<![CDATA[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 infections attributed 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 improves epidemic 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 vaccination and isolation strategies. The findings contribute to epidemiological research by offering valuable insights for policymakers in designing effective and resilient intervention strategies for epidemic management.]]>
