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This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models, considering the delay in converting susceptible individuals into infected ones. The significant delays eventually resulted in the pandemic's containment. To ensure the safety of the host population, this concept integrates quarantine and the COVID-19 vaccine. We investigate the stability of the proposed models. The fundamental reproduction number influences stability conditions. According to our findings, asymptomatic cases considerably impact the prevalence of Omicron infection in the community. The real data of the Omicron variant from Chennai, Tamil Nadu, India, is used to validate the outputs. [ABSTRACT FROM AUTHOR]

In this study, we formulate an eight-compartment mathematical model with vaccination as one of the compartments to analyze the dynamics of COVID-19 transmission. We examine the model's qualitative properties, such as positivity and boundedness of solutions, and stability analysis of the illness-free equilibrium with respect to the basic reproduction number. We estimate ten significant parameters and also compute the magnitude of the basic reproduction number for India by fitting the proposed model to daily confirmed and cumulative confirmed COVID-19 cases in India. Sensitivity analysis with respect to basic reproduction number is conducted, and the main parameters that impact the widespread of disease are determined. We further extend this model to an optimal control problem by including four non-pharmaceutical and pharmaceutical intervention measures as control functions. Our numerical results show that the four control strategy has greater impact than the three control strategies, two control strategies, and single control strategies on reducing the dynamics of COVID-19 transmission. [ABSTRACT FROM AUTHOR]