Kontrol Optimal pada Model Penyebaran SARS-CoV-2 dengan Pelaksanaan Testing dan Perawatan
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Published
Jan 28, 2024
Abstract
COVID-19 (Corona Virus Disease 2019) is a disease of the respiratory system caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The COVID-19 pandemic was declared active by WHO in March 2020 and the pandemic status was lifted on May 5, 2023. COVID-19 must still be watched out to prevent a new wave of pandemics, so an optimal control analysis is needed. The purpose of this study is to determine the optimal control form of the SARS-CoV-2 spread dynamics model in minimizing the number of exposed populations by implementing testing and minimizing the infected population by implementing treatment. Optimal control analysis is carried out using the Pontryagin Maximum Principle, while numerical calculations for simulation use the Forward-Backward Runge-Kutta method with the help of MATLAB R2021a software. The results of the optimal control analysis conducted on 3 simulations with different vaccination values and incubation periods show that the application of both control strategies to the COVID-19 spread model in Indonesia is effective in reducing the number of infected individuals to 99.9%, but cannot maintain the population size.
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How to Cite
Rohana Sianipar, A. D. and Pangarapan Sinaga, L. (2024) “Kontrol Optimal pada Model Penyebaran SARS-CoV-2 dengan Pelaksanaan Testing dan Perawatan”, Ranah Research : Journal of Multidisciplinary Research and Development, 6(1), pp. 94-105. doi: 10.38035/rrj.v6i1.800.
References
Annas, S., Isbar Pratama, M., Rifandi, M., Sanusi, W., & Side, S. (2020). Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia. Chaos, Solitons and Fractals, 139, 110072. https://doi.org/10.1016/j.chaos.2020.110072
Azzahra, N. F., Hariyanto, H., & Mardlijah, M. (2022). Kontrol Optimal Penyebaran COVID-19 Model SEIR di Jakarta. Jurnal Sains Dan Seni ITS, 11(2). https://doi.org/10.12962/j23373520.v11i2.76998
Gu, Y., Ullah, S., Khan, M. A., Alshahrani, M. Y., Abohassan, M., & Riaz, M. B. (2022). Mathematical modeling and stability analysis of the COVID-19 with quarantine and isolation. Results in Physics, 34(February). https://doi.org/10.1016/j.rinp.2022.105284
Hou, C., Chen, J., Zhou, Y., Hua, L., Yuan, J., He, S., Guo, Y., Zhang, S., Jia, Q., Zhao, C., Zhang, J., Xu, G., & Jia, E. (2020). The effectiveness of quarantine of Wuhan city against the Corona Virus Disease 2019 (COVID-19): A well-mixed SEIR model analysis. Journal of Medical Virology, 92(7), 841–848. https://doi.org/10.1002/jmv.25827
İğret Araz, S. (2021). Analysis of a Covid-19 model: Optimal control, stability and simulations. Alexandria Engineering Journal, 60(1), 647–658. https://doi.org/10.1016/j.aej.2020.09.058
Kompas. (2023). Peningkatan Covid-19 di Akhir Tahun, 2 Pasien Meninggal, dan Pentingnya Vaksinasi. KOMPAS.Com. https://nasional.kompas.com/read/2023/12/27/09164351/peningkatan-covid-19-di-akhir-tahun-2-pasien-meninggal-dan-pentingnya?page=all
Li, T., & Guo, Y. (2022). Optimal control and cost-effectiveness analysis of a new COVID-19 model for Omicron strain. Physica A: Statistical Mechanics and Its Applications, 606, 128134. https://doi.org/10.1016/j.physa.2022.128134
Nainggolan, J., Harianto, J., & Tasman, H. (2023). an Optimal Control of Prevention and Treatment of Covid-19 Spread in Indonesia. Communications in Mathematical Biology and Neuroscience, 2023, 1–22. https://doi.org/10.28919/cmbn/7820
Paul, A. K., & Kuddus, M. A. (2022). Mathematical analysis of a COVID-19 model with double dose vaccination in Bangladesh. Results in Physics, 35(February), 105392. https://doi.org/10.1016/j.rinp.2022.105392
Rangkuti, Y. M., Firmansyah, & Landong, A. (2022). Control optimal analysis of SEIR model of covid 19 spread in Indonesia. Journal of Physics: Conference Series, 2193(1). https://doi.org/10.1088/1742-6596/2193/1/012091
Royden, H. . (1968). Real Analysis 2nd Edition. McMillan Publishing Company Inc.
WHO. (2023). Statement on the Fifteenth Meeting of the IHR (2005) Emergency Committee on the COVID-19 Pandemic. World Health Organization. https://www.who.int/news/
Widodo, D. S. (2023c). The nexus of entrepreneurial orientation and knowledge management on business performance of smes in west java: Role of competitive advantage. Journal of Law and Sustainable Development, 11(7), e1364–e1364.
Widodo, D. S., & Silitonga, P. E. S. (2017). Company Performance Analysis: Leadership Style, Corporate Culture and Human Resource Development. International Review of Management and Marketing, 7(4), 34–41.
Widodo, D. S., Silitonga, P. E. S., & Azahra, D. (2019). The influence of transactional leadership to employee job motivation and satisfaction in Jakarta stock exchange. International Journal of Governmental Studies and Humanities, 2(1), 38–46.
Widodo, D. S., Zainal, V. R., Subagja, I. K., & Sari, E. (2019). What Is Important With English Language Skills Students? Survey in University at Bekasi City, Indonesia. International Journal of Linguistics, 11(3), 7.
Wikipedia. (n.d.). Pandemi COVID-19 di Indonesia. 2020. Retrieved June 15, 2023, from https://id.wikipedia.org/
Yong, B., Hoseana, J., & Owen, L. (2022). From pandemic to a new normal: Strategies to optimise governmental interventions in Indonesia based on an SVEIQHR-type mathematical model. Infectious Disease Modelling, 7(3), 346–363. https://doi.org/10.1016/j.idm.2022.06.004
Youssef, H. M., Alghamdi, N., Ezzat, M. A., El-Bary, A. A., & Shawky, A. M. (2022). A proposed modified SEIQR epidemic model to analyze the COVID-19 spreading in Saudi Arabia. Alexandria Engineering Journal, 61(3), 2456–2470. https://doi.org/10.1016/j.aej.2021.06.095
Zainal, V. R., Widodo, D. S., & Subagja, I. K. (2019). Indonesia Islamic Banking Readiness in Facing the ASEAN Economic Community, in Terms of Islamic Banking Disclosure and Performance Indices. Journal of Economics and Management Sciences, 2(2), p25–p25.
Zeb, A., Alzahrani, E., Erturk, V. S., & Zaman, G. (2020). Mathematical Model for Coronavirus Disease 2019 (COVID-19) Containing Isolation Class. BioMed Research International, 2020. https://doi.org/10.1155/2020/3452402
Azzahra, N. F., Hariyanto, H., & Mardlijah, M. (2022). Kontrol Optimal Penyebaran COVID-19 Model SEIR di Jakarta. Jurnal Sains Dan Seni ITS, 11(2). https://doi.org/10.12962/j23373520.v11i2.76998
Gu, Y., Ullah, S., Khan, M. A., Alshahrani, M. Y., Abohassan, M., & Riaz, M. B. (2022). Mathematical modeling and stability analysis of the COVID-19 with quarantine and isolation. Results in Physics, 34(February). https://doi.org/10.1016/j.rinp.2022.105284
Hou, C., Chen, J., Zhou, Y., Hua, L., Yuan, J., He, S., Guo, Y., Zhang, S., Jia, Q., Zhao, C., Zhang, J., Xu, G., & Jia, E. (2020). The effectiveness of quarantine of Wuhan city against the Corona Virus Disease 2019 (COVID-19): A well-mixed SEIR model analysis. Journal of Medical Virology, 92(7), 841–848. https://doi.org/10.1002/jmv.25827
İğret Araz, S. (2021). Analysis of a Covid-19 model: Optimal control, stability and simulations. Alexandria Engineering Journal, 60(1), 647–658. https://doi.org/10.1016/j.aej.2020.09.058
Kompas. (2023). Peningkatan Covid-19 di Akhir Tahun, 2 Pasien Meninggal, dan Pentingnya Vaksinasi. KOMPAS.Com. https://nasional.kompas.com/read/2023/12/27/09164351/peningkatan-covid-19-di-akhir-tahun-2-pasien-meninggal-dan-pentingnya?page=all
Li, T., & Guo, Y. (2022). Optimal control and cost-effectiveness analysis of a new COVID-19 model for Omicron strain. Physica A: Statistical Mechanics and Its Applications, 606, 128134. https://doi.org/10.1016/j.physa.2022.128134
Nainggolan, J., Harianto, J., & Tasman, H. (2023). an Optimal Control of Prevention and Treatment of Covid-19 Spread in Indonesia. Communications in Mathematical Biology and Neuroscience, 2023, 1–22. https://doi.org/10.28919/cmbn/7820
Paul, A. K., & Kuddus, M. A. (2022). Mathematical analysis of a COVID-19 model with double dose vaccination in Bangladesh. Results in Physics, 35(February), 105392. https://doi.org/10.1016/j.rinp.2022.105392
Rangkuti, Y. M., Firmansyah, & Landong, A. (2022). Control optimal analysis of SEIR model of covid 19 spread in Indonesia. Journal of Physics: Conference Series, 2193(1). https://doi.org/10.1088/1742-6596/2193/1/012091
Royden, H. . (1968). Real Analysis 2nd Edition. McMillan Publishing Company Inc.
WHO. (2023). Statement on the Fifteenth Meeting of the IHR (2005) Emergency Committee on the COVID-19 Pandemic. World Health Organization. https://www.who.int/news/
Widodo, D. S. (2023c). The nexus of entrepreneurial orientation and knowledge management on business performance of smes in west java: Role of competitive advantage. Journal of Law and Sustainable Development, 11(7), e1364–e1364.
Widodo, D. S., & Silitonga, P. E. S. (2017). Company Performance Analysis: Leadership Style, Corporate Culture and Human Resource Development. International Review of Management and Marketing, 7(4), 34–41.
Widodo, D. S., Silitonga, P. E. S., & Azahra, D. (2019). The influence of transactional leadership to employee job motivation and satisfaction in Jakarta stock exchange. International Journal of Governmental Studies and Humanities, 2(1), 38–46.
Widodo, D. S., Zainal, V. R., Subagja, I. K., & Sari, E. (2019). What Is Important With English Language Skills Students? Survey in University at Bekasi City, Indonesia. International Journal of Linguistics, 11(3), 7.
Wikipedia. (n.d.). Pandemi COVID-19 di Indonesia. 2020. Retrieved June 15, 2023, from https://id.wikipedia.org/
Yong, B., Hoseana, J., & Owen, L. (2022). From pandemic to a new normal: Strategies to optimise governmental interventions in Indonesia based on an SVEIQHR-type mathematical model. Infectious Disease Modelling, 7(3), 346–363. https://doi.org/10.1016/j.idm.2022.06.004
Youssef, H. M., Alghamdi, N., Ezzat, M. A., El-Bary, A. A., & Shawky, A. M. (2022). A proposed modified SEIQR epidemic model to analyze the COVID-19 spreading in Saudi Arabia. Alexandria Engineering Journal, 61(3), 2456–2470. https://doi.org/10.1016/j.aej.2021.06.095
Zainal, V. R., Widodo, D. S., & Subagja, I. K. (2019). Indonesia Islamic Banking Readiness in Facing the ASEAN Economic Community, in Terms of Islamic Banking Disclosure and Performance Indices. Journal of Economics and Management Sciences, 2(2), p25–p25.
Zeb, A., Alzahrani, E., Erturk, V. S., & Zaman, G. (2020). Mathematical Model for Coronavirus Disease 2019 (COVID-19) Containing Isolation Class. BioMed Research International, 2020. https://doi.org/10.1155/2020/3452402