  This article is devoted to the analysis of a particle system model for
epidemics among a finite population with susceptible, infective and removed
individuals (SIR). The infection mechanism depends on the relative distance
between susceptibles and infected so that an infected individual is more likely
to infect nearby sites than those further away. For fixed time, we prove that
the density fields weakly converge to the solution of a PDE's system, as the
number of particles increases. We find an implicit expression for the final
survivor density of the limit equation and we analyze the asymptotics of the
microscopic system, by taking first the time and after the number of particles
to infinity, showing a critical behaviour for some values of the parameters
when the system is set in the mean field regime.
