  In the context of SARS-CoV-2 pandemic, mathematical modelling has played a
fundamental role for making forecasts, simulating scenarios and evaluating the
impact of preventive political, social and pharmaceutical measures. Optimal
control theory can be a useful tool based on solid mathematical bases to plan
the vaccination campaign in the direction of eradicating the pandemic as fast
as possible. The aim of this work is to explore the optimal prioritisation
order for planning vaccination campaigns able to achieve specific goals, as the
reduction of the amount of infected, deceased and hospitalized in a fixed time
frame, among age classes. For this purpose, we introduce an age stratified
SIR-like epidemic compartmental model settled in an abstract framework for
modelling two-doses vaccination campaigns and conceived with the description of
COVID19 disease. Overall, we formalize an optimal control framework adopting
the model as state problem by acting on the administrations of vaccine-doses.
An extensive campaign of numerical tests, featured in the Italian scenario and
calibrated on available data from Dipartimento di Protezione Civile Italiana,
shows that the presented framework can be a valuable tool to support the
planning of vaccination campaigns minimizing specific goals.
