This study introduces a detailed compartmental model developed to understand the complex dynamics of COVID-19 transmission, focusing on the Delta and Omicron variants in India. The model tracks disease progression through different population compartments, considering factors like vaccination, time-dependent transmission, economic burden and COVID-19 death rates, loss of vaccine-induced immunity, and the transition of asymptomatic cases to recovery. The model is validated against established epidemiological knowledge and real-world data, emphasizing dynamic parameterization and accurate representation of immunity dynamics. The basic reproduction number for both variants is calculated, and sensitivity analysis for various parameters is conducted. Time-dependent parameters are estimated using the discrete inverse method. The study also explores the economic burden, impact of different types of masks, vaccine efficacy, and vaccine-induced immunity through numerical analysis.Subject Classification; Primary 92B05, Secondary 62P10.