Optimal Social Limitation Reduction under Vaccination and Booster Doses

In the paper an optimal control solution is provided for the containment of the number of infected individuals in COVID-19 pandemic under vaccination campaign. The possibility to dynamically change the cost of the controls according to the ongoing evolution within the design procedure allows to get great efforts in presence of very serious disease conditions, saving resources otherwise. The different contribution of vaccinated and unvaccinated individuals to the epidemic spread is investigated, optimising the controls which describe the individual contact restrictions separately for the two classes and showing that it would have been possible to reduce all the social limitations introduced by many governments for the vaccinated individuals since the beginning of the vaccination campaign.