  The outbreak of a novel coronavirus causing severe acute respiratory syndrome
in December 2019 has escalated into a worldwide pandemic. In this work, we
propose a compartmental model to describe the dynamics of transmission of
infection and use it to obtain the optimal vaccination control. The model
accounts for the various stages of the vaccination and the optimisation is
focused on minimising the infections to protect the population and relieve the
healthcare system. As a case study we selected the Republic of Ireland. We use
data provided by Ireland's COVID-19 Data-Hub and simulate the evolution of the
pandemic with and without the vaccination in place for two different scenarios,
one representative of a national lockdown situation and the other indicating
looser restrictions in place. One of the main findings of our work is that the
optimal approach would involve a vaccination programme where the older
population is vaccinated in larger numbers earlier while simultaneously part of
the younger population also gets vaccinated to lower the risk of transmission
between groups. We compare our simulated results with that of the vaccination
policy taken by the Irish government to explore the advantages of our
optimisation method. Our comparison suggests that a similar reduction in cases
may have been possible even with a reduced set of vaccinations being available
for use.
