One year after the beginning of COVID-19 pandemic, vaccination seems to be the main instrument to block its spread, by raising the percentage of unsusceptible population. The best tool to overcome the pandemic is obviously the development of a sufficiently effective vaccine. Thus since the beginning of the pandemic considerable R&D effort is made. In the meantime, the lockdown still remains the most effective tool to contrast this virus. Assuming that the discovery time of such successful vaccine is not known a priori, we formalize a two-stage optimal control problem with stochastic switching time, where in the first period (before the vaccination entry) the control functions are the research effort and the lockdown, while in the second period both vaccination and lockdown tools act in synergy.

(with Stefan Wrzaczek, Maddalena Muttoni, Michael Freiberger)