  We study by analytical methods and large scale simulations a dynamical model
for the spreading of epidemics in complex networks. In networks with
exponentially bounded connectivity we recover the usual epidemic behavior with
a threshold defining a critical point below which the infection prevalence is
null. On the contrary, on a wide range of scale-free networks we observe the
absence of an epidemic threshold and its associated critical behavior. This
implies that scale-free networks are prone to the spreading and the persistence
of infections whatever spreading rate the epidemic agents might possess. These
results can help understanding computer virus epidemics and other spreading
phenomena on communication and social networks.
