Thresholds for epidemic outbreaks in finite scale-free networks

We numerically investigate the existence of a threshold for epidemic outbreaks in a class of scale-free networks characterized by a parametrical dependence of the scaling exponent, influencing the convergence of fluctuations in the degree distribution. In finite-size networks, finite thresholds for the spreading of an epidemic are always found. However, both the thresholds and the behavior of the epidemic prevalence are quite different with respect to the type of network considered and the system size. We also discuss agreements and differences with some analytical claims previously reported.