IJBTT

Optimal Control of Mathematical Model for COVID-19 with Quarantine and Isolation

Optimal Control of Mathematical Model for COVID-19 with Quarantine and Isolation
	© 2021 by IJETT Journal
	Volume-69 Issue-6
	Year of Publication : 2021
	Authors : Muhammad Abdurrahman Rois, Trisilowati, Ummu Habibah
	DOI :  10.14445/22315381/IJETT-V69I6P223

How to Cite?

Muhammad Abdurrahman Rois, Trisilowati, Ummu Habibah, "Optimal Control of Mathematical Model for COVID-19 with Quarantine and Isolation," International Journal of Engineering Trends and Technology, vol. 69, no. 6, pp. 154-160, 2021. Crossref, https://doi.org/10.14445/22315381/IJETT-V69I6P223

Abstract
This study discusses the solution to the optimal control problem of the COVID-19 model with preventive action through education and treatment of infected individuals. In this model, the population is divided into seven subpopulations: subpopulation of susceptible, exposed, symptomatic, asymptomatic, quarantine, isolated, and recovered. Optimal control is obtained using the Pontryagin minimum principle and solved numerically using the Forward-Backward Sweep method. Furthermore, given control measures can minimize the number of subpopulations: exposed, symptomatic, and asymptomatic, and significant costs associated with control.

Keywords
COVID-19 model, Optimal control, Pontryagin minimum principle, Forward-Backward Sweep method.

Reference
[1] Y. Rao, D. Hu, and G. Huang, Dynamical Analysis of COVID-19 Epidemic Model with Individual Mobility, Commun. Math. Biol. Neurosci., (2021) 1–18.
[2] T. M. Chen, J. Rui, Q. P. Wang, Z. Y. Zhao, J. A. Cui, and L. Yin, A mathematical model for simulating the phase-based transmissibility of a novel coronavirus, Infect. Dis. Poverty, 9(1), (2020) 1–8.
[3] B. Tang et al., Estimation of Transmission Risk of 2019-nCoV and Its Implication for Public Health Interventions, J. Clin. Med., 9(2) (2020) 462.
[4] WHO, Novel Coronavirus. [Online]. Available: https://www.who.int/indonesia/news/novel-coronavirus/qa-for-public. [Accessed: 08-Jul-2020]. (2020)
[5] A. Yousefpour, H. Jahanshahi, and S. Bekiros, Optimal policies for control of the novel coronavirus disease (COVID-19) outbreak, Chaos, Solitons and Fractals, 136 (2020).
[6] E. U. Nainggolan, Virus Corona, Mahkota yang Membahayakan, www.djkn.kemenkeu.go.id. [Online]. Available: https://www.djkn.kemenkeu.go.id/artikel/baca/ 13002/Virus-Corona-Mahkota-yang-Membahayakan.html. [Accessed: 08-Jul-2020]. (2020)
[7] S. Usaini, A. S. Hassan, S. M. Garba, and J. M. S. Lubuma, Modeling the transmission dynamics of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) with latent immigrants, J. Interdiscip. Math., vol. 22, no. 6, pp. 903–930, 2019.
[8] WHO, Pertimbangan-pertimbangan untuk karantina individu dalam konteks penanggulangan penyakit coronavirus (COVID-19), 2020.
[9] Z. Feng, Final and Peak Epidemic Sizes for SEIR Models with Quarantine and Isolation, Math. Biosci. Eng., vol. 4, no. 4, pp. 675–686, 2007.
[10] M. Tahir, S. I. Ali Shah, G. Zaman, and T. Khan, Stability behavior of mathematical model MERS coronavirus spread in the population, Filomat, vol. 33, no. 12, pp. 3947–3960, 2019.
[11] E. Soewono, On the analysis of Covid-19 transmission in Wuhan, Diamond Princess, and Jakarta-cluster, Commun. Biomath. Sci., 3(1) (2020) 9–18.
[12] Y. Belgaid, M. Helal, and E. Venturino, Analysis of a Model for Coronavirus Spread, Mathematics, 8 (5) (2020) 1–30.
[13] A. Zeb, E. Alzahrani, V. S. Erturk, and G. Zaman, Mathematical Model for Coronavirus Disease 2019 (COVID-19) Containing Isolation Class, Biomed Res. Int., 2020, (2020).
[14] J. Jia et al., Modeling the control of COVID-19: Impact of policy interventions and meteorological factors, Electron. J. Differ. Equations, 2020 (23) (2020)1–24.
[15] S. Olaniyi, O. S. Obabiyi, K. O. Okosun, A. T. Oladipo, and S. O. Adewale, Mathematical modeling and optimal cost-effective control of COVID-19 transmission dynamics, Eur. Phys. J. Plus, 135 (11) 2020.
[16] C. T. Deressa and G. F. Duressa, Modeling and optimal control analysis of transmission dynamics of COVID-19: The case of Ethiopia, Alexandria Eng. J., (2020).
[17] R. M. Neilan and S. Lenhart, An Introduction to Optimal Control with an Application in Disease Modeling, DIMACS Ser. Discret. Math. Theor. Comput. Sci., 75 (2010) 67–81.
[18] S. Lenhart and J. T. Workman, Optimal Control Applied to Biological Models. New York: Chapman and Hall/CRC, (2007).
[19] D. Aldila, M. Z. Ndii, and B. M. Samiadji, Optimal control on COVID-19 eradication program in Indonesia under the effect of community awareness, Math. Biosci. Eng., 17 (6) (2020) 6355–6389.
[20] N. R. Sasmita, M. Ikhwan, S. Suyanto, and V. Chongsuvivatwong, Optimal control on a mathematical model to pattern the progression of coronavirus disease 2019 (COVID-19) in Indonesia, Glob. Heal. Res. Policy, 5, (2020).
[21] M. A. Rois, Trisilowati, and U. Habibah, Local Sensitivity Analysis of COVID-19 Epidemic with Quarantine and Isolation using Normalized Index, Telematika, 14 (1) (2021) 13–24.