The paper by Romualdo Pastor-Satorras and Alessandro Vespignani explores the dynamics of epidemic spreading on scale-free networks, which are characterized by a power-law distribution of node degrees. They analyze real data from computer virus infections to understand the average lifetime and prevalence of viral strains on the Internet. The authors define a dynamical model for infection spreading on scale-free networks and find that there is no epidemic threshold, meaning that infections can persist regardless of the spreading rate. This finding contradicts the standard model in mathematical epidemiology, where an epidemic threshold is typically absent in networks with bounded connectivity. The absence of a threshold implies that infections can spread and persist in scale-free networks, even if the spreading rate is below the threshold. The study also reveals that the characteristic lifetime of viral strains depends on the spreading rate and the network size. The analytical and numerical results support the idea that the topology of scale-free networks plays a crucial role in the dynamics of epidemic spreading, with implications for understanding computer virus behavior and potentially other spreading phenomena on communication and social networks.The paper by Romualdo Pastor-Satorras and Alessandro Vespignani explores the dynamics of epidemic spreading on scale-free networks, which are characterized by a power-law distribution of node degrees. They analyze real data from computer virus infections to understand the average lifetime and prevalence of viral strains on the Internet. The authors define a dynamical model for infection spreading on scale-free networks and find that there is no epidemic threshold, meaning that infections can persist regardless of the spreading rate. This finding contradicts the standard model in mathematical epidemiology, where an epidemic threshold is typically absent in networks with bounded connectivity. The absence of a threshold implies that infections can spread and persist in scale-free networks, even if the spreading rate is below the threshold. The study also reveals that the characteristic lifetime of viral strains depends on the spreading rate and the network size. The analytical and numerical results support the idea that the topology of scale-free networks plays a crucial role in the dynamics of epidemic spreading, with implications for understanding computer virus behavior and potentially other spreading phenomena on communication and social networks.