Probabilistic framework for epidemic spreading in complex networks

The discovery of the important role played by the complex connectivity structure between individuals has lead to an increasing interest in the analysis of epidemic spreading in complex networks. Here we propose a discrete-time formulation of the problem of contact-based epidemic spreading, within the context of susceptible-infected-susceptible epidemic models. The proposed equations establish the relations between the probabilities of infection of individual nodes. They can be easily solved by iteration, showing an almost perfect agreement with Monte Carlo experiments throughout the whole phase diagram. This framework also allows the determination of the epidemic threshold and, unlike heterogeneous mean-field approaches, it is valid for any finite-size and weighted network.