FUZZY SLIDING MODE CONTROLLER FOR SEIR MODEL OF EPIDEMIC DISEASE

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Volume 5 (1), June 2022, Pages 143-164

Mohammad Azimnezhad¹, Mohammad Manthouri² and  Mohammad Teshnehlab³

¹ Science and Research Islamic Azad University, Tehran, Iran, This email address is being protected from spambots. You need JavaScript enabled to view it.

² Shahed University, Tehran, Iran, This email address is being protected from spambots. You need JavaScript enabled to view it.

³ K.N. Toosi university, Tehran, Iran, This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract

This paper proposes a vaccination approach based on robust control for the SEIR (susceptible plus exposed plus infectious plus recovered populations) model of epidemic diseases. First, a classic sliding mode controller is investigated based on the SEIR model. Next, fuzzy logic is utilized to better approximate the uncertainties in the SEIR system using the sliding mode controller. Therefore, the proposed controller is a fuzzy sliding mode controller, which, compared to the sliding mode controller, provides an appropriate estimation of systems' actual parameters and removes the chattering phenomenon from the control signal. The stability of the controlled system is guaranteed using the Lyapunov theory simulations in which the classical sliding mode and the proposed controllers are compared, Using data from previous articles. Simulation results show that the proposed controller eliminates the susceptible subpopulation, incubated disease, and infectious diseases, eradicating the disease. Comparison with other methods reveals the better efficiency of the proposed method.

Keywords:

Epidemic Disease, SEIR Model, Sliding Mode Controller, Fuzzy Controller, Vaccination, Uncertainty, Lyapunov.

DOI: https://doi.org/10.32010/26166127.2022.5.1.143.164

Reference 

Alonso-Quesada, S., De la Sen, M., Agarwal, R. P., & Ibeas, A. (2012). An observer-based vaccination control law for an SEIR epidemic model based on feedback linearization techniques for nonlinear systems. Advances in Difference Equations, 2012(1), 1-32.

Bai, Z., & Zhou, Y. (2012). Global dynamics of an SEIRS epidemic model with periodic vaccination and seasonal contact rate. Nonlinear Analysis: Real World Applications, 13(3), 1060-1068.

Bartoszewicz, A. (1995). A comment on ‘A time-varying sliding surface for fast and robust tracking control of second-order uncertain systems’. Automatica, 31(12), 1893-1895.

Cheng, Y., Pan, Q., & He, M. (2013). Disease control of delay SEIR model with nonlinear incidence rate and vertical transmission. Computational and Mathematical Methods in Medicine, 2013.

Di Giamberardino, P., & Iacoviello, D. (2017). Optimal control of SIR epidemic model with state dependent switching cost index. Biomedical signal processing and control, 31, 377-380.

Dong, N. P., Long, H. V., & Khastan, A. (2020). Optimal control of a fractional order model for granular SEIR epidemic with uncertainty. Communications in nonlinear science and numerical simulation, 88, 105312.

Edwards, C., & Spurgeon, S. (1998). Sliding mode control: theory and applications. Crc Press.

G. Drakopoulos, P. Mylonas and S. Sioutas (2019). A Case of Adaptive Nonlinear System Identification with Third Order Tensors in TensorFlow. In IEEE International Symposium on INnovations in Intelligent SysTems and Applications (INISTA), 1-6.

Hung, J. Y., Gao, W., & Hung, J. C. (1993). Variable structure control: A survey. IEEE transactions on industrial electronics, 40(1), 2-22.

Ibeas, A., De La Sen, M., & Alonso-Quesada, S. (2014). Robust sliding control of SEIR epidemic models. Mathematical Problems in Engineering, 2014.

Ibeas, A., de la Sen, M., & Alonso-Quesada, S. (2014, December). Adaptive control of SEIR discrete-time epidemic models. In AIP Conference Proceedings (Vol. 1637, No. 1, pp. 37-46). American Institute of Physics.

Ibeas, A., de la Sen, M., Alonso-Quesada, S., & Nistal, R. (2015, May). Partial stability-based vaccination control of SEIR epidemic models. In 2015 10th Asian Control Conference (ASCC) (pp. 1-6). IEEE.

Ibeas, A., Shafi, M., Ishfaq, M., & Ali, M. (2017). Vaccination controllers for SEIR epidemic models based on fractional order dynamics. Biomedical Signal Processing and Control, 38, 136-142.

Jang, J. S. (1992, March). Fuzzy controller design without domain experts. In [1992 Proceedings] IEEE International Conference on Fuzzy Systems (pp. 289-296). IEEE.

Jiao, H., & Shen, Q. (2020). Dynamics analysis and vaccination-based sliding mode control of a more generalized SEIR epidemic model. IEEE Access, 8, 174507-174515.

Lee, H., Kim, E., Kang, H. J., & Park, M. (1998). Design of a sliding mode controller with fuzzy sliding surfaces. IEE Proceedings-Control Theory and Applications, 145(5), 411-418.

Lee, H. J. (2022). Robust static output-feedback vaccination policy design for an uncertain SIR epidemic model with disturbances: Positive Takagi–Sugeno model approach. Biomedical Signal Processing and Control, 72, 103273. 

Manthouri, M., Aghajari, Z., & Safary, S. (2022). Computational Intelligence Method for Detection of White Blood Cells Using Hybrid of Convolutional Deep Learning and SIFT. Computational and Mathematical Methods in Medicine, 2022. 

Mattsson, P., Zachariah, D., & Stoica, P. (2018). Recursive nonlinear-system identification using latent variables. Automatica, 93, 343-351.

McCluskey, C. C. (2010). Complete global stability for an SIR epidemic model with delay—distributed or discrete. Nonlinear Analysis: Real World Applications, 11(1), 55-59.

Ohtake, H., Tanaka, K., & Wang, H. O. (2006). Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 36(1), 13-23.

Schoukens, J., & Ljung, L. (2019). Nonlinear system identification: A user-oriented road map. IEEE Control Systems Magazine, 39(6), 28-99.

Tokat, S., Eksin, I., & Güzelkaya, M. (2003). New approaches for on-line tuning of the linear sliding surface slope in sliding mode controllers. Turkish Journal of Electrical Engineering and Computer Sciences, 11(1), 45-60.

Wu, S. J., & Lin, C. T. (2000). Optimal fuzzy controller design: local concept approach. IEEE Transactions on Fuzzy Systems, 8(2), 171-185. 

Yang, F., Liu, H., Qi, H., & Liu, X. (2016, December). SEIR evolutionary simulation model of the infectious disease emergency. In 2016 International Conference on Industrial Informatics-Computing Technology, Intelligent Technology, Industrial Information Integration (ICIICII) (pp. 315-318). IEEE. 

Yi, N., Zhang, Q., Mao, K., Yang, D., & Li, Q. (2009). Analysis and control of an SEIR epidemic system with nonlinear transmission rate. Mathematical and computer modelling, 50(9-10), 1498-1513.