Control of rare events in reaction and population systems by deterministic processes and the speedup of disease extinction

We consider control of reaction and population systems by deterministically imposed transitions between the states with different numbers of particles or individuals. Even where the imposed transitions are significantly less frequent than spontaneous transitions, they can exponentially strongly modify the rates of rare events, including switching between metastable states or population extinction. We also study optimal control of rare events, and specifically, optimal control of disease extinction for a limited vaccine supply. A comparison is made with control of rare events by modulating the rates of elementary transitions rather than imposing transitions. It is found that, unexpectedly, for the same mean control parameters, controlling the transitions rates can be more efficient.