The paper by Pastor-Satorras and Vespignani investigates the dynamics of epidemic spreading on complex networks, focusing on both exponentially bounded and scale-free (SF) networks. They use analytical methods and large-scale simulations to study the susceptible-infected-susceptible (SIS) model. For exponentially bounded networks, such as the Watts-Strogatz model, they find a typical epidemic threshold where the infection prevalence is null below this threshold. However, for SF networks, they observe the absence of an epidemic threshold, meaning that infections can spread and persist regardless of the spreading rate. This behavior is attributed to the high connectivity of nodes in SF networks, which allows for the rapid spread of infections. The authors also discuss the implications of these findings for understanding computer virus epidemics and other spreading phenomena on communication and social networks. They conclude that the lack of an epidemic threshold in SF networks challenges traditional epidemic modeling and has significant implications for various biological and social systems.The paper by Pastor-Satorras and Vespignani investigates the dynamics of epidemic spreading on complex networks, focusing on both exponentially bounded and scale-free (SF) networks. They use analytical methods and large-scale simulations to study the susceptible-infected-susceptible (SIS) model. For exponentially bounded networks, such as the Watts-Strogatz model, they find a typical epidemic threshold where the infection prevalence is null below this threshold. However, for SF networks, they observe the absence of an epidemic threshold, meaning that infections can spread and persist regardless of the spreading rate. This behavior is attributed to the high connectivity of nodes in SF networks, which allows for the rapid spread of infections. The authors also discuss the implications of these findings for understanding computer virus epidemics and other spreading phenomena on communication and social networks. They conclude that the lack of an epidemic threshold in SF networks challenges traditional epidemic modeling and has significant implications for various biological and social systems.