This study introduces a novel 2 model, where "2" denotes two infectious classes representing asymptomatic and symptomatic infections, aiming to investigate and analyze the cost-effective optimal control measures for managing COVID-19. The model incorporates a novel concept of infectious density-induced additional screening (IDIAS) and accounts for treatment saturation. Furthermore, the model considers the possibility of reinfection and the loss of immunity in individuals who have previously recovered. To validate and calibrate the proposed model, real data from November-December 2022 in Hong Kong are utilized. The estimated parameters obtained from this calibration process are valuable for prediction purposes and facilitate further numerical simulations. An analysis of the model reveals that delays in screening, treatment, and quarantine contribute to an increase in the basic reproduction number , indicating a tendency towards endemicity. In particular, from the elasticity of , we deduce that normalized sensitivity indices of baseline screening rate (), quarantine rates (, ), and treatment rate () are negative, which shows that delaying any of these may cause huge surge in , ultimately increases the disease burden. Further, by the contour plots, we note the two-parameter behavior of the infectives (both symptomatic and asymptomatic). Expanding upon the model analysis, an optimal control problem (OCP) is formulated, incorporating three control measures: precautionary interventions, boosted IDIAS, and boosted treatment. The Pontryagin's maximum principle and the forward-backward sweep method are employed to solve the OCP. The numerical simulations highlight that enhanced screening and treatment, coupled with preventive interventions, can effectively contribute to sustainable disease control. However, the cost-effectiveness analysis (CEA) conducted in this study suggests that boosting IDIAS alone is the most economically efficient and cost-effective approach compared to other strategies. The CEA results provide valuable insights into identifying specific strategies based on their cost-efficacy ranking, which can be implemented to maximize impact while minimizing costs. Overall, this research offers significant insights for policymakers and healthcare professionals, providing a framework to optimize control efforts for COVID-19 or similar epidemics in the future.
