Volume 14 - Journal of Control, Vol. 14, No. 5, Special Issue on COVID-19                   JoC 2021, 14 - Journal of Control, Vol. 14, No. 5, Special Issue on COVID-19: 59-70 | Back to browse issues page


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Amiri Mehra A H, Shafieirad M, Abbasi Z, Zamani I, Aarabi Z. Fuzzy Sliding Mode Controller Design and Analysis of an SQEIAR Epidemic Model for COVID-19 to Determine the Quarantine Rate. JoC 2021; 14 (S1) :59-70
URL: http://joc.kntu.ac.ir/article-1-820-en.html
1- University of Kashan
2- Shahed University
3- Kashan University of Medical Sciences
Abstract:   (4404 Views)
According to the global prevalence of coronavirus (COVID-19) pandemic, mathematical models can predict and control the dynamic behavior of the pandemic. Therefore, in this study, a comprehensive model is considered to examine the trend of COVID-19 based on Susceptible, Exposed, Infected (Symptomatic and Asymptomatic), and Recovered individuals. In the absence of a curative treatment or vaccination campaign, the group of "quarantined people" is added to the model. Then, a positivity analysis of states is examined, and the threshold criterion (R_0) is determined. The equilibrium points (disease-free and endemic) are also calculated, and their stability is investigated using the Jacobin matrix. The quarantine rate is regulated as the only control input using the fuzzy sliding mode controller. The efficiency of the controller is also investigated in the presence of uncertainty in model parameters. Also, the impact of the infected community on other communities, considering the controller, will be examined. Finally, the performance and efficiency of the proposed controller are evaluated.
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Type of Article: Research paper | Subject: COVID-19
Received: 2020/12/30 | Accepted: 2021/03/8 | Published: 2021/02/28

References
1. مرکز تحقیقات ویروس شناسی (www.vrc.sbmu.ac.ir)
2. World Health Organization (WHO) (www.who.int/ar/emergencies/diseases/novel-coronavirus-2019-farsi)
3. Centers for Disease Control and Prevention (CDC) (https://www.cdc.gov/coronavirus/2019-ncov/long-term-effects.html)
4. "Iran Reports Its First 2 Cases of the New Coronavirus", New York Times. Archived from the original on 19 February 2020. Retrieved 19 February 2020.
5. Cooper, I., Mondal, A. and Antonopoulos, C.G., "A SIR Model Assumption for The Spread of COVID-19 in Different Communities", Chaos, Solitons & Fractals, 139, p.110057, 2020. [DOI:10.1016/j.chaos.2020.110057]
6. Comunian, A., Gaburro, R. and Giudici, M., "Inversion of an SIR-Based Model: A Critical Analysis About the Application To COVID-19 Epidemic", Physica D: Nonlinear Phenomena, 413, p.132674, 2020. [DOI:10.1016/j.physd.2020.132674]
7. Abbasi, Z., Zamani, I., Amiri Mehra, A.H., and Shafieirad, M., "Optimal Control of SEIR Epidemic Model Considering Nonlinear Transmission Rate and Time Delay", In 2021 7th International Conference on Control, Instrumentation and Automation (ICCIA). IEEE, 2021. [DOI:10.1109/ICCIA52082.2021.9403558]
8. Kada, D., Kouidere, A., Balatif, O., Rachik, M. and Labriji, E.H., "Mathematical Modeling of The Spread of COVID-19 Among Different Age Groups in Morocco: Optimal Control Approach for Intervention Strategies", Chaos, Solitons & Fractals, p.110437, 2020. [DOI:10.1016/j.chaos.2020.110437]
9. Samui, P., Mondal, J. and Khajanchi, S., "A Mathematical Model for COVID-19 Transmission Dynamics with A Case Study of India", Chaos, Solitons & Fractals, 140, p.11017, 2020. [DOI:10.1016/j.chaos.2020.110173]
10. Ndairou, F., Area, I., Nieto, J.J. and Torres, D.F., "Mathematical Modeling of COVID-19 Transmission Dynamics with a Case Study of Wuhan". Chaos, Solitons & Fractals, p.109846, 2020. [DOI:10.1016/j.chaos.2020.109846]
11. Amiri Mehra, A.H., Zamani, I., Abbasi, Z. and Ibeas, A., "Observer-Based Adaptive PI Sliding Mode Control of Developed Uncertain SEIAR Influenza Epidemic Model Considering Dynamic Population", Journal of Theoretical Biology, 482, p.109984, 2019. [DOI:10.1016/j.jtbi.2019.08.015]
12. Abbasi, Z., Zamani, I., Amiri Mehra, A.H., Shafieirad, M. and Ibeas, A., "Optimal Control Design of Impulsive SQEIAR Epidemic Models with Application to COVID-19", Chaos, Solitons & Fractals, 139, p.110054, 2020. [DOI:10.1016/j.chaos.2020.110054]
13. Amiri Mehra, A.H., Shafieirad, M, Abbasi, Z. and Zamani, I., "Parameter Estimation and Prediction of COVID-19 Epidemic Turning Point and Ending Time of a Case Study on SIR/SQAIR Epidemic Models", Computational and Mathematical Methods in Medicine, 2020, 2020. [DOI:10.1155/2020/1465923]
14. Rohith, G. and Devika, K.B., "Dynamics and Control of COVID-19 Pandemic with Nonlinear Incidence Rates", Nonlinear Dynamics, 101(3), pp.2013-2026, 2020. [DOI:10.1007/s11071-020-05774-5]
15. Xiao, Y., Xu, X. and Tang, S., "Sliding Mode Control of Outbreaks of Emerging Infectious Diseases", Bulletin of Mathematical Biology, 74(10), pp.2403-2422, 2012. [DOI:10.1007/s11538-012-9758-5]
16. Ibeas, A., de la Sen, M. and Alonso-Quesada, S., "Sliding Mode Robust Control of SEIR Epidemic Models", In 2013 21st Iranian Conference on Electrical Engineering (ICEE). pp. 1-6. IEEE, 2013. [DOI:10.1109/IranianCEE.2013.6599820]
17. Ozer, H.O., Hacioglu, Y., Yagiz, N., "Controlling the Building Model Using High Order Sliding Mode Control Optimized by Multi Objective Genetic Algorithm", Periodicals of Engineering and Natural Sciences, 5(3), 2017. [DOI:10.21533/pen.v5i3.91]
18. Yakut, O. and Alli, H., "Neural Based Sliding-Mode Control with Moving Sliding Surface for the Seismic Isolation of Structures", Journal of Vibration and Control, 17(14), pp.2103-2116, 2011. [DOI:10.1177/1077546310395964]
19. Li, Z., Deng, Z. and Gu, Z., "New Sliding Mode Control of Building Structure Using RBF Neural Networks", In 2010 Chinese Control and Decision Conference. pp. 2820-2825. IEEE, 2010.
20. Adhikari, R. and Yamaguchi, H., "Sliding Mode Control of Buildings with ATMD", Earthquake Engineering & Structural Dynamics, 26(4), pp.409-422, 1997. https://doi.org/10.1002/(SICI)1096-9845(199704)26:4<409::AID-EQE647>3.0.CO;2-0 [DOI:10.1002/(SICI)1096-9845(199704)26:43.0.CO;2-0]
21. Baghaei, K., Ghaffarzadeh, H., Hadigheh, A. and Dias-da-Costa, D., "Chattering-Free Sliding Mode Control with A Fuzzy Model for Structural Applications", 2019.
22. Samantaray, J. and Chakrabarty, S., "A Fuzzy Sliding Mode Control Design for Quadcopter", In International Conference on Unmanned Aerial System in Geomatics. pp. 191-200, 2019, April. [DOI:10.1007/978-3-030-37393-1_17]
23. Ardakani, F.F., Vatankhah, R. and Sharifi, M., "Fuzzy Sliding‐Mode Control of a Human Arm in The Sagittal Plane with Optimal Trajectory", ETRI Journal, 40(5), pp.653-663, 2018. [DOI:10.4218/etrij.2018-0067]
24. Zamani, I., Amiri Mehra, A.H., Abbasi, Z. and Shafiee, M., "Robust Stability for Affine TS Fuzzy Impulsive Control Systems Subject to Parametric Uncertainties", In 2019 27th Iranian Conference on Electrical Engineering (ICEE). pp. 1102-1107. IEEE, 2019. [DOI:10.1109/IranianCEE.2019.8786425]
25. Lin, B., Su, X. and Li, X., "Fuzzy Sliding Mode Control for Active Suspension System with Proportional Differential Sliding Mode Observer", Asian Journal of Control, 21(1), pp.264-276, 2019. [DOI:10.1002/asjc.1882]
26. Palm, R., 1992, "Sliding Mode Fuzzy Control", In [1992 Proceedings] IEEE International Conference on Fuzzy Systems. pp. 519-526. IEEE, 1992.
27. Ha, Q.P., Nguyen, Q.H., Rye, D.C. and Durrant-Whyte, H.F., "Fuzzy Sliding-Mode Controllers with Applications", IEEE Transactions on Industrial Electronics, 48(1), pp.38-46, 2001. [DOI:10.1109/41.904548]
28. Zamani, I. and Zarif, M.H., "Nonlinear Controller for Fuzzy Model of Double Inverted Pendulums". World Academy of Science, Engineering and Technology, 1(10), pp.1596-1602, 2007.
29. Zamani, I. and Shafie, M., "Fuzzy Affine Impulsive Controller". In 2009 IEEE International Conference on Fuzzy Systems. pp. 361-366, 2009. [DOI:10.1109/FUZZY.2009.5277121]
30. Zamani, I. and Zarif, M.H., "An Approach for Stability Analysis of TS Fuzzy Systems Via Piecewise Quadratic Stability", International Journal of Innovative Computing, Information and Control, 6(9), pp.4041-4054, 2010.
31. Zamani, I. and Zarif, M.H., "On the Continuous-Time Takagi-Sugeno Fuzzy Systems Stability Analysis", Applied Soft Computing, 11(2), pp.2102-2116, 2011. [DOI:10.1016/j.asoc.2010.07.009]
32. Zamani, I. and Sadati, N., "Fuzzy Large-Scale Systems Stabilization with Nonlinear State Feedback Controller", 2009 IEEE International Conference on Systems, Man and Cybernetics, 5156-5161. [DOI:10.1109/ICSMC.2009.5346005]
33. Shafieirad, M., Shafiee, M. and Abedi, M., "Recursive Identification of Continuous Two-Dimensional Systems in The Presence of Additive Colored Noise", IETE Journal of Research, 60(1), pp.74-84, 2014. [DOI:10.1080/03772063.2014.890830]
34. Shafieirad, M., Shafiee, M. and Abedi, M., "Estimation of Space and Time Shifts in Continuous 2-D Systems Using Instrumental Variable", Canadian Journal of Electrical and Computer Engineering, 37(1), pp.42-47, 2014. [DOI:10.1109/CJECE.2014.2311927]
35. Shafieirad, M., Shafiee, M. and Abedi, M., "Identification of Linear Partial Difference Equations with Constant Coefficients", Journal of Basic and Applied Scientific Research, 3(1), pp.655-660, 2013.
36. Van Den Driessche, P., Watmough, J., "Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission", Mathematical Biosciences, 180, (1), pp. 29-48, 2002. [DOI:10.1016/S0025-5564(02)00108-6]
37. Hernandez-Vargas, A. E. and Meyer-Hermann, M., "Innate Immune System Dynamics to Influenza Virus", IFAC Proceedings Volumes, 45, (18), pp. 260-265. 2012. [DOI:10.3182/20120829-3-HU-2029.00029]
38. Slotine, J. J. E., Li, W., "Applied Nonlinear Control", Prentice Hall Englewood Cliffs, NJ, 199, 1991.

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