  This work describes a simple agent model for the spread of an epidemic
outburst, with special emphasis on mobility and geographical considerations,
which we characterize via statistical mechanics and numerical simulations. As
the mobility is decreased, a percolation phase transition is found separating a
free-propagation phase in which the outburst spreads without finding spatial
barriers and a localized phase in which the outburst dies off. Interestingly,
the number of infected agents is subject to maximal fluctuations at the
transition point, building upon the unpredictability of the evolution of an
epidemic outburst. Our model also lends itself to test with vaccination
schedules. Indeed, it has been suggested that if a vaccine is available but
scarce it is convenient to select carefully the vaccination program to maximize
the chances of halting the outburst. We discuss and evaluate several schemes,
with special interest on how the percolation transition point can be shifted,
allowing for higher mobility without epidemiological impact.
