Epidemiology in complex networks - modified heterogeneous mean-field model

The study of complex networks presented a huge development in last decades.In this dissertation we want to analyze the epidemic spread in scale-free networks through the Susceptible -Infected -Susceptible (SIS) model.We review the fundamental concepts to describe complex networks and the classical epidemiological models.We implement an algorithm that produces a scale-free network and explore the Quenched Mean-Field (QMF) dynamics in a scale-free network.Moreover, we simulate a change on the topology of the network according to the states of the nodes, and it generates a positive epidemic threshold.We show analytically that the fraction of infected vertices follows a power-law distribution in the vicinity of this critical point.