DESAIN KONTROL PENGOBATAN PADA MODEL SIRD UNTUK PENYEBARAN VIRUS COVID-19 MENGGUNAKAN BACKSTEPPING
Abstract
In this article, we present a control design on a SIRD model with treatment in infected individuals. The SIRD model with treatment is obtained from literature study and the parameter model is obtained from covid-19 daily case in the Riau province using the Particle Swarm Optimization method. The control design is carried out based on the backstepping method combined with feedback linearization based on input and output (IOFL). The SIRD model which is a nonlinear system will be transformed into a normal form using IOFL. Each variable is then stabilized Lyapunov using virtual control which at the same time generates a new state variable. This stage will be carried out iteratively until the last state variable is stabilized using a real control function. This control function is then applied to the SIRD model using the inverse of IOFL transformation. The simulation results compared with the Pontryagin Minimum Principle (PMP) method show that by selecting the appropriate control parameters, backstepping obtains better control performance which is a smaller number of infected populations.
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References
Y. Li dkk., “Mathematical Modeling and Epidemic Prediction of COVID-19 and Its Significance to Epidemic Prevention and Control Measures,” vol. 5, no. 1, hlm. 9, 2020.
W. Zhou dan W. Wang, “Fast-spreading SARS-CoV-2 variants: challenges to and new design strategies of COVID-19 vaccines,” Signal Transduct. Target. Ther., vol. 6, no. 1, hlm. 226, Des 2021, doi: 10.1038/s41392-021-00644-x.
Y. Ophinni dkk., “COVID-19 Vaccines: Current Status and Implication for Use in Indonesia,” Acta Med Indones, vol. 52, no. 4, hlm. 25, 2020.
F. P. Polack dkk., “Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine,” N. Engl. J. Med., vol. 383, no. 27, hlm. 2603–2615, Des 2020, doi: 10.1056/NEJMoa2034577.
E. Ong, M. U. Wong, A. Huffman, dan Y. He, “COVID-19 coronavirus vaccine design using reverse vaccinology and machine learning,” Bioinformatics, preprint, Mar 2020. doi: 10.1101/2020.03.20.000141.
W. C. Roda, M. B. Varughese, D. Han, dan M. Y. Li, “Why is it difficult to accurately predict the COVID-19 epidemic?,” Infect. Dis. Model., vol. 5, hlm. 271–281, 2020, doi: 10.1016/j.idm.2020.03.001.
J. Zhou dan C. Wen, Adaptive Backstepping Control of Uncertain Systems Nonsmooth Nonlinearities, Interactions or Time-Variations. Heidelberg: Springer, 2008.
H. G. Tanner dan K. J. Kyriakopoulos, “Backstepping for nonsmooth systems,” Automatica, vol. 39, no. 7, hlm. 1259–1265, Jul 2003, doi: 10.1016/S0005-1098(03)00081-5.
A. Witkowska dan R. S̀mierzchalski, “Nonlinear backstepping ship course controller,” Int. J. Autom. Comput., vol. 6, no. 3, hlm. 277–284, Agu 2009, doi: 10.1007/s11633-009-0277-2.
D. Bresch-Pietri, J. Chauvin, dan N. Petit, “Adaptive backstepping controller for uncertain systems with unknown input time-delay. Application to SI engines,” dalam 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, USA, Des 2010, hlm. 3680–3687. doi: 10.1109/CDC.2010.5717253.
V. Mañosa, F. Ikhouane, dan J. Rodellar, “Control of uncertain non-linear systems via adaptive backstepping,” J. Sound Vib., vol. 280, no. 3–5, hlm. 657–680, Feb 2005, doi: 10.1016/j.jsv.2003.12.033.
D. Karagiannis dan A. Astolfi, “Nonlinear adaptive control of systems in feedback form: An alternative to adaptive backstepping,” Syst. Control Lett., vol. 57, no. 9, hlm. 733–739, Sep 2008, doi: 10.1016/j.sysconle.2008.02.006.
G. G. Alcaraz dan C. Vargas-De-Leon, “Modeling control strategies for influenza A H1N1 epidemics: SIR models,” hlm. 7, 2012.
K. Mu’tamar, “Optimal Control Strategy for Alcoholism Model with Two Infected Compartments,” J. Math., vol. 14, no. 3, hlm. 58–67, 2018.
E. V. Grigorieva, P. B. Deignan, dan E. N. Khailov, “OPTIMAL CONTROL PROBLEM FOR A SEIR TYPE MODEL OF EBOLA EPIDEMICS,” Rev. Matemática Teoría Apl., vol. 24, no. 1, hlm. 79, Jan 2017, doi: 10.15517/rmta.v24i1.27771.
A. Ali Lashari, “Optimal Control of an SIR Epidemic Model with a Saturated Treatment,” Appl. Math. Inf. Sci., vol. 10, no. 1, hlm. 185–191, Jan 2016, doi: 10.18576/amis/100117.
S. Putra, K. Mu’tamar, dan Zulkarnain, “Estimation of Parameters in the SIR Epidemic Model Using Particle Swarm Optimization,” Am. J. Math. Comput. Model., vol. 4, no. 4, hlm. 83, 2019, doi: 10.11648/j.ajmcm.20190404.11.
K. Mu’tamar, D. Rahmalia, dan Sutimin, “Vaksinasi dan Treatment pada Predator-Prey dengan Dua Jenis Pemangsa yang Salah Satunya Terinfeksi,” EKSAKTA J. Sci. Data Anal., hlm. 128–142, Agu 2019, doi: 10.20885/eksakta.vol19.iss2.art4.
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