproduction number is more than one, meaning there is disease spread in the population.

Keywords


tuberculosis; SEIRS; epidemic model; stability of equilibrium points; basic reproduction number

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DOI: https://doi.org/10.15548/jostech.v3i2.6064
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References


A. Puspitasari, Kamira, dan N. Asiyah, “Analisis Kestabilan dan Kontrol Optimal Model Penyebaran Tuberkulosis ( TB ) dengan Terapi dan,” J. Sains Dan Seni ITS, vol. 8, no. 2, hal. A58–A64, 2019.

A. Wahdi dan D. R. Puspitosari, Mengenal Tuberkulosis. Purwokerto: CV.Pena Persada, 2021.

F. Brauer, P. van den Driessche, dan J. Wu, Mathematical Epidemology (Lecturer Notes in Mathematics 1945). Berlin Heidelberg: Springer, 2008.

H. Anton dan C. Rorres, Elementary Linear Algebra: Applications Version, 11th Ed. Hoboken, New Jersey: John Wiley & Sons, Inc, 2014.

J. Crofton, H. L. Rieder, C.-Y. Chiang, R. Gie, dan D. Enarson, Clinical Tuberculosis, 3rd Ed. Oxford: Macmillan Publishers Limited, 2009.

L. N. Nkamba, T. T. Manga, F. Agouanet, dan M. L. M. Manyombe, “Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis,” J. Biol. Dyn., vol. 13, no. 1, hal. 26–42, 2019.

M. Soleh dan S. Rahma, “Model SEIR Penyakit Campak Dengan Vaksinasi Dan Migrasi,” J. Sains, Teknol. dan Ind., vol. 9, no. 2, hal. 113–123, 2012.

M. Iannelli dan F. Milner, The Basic Approach to Age-Structured Population Dynamics. Models, methods and numerics. Dordrecht: Springer Science + Business Media, 2017.

O. Diekmann dan J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Disease: Model Building, Analysis and Interpretation. Chichester: John Wiley & Sons Ltd, 2000.

P. N. V. Tu, Dynamical System: An Introduction with Applications in Economics and Biology. New York: Springer-Verlag, 1992.

R. T. Putra, Sukatik, dan S. Nita, “Kestabilan Model Epidemi Seir dengan Matriks Hurwitz,” Poli Rekayasa, vol. 11, no. 2, hal. 74–82, 2016.

S. Side, W. Sanusi, dan A. Bohari, “Pemodelan Matematika SEIR Penyebaran Penyakit Pneumonia pada Balita dengan Pengaruh Vaksinasi di Kota Makassar,” JMathCos (Journal Math. Comput. Stat., vol. 4, no. 1, hal. 1–12, 2021.

T. Atkins, “Modeling Transmission Dynamics Of Tuberculosis Including Various Latent Periods,” Electron. Theses Diss., vol. 3682, hal. 2004–2019, 2008.

WHO, “World Healt Organization, Factsheet on the world tuberculosis report,” 2021. https://www.who.int/en/news-room/fact-sheets/detail/tuberculosis

Z. Guo, H. Xiang, dan H. Huo, “Analysis of an age-structured tuberculosis model with treatment and relapse,” J. Math. Biol., vol. 82, no. 45, hal. 1–37, 2021.


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