  The current work deals with an epidemic model on the complete graph K_n on n
vertices in a non-homogeneous setting, where the vertices may have distinct
types. Different types differ in the probability of getting infected, and/or in
the capacity of infecting other vertices. This generalizes previous models
where vertices are all of the same type and have equal probabilities of being
infected. We prove laws of large numbers and central limit theorems for the the
total duration of the process and for the number of infected vertices,
respectively, when n goes to infinity. By coupling the epidemic model with a
Poisson process, we also obtain continuous-time counterparts of the
above-mentioned limit results. Moreover, we also prove that when all
individuals have the same spread capacity, then a population with inhomogeneous
susceptibility is less affected by the epidemics than a homogeneous population.
