  We consider two approaches to study the spread of infectious diseases within
a spatially structured population distributed in social clusters. According
whether we consider only the population of infected individuals or both
populations of infected individuals and healthy ones, two models are given to
study an epidemic phenomenon. Our first approach is at a microscopic level, its
goal is to determine if an epidemic may occur for those models. The second one
is the derivation of hydrodynamics limits. By using the relative entropy method
we prove that the empirical measures of infected and healthy individuals
converge to a deterministic measure absolutely continuous with respect to the
Lebesgue measure, whose density is the solution of a system of
reaction-diffusion equations.
