DOI: https://doi.org/10.14710/jfma.v3i2.8546

OPTIMAL CONTROL MODELLING OF COVID-19 OUTBREAK IN SEMARANG CITY INDONESIA

*Dhimas Mahardika  -  Dept. of Mathematics, Diponegoro University, Indonesia
R. Heru Tjahjana  -  Dept. of Mathematics, Diponegoro University, Indonesia
Sunarsih Sunarsih  -  Dept. of Mathematics, Diponegoro University, Indonesia

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Abstract
Corona virus infection is lethal and life threatening to human life, for prevention it is necessary to carry out quarantined for a portion of susceptible, exposed, and infected population, this kind of quarantine is intended to reduce the spread of the corona virus. The optimal control that will be carried out in this research is conducting quarantine for a portion of susceptible, exposed, and infected individuals. This control function will be applied to the dynamic modelling of Covid-19 spread using Pontryagin Minimum Principle. We will describe the formulation of dynamic system of Covid-19 spread with optimal control, then we use Pontryagin Minimum Principle to find optimal solution of the control. The optimal control will aim to minimize the number of infected population and control measures. Numerical experiments will be performed to illustrate and compare the graph of Covid-19 spread model with and without control.
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Keywords: Covid-19; Dynamical System; Pontryagin Minimum Principle; Fixed time and fixed end point optimal control;

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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  3. M. A. Shereen, S. Khan, A. Kazmi, N. Bashir, and R. Siddique, “COVID-19 infection: Origin, transmission, and characteristics of human coronaviruses,” Journal of Advanced Research, vol. 24, pp. 91–98, 2020. https://doi.org/10.1016/j.jare.2020.03.005
  4. C. Wang, P. W. Horby, F. G. Hayden, and G. F. Gao, “A novel coronavirus outbreak of global health concern,” The Lancet, vol. 395, no. 10223, pp. 470–473, 2020. https://doi.org/10.1016/s0140-6736(20)30185-9
  5. B. Kan, M. Wang, H. Jing, H. Xu, X. Jiang, M. Yan, W. Liang, H. Zheng, K. Wan, Q. Liu, B. Cui, Y. Xu, E. Zhang, H. Wang, J. Ye, G. Li, M. Li, Z. Cui, X. Qi, K. Chen, L. Du, K. Gao, Y.-T. Zhao, X.-Z. Zou, Y.-J. Feng, Y.-F. Gao, R. Hai, D. Yu, Y. Guan, and J. Xu, “Molecular Evolution Analysis and Geographic Investigation of Severe Acute Respiratory Syndrome Coronavirus-Like Virus in Palm Civets at an Animal Market and on Farms,” Journal of Virology, vol. 79, no. 18, pp. 11892–11900, 2005. https://doi.org/10.1016/s0140-6736(20)30185-9
  6. B. J. Zheng, Y. Guan, K. H. Wong, J. Zhou, K. L. Wong, B. W. Y. Young, L. W. Lu, and S. S. Lee, “SARS-related Virus Predating SARS Outbreak, Hong Kong,” Emerging Infectious Diseases, vol. 10, no. 2, pp. 176–178, 2004. https://doi.org/10.3201/eid1002.030533
  7. Z. Shi and Z. Hu, “A review of studies on animal reservoirs of the SARS coronavirus,” Virus Research, vol. 133, no. 1, pp. 74–87, 2008. https://doi.org/10.1016/j.virusres.2007.03.012
  8. Anita S, Arnautu V, & Capasso V, An introduction to optimal control problems in life sciences and economics: From mathematical models to numerical simulation with MATLAB®, Birkhäuser 2010
  9. Kamien MI , Schwartz NL Dynamic Optimization, Advanced Textbooks in Economics 31. second ed. Amsterdam: North-Holland Publishing Co 1991
  10. Naidu, D. S., Pontryagin minimum principle in Optimal Control Systems, Boca Raton: CRC Press, pp. 249-291, 2003. https://doi.org/10.1201/9781315214429-6 2018
  11. Yang Z, Zeng Z, Wang K, Wong S-S, Liang W, Zanin M, et al., "Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions," Journal of Thoracic Disease, vol. 12, no. 3, pp. 165-174 2020. https://doi.org/10.21037/jtd.2020.02.64
  12. Cui, Q., Hu, Z., Li, Y., Han, J., Teng, Z., & Qian, J., " Dynamic variations of the COVID-19 disease at different quarantine strategies in Wuhan and Mainland China," Journal of Infection and Public Health, vol. 13, no. 6, pp. 849-855, 2020 https://doi.org/10.1016/j.jiph.2020.05.014
  13. Driss K, Abderrahim L, Omar B, Mostafa R, El H L., "Spread of COVID-19 in Morocco discrete mathematical modeling: Optimal control strategies and cost-effectiveness analysis," Journal of Mathematical and Computational Science, vol. 5, pp. 2070-2093, 2020. https://doi.org/10.28919/jmcs/4817
  14. Pérez López, C., Numerical Calculus with MATLAB. Applications to differential equations, Berkeley, CA: Apress, pp. 73-100, 2014. https://doi.org/10.1007/978-1-4842-0310-1_6
  15. Cannarsa, P., & Frankowska, H., "Infinite horizon optimal control: Transversality conditions and sensitivity relations," American Control Conference (ACC) 2017. https://doi.org/10.23919/acc.2017.7963349
  16. Frank L. Lewis Draguna L. Vrabie Vassilis L., Syrmos Final-time-free and constrained input control in Optimal Control, (eds F.L. Lewis, D.L. Vrabie and V.L. Syrmos), pp. 213-259, 2012. https://doi.org/10.1002/9781118122631.ch5
  17. Wang, M and Hu, Z ., "Bats as animal reservoirs for the SARS coronavirus: Hypothesis proved after 10 years of virus hunting," Virologica Sinica, vol. 28, no. 6, pp. 315-317, 2013. https://doi.org/10.1007/s12250-013-3402-x

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