Development of a SEIR Model with Two Optimal Controls for Infectious Disease Control: Computational Simulation Using MATLAB
DOI:
https://doi.org/10.30736/voj.v8i1.1293Keywords:
SEIR Model, Optimal Control, Mathematical Modeling, MATLAB simulationAbstract
This study develops a Susceptible–Exposed–Infectious–Recovered (SEIR) mathematical model with two time-dependent optimal control strategies educational campaigns and medical treatment to analyze Ebola transmission. The nonlinear system is examined using Pontryagin’s Minimum Principle, and the optimality system is solved numerically through the Forward–Backward Sweep Method in MATLAB. Simulation results show that combined controls substantially reduce the peak number of infected individuals, decrease cumulative infection cases, and shorten the epidemic duration compared to the uncontrolled scenario. Early implementation of both interventions further improves epidemic suppression and reduces the overall cost functional value. These results demonstrate the effectiveness of integrated control strategies and highlight mathematical modeling as a decision-support tool in public health planning.
Downloads
References
Asmianto, A., Suwarman, R. F., Ilmayasinta, N., & Norasia, Y. (2025). Optimizing Educational Control in a Tuberculosis Transmission Model Using the Pontryagin Maximum Principle. CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS, 6(1), 61-69.
Cacace, S., & Oliviero, A. (2024). Reliable Optimal Controls for SEIR Models in Epidemiology. Mathematics and Computers in Simulation, 223, 523–542. https://doi.org/10.1016/j.matcom.2024.04.034
Chowell, G., Hengartner, N. W., Castillo-Chavez, C., Fenimore, P. W., & Hyman, J. M. (2004). The Basic Reproductive Number of Ebola and the Effects of Public Health Measures: The Cases of Congo and Uganda. Journal of Theoretical Biology, 229(1), 119–126. https://doi.org/10.1016/j.jtbi.2004.03.006
Funk, S., Gilad, E., Watkins, C., & Jansen, V. A. A. (2009). The Spread of Awareness and Its Impact on Epidemic Outbreaks. Proceedings of the National Academy of Sciences, 106(16), 6872–6877. https://doi.org/10.1073/pnas.0810762106
Hethcote, H. W. (2000). The Mathematics of Infectious Diseases. SIAM Review, 42(4), 599–653. https://doi.org/10.1137/S0036144500371907
Higham, D. J., & Higham, N. J. (2016). MATLAB Guide, Third Edition. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611974669
Lenhart, S., & Workman, J. T. (2007). Optimal Control Applied to Biological Models. Chapman & Hall/CRC.
Li, Z., Teng, Z., Feng, X., Li, Y., & Zhang, H. (2015). Dynamical Analysis of an SEIT Epidemic Model with Application to Ebola Virus Transmission in Guinea. Computational and Mathematical Methods in Medicine, 2015, 1–11. https://doi.org/10.1155/2015/582625
Okosun, K. O., Ouifki, R., & Marcus, N. (2011). Optimal Control Analysis of a Malaria Disease Transmission Model that Includes Treatment and Vaccination with Waning Immunity. Biosystems, 106(2–3), 136–145. https://doi.org/10.1016/j.biosystems.2011.07.006
Polak, E. (1997). Optimization: Algorithms and Consistent Approximations. Springer.
Rachah, A., & Torres, D. F. M. (2015). Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa. Discrete Dynamics in Nature and Society, 2015, 1–9. https://doi.org/10.1155/2015/842792
Sariadji, K. (2022, October 11). Kasus Ebola di Kongo: Jauh Dari Indonesia Tapi Terasa Dekat, Bagaimana Antisipasinya? Kemenkes BKPK.
Seck, R., Ngom, D., Ivorra, B., & Ramos, Á. M. (2021). An Optimal Control Model to design Strategies for Reducing the Spread of the Ebola Virus Disease. Mathematical Biosciences and Engineering, 19(2), 1746–1774. https://doi.org/10.3934/mbe.2022082
Sumardi, S. R. (2022). Analisis Kendali Optimal Pada Penyebaran Virus Ebola dengan Mempertimbangkan Pengaruh Perubahan Perilaku Manusia dan Iklim. J-HEST Journal of Health Education Economics Science and Technology, 5(1), 157–163. https://doi.org/10.36339/jhest.v5i1.93
Wang, W., & Zhao, X.-Q. (2008). Threshold Dynamics for Compartmental Epidemic Models in Periodic Environments. Journal of Dynamics and Differential Equations, 20(3), 699–717. https://doi.org/10.1007/s10884-008-9111-8
World Health Organization. (2018). Risk Communication and Community Engagement (RCCE) Considerations: Ebola Response in the Democratic Republic of the Congo.
Zinihi, A., Ehrhardt, M., & Ammi, M. R. (2025). Spatiotemporal SEIQR Epidemic Modeling with Optimal Control for Vaccination, Treatment, and Social Measures. University of Wuppertal.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Sitti Rosnafian Sumardi, Muhammad Hisyam
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Copyright:
Authors who publish their manuscripts in this Journal agree to the following conditions:
- Copyright of any article on Vygotsky: Jurnal Pendidikan Matematika dan Matematika is held solely by the author under the Creative Commons Attribution 4.0 International license (CC BY NC SA).
- Authors can submit papers separately, arrange non-exclusive distribution of manuscripts that have been published in this journal into other versions (e.g. sending to the author's institutional repository, publication in a book, etc.) by acknowledging that the manuscript has been published for the first time in Vygotsky: Jurnal Pendidikan Matematika dan Matematika.
License:
Vygotsky: Jurnal Pendidikan Matematika dan Matematika is published under the terms of the Creative Commons Attribution 4.0 International License (CC BY NC SA). This license permits anyone to copy and redistribute this material in any form or format, compile, modify and develop this material for any purpose as long as it is not for commercial purposes. Additionally, anyone must provide credit and distribute contributions under the license of the creator of the original work.
