Optimal Control Design for Analysis of Effects of Booster Vaccination on COVID‐19 Model

ABSTRACT The COVID‐19 pandemic has highlighted the critical importance of effective vaccination strategies in controlling the spread of the virus. With the emergence of new variants and waning immunity, booster vaccinations have gained attention as a potential tool to enhance individual and population‐level protection. Using the principles of optimal control theory, this study aims to ascertain the impact of boosters on the patterns of COVID‐19 propagation. By formulating an appropriate mathematical model, we will design optimal control strategies to evaluate the impact of booster doses on key epidemiological parameters. Further, the conditions for disease‐free equilibrium, stability, and reproduction number for the addressed model are calculated. In particular, global stability is examined using the Lyapunov function. The corresponding crucial optimality requirements were also derived. To represent the memory effect in epidemics, the proposed model is driven using fractional differential equations. The existence and uniqueness and boundedness of fractional model are derived. We undertake numerical simulations by taking real‐time data in India for reflecting the impact of booster vaccination efficacy. Finally, graphical interpretation is shown and explored in depth. Our results reveal that to control the COVID‐19 pandemic, booster vaccination is effective and efficient in addition to vaccination and quarantine.