  Covid-19 has caused hundred of thousands of deaths and an economic damage
amounting to trillions of dollars, creating a desire for the rapid development
of vaccine. Once available, vaccine is gradually produced, evoking the question
on how to distribute it best. While official vaccination guidelines largely
focus on the question to whom vaccines should be provided first (e.g. to risk
groups), here we propose a strategy for their distribution in time and space,
which sequentially prioritizes regions with a high local infection growth rate.
To demonstrate this strategy, we develop a simple statistical model describing
the time-evolution of infection patterns and their response to vaccination, for
infectious diseases like Covid-19. For inhomogeneous infection patterns,
locally well-mixed populations and basic reproduction numbers $R_0\sim 1.5-4$
the proposed strategy at least halves the number of deaths in our simulations
compared to the standard practice of distributing vaccines proportionally to
the population density. For $R_0\sim 1$ we still find a significant increase of
the survival rate. The proposed vaccine distribution strategy can be further
tested in detailed modelling works and could excite discussions on the
importance of the spatiotemporal distribution of vaccines for official
guidelines.
