A Vaccination and Isolation Strategy Based on an Adaptive Sliding Mode Control Design for the COVID-19 Virus (Omicron Variant) in Jakarta, Indonesia

Dewi Suhika; Roberd Saragih; Dewi Handayani; Mochamad Apri

doi:10.5614/cbms.2025.8.1.2

Authors

Dewi Suhika Departement of Mathematics, Institut Teknologi Bandung, Bandung 40132, Indonesia & Mathematics Study Program, Institut Teknologi Sumatera, Lampung 35365, Indonesia
Roberd Saragih Departement of Mathematics, Institut Teknologi Bandung, Bandung 40132, Indonesia
Dewi Handayani Departement of Mathematics, Institut Teknologi Bandung, Bandung 40132, Indonesia
Mochamad Apri Departement of Mathematics, Institut Teknologi Bandung, Bandung 40132, Indonesia

DOI:

https://doi.org/10.5614/cbms.2025.8.1.2

Keywords:

COVID-19, Omicron, control strategy, sliding mode control, adaptive

Abstract

The Omicron variant, identified as B.1.1.529, has been recognized as a variant of concern (VOC) by the World Health Organization (WHO), necessitating continuous monitoring and a proactive response. This study develops a mathematical model to analyze the spread of COVID-19 mutations, considering a population that, despite vaccination, remains susceptible to infection. The model also accounts for key epidemiological factors, including the incubation period, quarantine measures, and various intervention strategies. This study focuses on the epidemiological conditions in Jakarta Province, where the highest number of Omicron cases in Indonesia has been recorded. Real-world epidemiological data related to Omicron in Jakarta were collected between February 6, 2022, and May 6, 2022. Model parameters were estimated using genetic algorithm optimization. A significant challenge in epidemic modeling is the uncertainty of parameters, which can substantially affect the effectiveness of control measures. To address this challenge, an adaptive sliding mode control approach is introduced, allowing dynamic adjustments to parameter variations without requiring precise parameter estimation. This approach maintains system stability by enforcing a predefined sliding surface, making it inherently robust against uncertainties. The main goal of this approach is to gradually minimize infectionsattributed to the initial COVID-19 strain and the Omicron variant, while simultaneously decreasing the count of susceptible individuals by ensuring the system follows a specified reference trajectory. Additionally, an adaptive mechanism is implemented to account for unknown variations in the system using the Lyapunov stability theorem. Numerical simulations illustrate that adaptive sliding mode control significantly improvesepidemic management, reducing infections by 92.8% for the original strain and by 96.87% for the Omicron variant when compared to an uncontrolled scenario. Furthermore, the basic reproduction number (R0) is lowered by 85.92%, confirming the efficiency of adaptive sliding mode control in mitigating the outbreak. Moreover, this study incorporates a cost-effectiveness analysis to assess the viability of various vaccinationand isolation strategies. The findings contribute to epidemiological research by offering valuable insights for policymakers in designing effective and resilient intervention strategies for epidemic management.

References

Khan, M.A. and Atangana A., Mathematical modeling and analysis of COVID-19: A study of new variant Omicron, Physica A:Statistical Me chanics and its Applications, 599(2022), p. 127452, 2022.

WHO, WHO Classification of Omicron (B.1.1.529): SARS-CoV-2 Variant of Concern, WHO. https://www.who.int/news/item/26-11-2021-classification-of-omicron-(b.1.1.529)-sars-cov-2-variant-of-concern, Accessed on February 15, 2023.

Manjunath, R., Gaonkar, S.L., Saleh, E.A.M. and Husain, K., A comprehensive review on Covid-19 Omicron (B.1.1. 529) variant, Saudi Journal of Biological Sciences, 29(9), p. 103372, 2022.

Liang, S., Jiang, T., Jiao, Z. and Zhou, Z., A model simulation on the SARS-CoV-2 Omicron variant containment in Beijing, China, Intelligent Medicine, 3(1), pp. 10-15, 2023.

Khan, M.A. and Atangana, A., Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative, Alexandria Engineering Journal, 59(4), pp. 2379-2389, 2020.

Li, A., Wang, Y., Cong, P. and Zou, X., Re-examination of the impact of some non-pharmaceutical interventions and media coverage on the COVID-19 outbreak in Wuhan, Infectious Disease Modelling, 6, pp. 975-987, 2021.

Liu, K. and Lou, Y., Optimizing COVID-19 vaccination programs during vaccine shortages, Infectious Disease Modelling, 7(1), pp. 286-298, 2022.

Lambora, A., Gupta, K. and Chopra, K., Genetic algorithm-A literature review, 2019 International Conference on Machine Learning, Big Data, Cloud and Parallel Computing (COMITCon), pp. 380-384, 2019.

Windarto, Indratno, S.W., Nuraini, N. and Soewono, E., A comparison of binary and continuous genetic algorithm in parameter estimation of a logistic growth model, AIP Conference Proceedings, 1587(1), pp. 139-142, 2014.

Yarsky, P., Using a genetic algorithm to fit parameters of a COVID-19 SEIR model for US states, Mathematics and Computers in Simulation, 185, pp. 687-695, 2021.

Qiu, Z., Sun, Y., He, X., Wei, J., Zhou, R., Bai, J. and Du, S., Application of genetic algorithm combined with improved SEIR model in predicting the epidemic trend of COVID-19, China, Scientific Reports, 12(1), p. 8910, 2022.

Bera, M.K., Kumar, P. and Biswas, R.K., Robust control of HIV infection by antiretroviral therapy: a super-twisting sliding mode control approach, IET Systems Biology, 13(3), pp. 120-128, 2019.

Tran, D.T., Ba, D.X. and Ahn, K.K., Adaptive backstepping sliding mode control for equilibrium position tracking of an electrohydraulic elastic manipulator, IEEE Transactions on Industrial Electronics, 67(5), pp. 3860-3869, 2019.

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

Assegaf, F., Saragih, R. and Handayani, D., Adaptive sliding mode control for cholera epidemic model, IFAC-PapersOnLine, 53(2), pp. 16092-16099, 2020.

Santos, D.M.L., Rodrigues, V.H.P. and Oliveira, T.R., Epidemiological control of COVID-19 through the theory of variable structure and sliding mode systems, Journal of Control, Automation and Electrical Systems, 33(1), pp. 63-77, 2022.

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

Brauer, F., Castillo-Chavez, C. and Feng, Z., Mathematical models in epidemiology, New York: Springer, 2019.

Edwards, K.M., Maternal antibodies and infant immune responses to vaccines, Vaccine, 33(47), pp. 6469-6472, 2015.

Suhika, D., Saragih, R., Handayani, D. and Apri, M., Optimal control strategies based on extended Kalman filter in mathematical models of COVID-19, International Journal of Electrical and Computer Engineering, 14(6), pp. 6300-6312, 2024.

Kim, Y.R., Choi, Y.J. and Min, Y., A model of COVID-19 pandemic with vaccines and mutant viruses, Plos One, 17(10), p. e0275851, 2022.

Onishchenko, G.G., Sizikova, T.E., Lebedev, V.N. and Borisevich, S.V., The Omicron variant of the SARS-CoV-2 virus as the dominant agent of a new risk of disease amid the COVID-19 pandemic, Herald of the Russian Academy of Sciences, 92(4), pp. 381-391, 2022.

Mwalili, S., Kimathi, M., Ojiambo, V., Gathungu, D. and Mbogo, R., SEIR model for COVID-19 dynamics incorporating the environment and social distancing, BMC Research Notes, 13(1), p. 352, 2020.

Madubueze, C.E., Dachollom, S. and Onwubuya, I.O., Controlling the spread of COVID-19: optimal control analysis, Computational and Mathematical methods in Medicine, 2020(1), p. 6862516, 2020.

Zelenkov, Y. and Reshettsov, I., Analysis of the COVID-19 pandemic using a compartmental model with time-varying parameters fitted by a genetic algorithm, Expert Systems with Applications, 224, p. 120034, 2023.

DKI Jakarta, Provincial Health Office, DKI Jakarta Covid-19 Monitoring Data. https://corona.jakarta.go.id/id, Accessed on March 30, 2022.

BPS, Life expectancy by province and sex (Year) 2018-2020. https://www.bps.go.id/indicator/40/501/1/angka-harapan-hidup-ahh-menurut-provinsi-dan-jenis-kelamin.html, Accessed on July 31, 2021.

Suhika, D., Roberd, S. and Handayani, D., Application of nonlinear robust sliding mode control on mathematical model for spreading of Covid-19, In AIP Conference Proceedings, 3095(1), 2024.

Tregoning, J.S., Flight, K.E., Higham, S.L., Wang, Z. and Pierce, B.F., Progress of the COVID-19 vaccine effort: viruses, vaccines and variants versus efficacy, effectiveness and escape, Nature Reviews Immunology, 21(10), pp. 626-636, 2021.

Chi, W.Y., Li, Y.D., Huang, H.C., Chan, T.E.H., Chow, S.Y., Su, J.H., Ferrall, L., Hung, C.F. and Wu, T.C., COVID-19 vaccine update: vaccine effectiveness, SARS-CoV-2 variants, boosters, adverse effects, and immune correlates of protection, Journal of Biomedical Science, 29(1), pp. 1-27, 2022.

Khalil, H., Nonlinear Systems, 3rd Edition, New Jersey: Prentice Hall, 2002.

Asamoah, J.K.K., Okyere, E., Abidemi, A., Moore, S.E., Sun, G.Q., Jin, Z., Acheampong, E. and Gordon, J.F., Optimal control and comprehensive cost-effectiveness analysis for COVID-19, Results in Physics, 33, p. 105177, 2022.