KESTABILAN TITIK TETAP MODEL SEIR PENYEBARAN PENYAKIT TUBERKULOSIS
DOI:
https://doi.org/10.25077/jmua.13.3.149-156.2024Keywords:
Model SEIR, kestabilan, titik tetap, tuberkulosisAbstract
Makalah ini mengkaji kestabilan titik tetap model SEIR penyebaran penyakit tuberkulosis pada populasi manusia. Ada dua titik titik tetap dari model SEIR, yaitu titik titik tetap bebas penyakit dan titik tetap endemik. Kestabilan kedua titik titik tetap ditentukan dengan menggunakan kriteria Routh-Hurwitz. Simulasi numerik memperlihatkan bahwa jumlah subpopulasi terekspose dan terinfeksi cenderung berkurang dengan berlalunya waktu.
References
Brauer, F. dan C. Chavez, 2012, Mathematical Models in Population Biology and Epidemiology, Springer, New York
Keeling, M.J. dan P. Rohani, 2008, Modeling Infectious Diseases. Princeton University Press, New Jersey
Li, Z., Z. Teng, X. Feng, Y. Li, dan H. Zhang, 2015, Dynamical Analysis of a SEIT Epidemic Model with Application to Ebola Virus Transmission in Guinea, Computational and Mathematical Methods in Medicine, Article ID 582625, https://dx.doi.org/10.1155/2015/582625
Kelley, W. dan A.C. Peterson, 2010, The Theory of Differential Equations. Springer, New York
Martcheva, M., 2010, An Introduction to Mathematical Epidemiology, Springer, New York
Okuonghaea, D. dan A. Korobeinikov, 2007, Dynamics of Tuberculosis: The effect of Direct Observation Therapy Strategy (DOTS) in Nigeria, Mathematical Modeling of Natural Phenomena Vol. 2(1): 3 – 11
Tanjung, R.W., Muhafzan, dan Zulakmal, 2021, Model Penyebaran Penyakit Tuberkulosis dengan Kontrol Vaksinasi, Jurnal Matematika UNAND, 10(3): 280 – 287
Mettle, F. O., Affi, P. O. dan C. Twumasi, 2020, Modeling the transmission dynamics of tuberculosis in the Ashanti Region of Ghana, Interdisciplinary Perspectives on Infectious Diseases, ID 4513854, https://doi.org/10.1155/2020/4513854
Romanovsky, V. G, 2023, On some SEIRS epidemic models, Journal of Nonlin- ear Modeling and Analysis Vol. 5(4), https://doi.org/10.12150/jnma.2023.753.
Das, K., Murthy, B. S. N, Samad, S. A, Biswas, M. H. A, 2021, Mathematical transmission analysis of SEIR tuberculosis disease model, Sensors International 2(100120), https://doi.org/10.1016/j.sintl.2021.100120.
Piovella, N., 2020, Analytical solution of SEIR model describing the free spread of the COVID-19 pandemic, Chaos, Solitons and Fractals 140(110243), https://doi.org/10.1016/j.chaos.2020.110243.
Lynch, S., 2017, Dynamical System with Application using MATLAB, Birkhauser, Manchester
Pierre, T., 1994, Dynamical System an Introduction with Applications in Eco-nomics and Biology, Second Revised and Enlarged Edition, Springer-Verlag, Berlin
Fisher, S. 1990. Complex Variables, Second Edition, Dover Publications Inc., New York
Downloads
Published
Issue
Section
License
All articles published in Jurnal Matematika UNAND (JMUA) are open access and licensed under the Creative Commons Attribution-ShareAlike (CC BY-SA) license. This ensures that the content is freely available to all users and can be shared and adapted, provided appropriate credit is given and any adaptations are distributed under the same license.
Copyright Holder
The copyright of all articles published in Jurnal Matematika UNAND is held by the Departemen Matematika dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA), Universitas Andalas (UNAND). This applies to all published versions, including the HTML and PDF formats of the articles.
Author Rights
While the Departemen Matematika dan Sains Data FMIPA UNAND holds the copyright for all published content, authors retain important rights under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA). This license grants authors and users the following rights:
- Reuse: Authors can reuse and distribute their work for any lawful purpose, including sharing on personal websites, institutional repositories, or in subsequent publications.
- Attribution and Adaptation: Authors and others may remix, adapt, and build upon the published work for any purpose, even commercially, as long as proper credit is given to the original authors, and any derivative works are distributed under the same CC BY-SA license.
Creative Commons License (CC BY-SA)
Under the terms of the CC BY-SA license, users are free to:
- Share: Copy and redistribute the material in any medium or format.
- Adapt: Remix, transform, and build upon the material for any purpose, even commercially.
However, the following conditions apply:
- Attribution: Users must give appropriate credit to the original author(s) and Departemen Matematika dan Sains Data FMIPA UNAND, provide a link to the license, and indicate if changes were made. Attribution must not imply endorsement by the author or the journal.
- ShareAlike: If users remix, transform, or build upon the material, they must distribute their contributions under the same license as the original.
For more information about the CC BY-SA license, please visit the Creative Commons website.
Third-Party Content
If authors include third-party material (such as figures, tables, or images) that is not covered by a Creative Commons license, they must obtain the necessary permissions for reuse and provide proper attribution. Authors are required to ensure that any third-party content complies with open-access licensing requirements or includes permissions for redistribution under similar terms.
Copyright and Licensing Information Display
The copyright and licensing terms will be clearly displayed on each article's landing page, as well as within the full-text versions (HTML and PDF) of all published articles.
No "All Rights Reserved"
As an open-access journal, JMUA does not use "All Rights Reserved" policies. Instead, the CC BY-SA license ensures that the works remain accessible and reusable for a wide audience while still protecting both the authors' and the copyright holder's rights.
Â
