This paper analyzes the spread of computer viruses on scale-free networks, which are networks where the probability of a node having k connections follows a power-law distribution $ P(k) \sim k^{-\gamma} $, with $ \gamma $ between 2 and 3. The authors find that scale-free networks lack an epidemic threshold, meaning that infections can persist regardless of the spreading rate. This is a significant departure from traditional epidemic models, which assume a threshold for an epidemic to occur. The study uses real data from computer virus infections to show that the average lifetime and prevalence of viral strains on the Internet are consistent with the properties of scale-free networks. The authors also perform simulations of the susceptible-infected-susceptible (SIS) model on scale-free networks and find that the prevalence of infections decays exponentially with decreasing spreading rate. The results suggest that the persistence of infections is more related to the implementation of prophylactic safety measures than to the availability of specific anti-virus software. The study also shows that the spreading of infections on scale-free networks follows an algebraic form, which is consistent with real data. The authors conclude that the topology of scale-free networks plays a crucial role in epidemic modeling and that the absence of an epidemic threshold in these networks has important implications for understanding the spread of infections in complex systems. The results also have implications for other fields, such as epidemiology and pollution control. The study is supported by grants from the European Network Contract and the CICYT grant.This paper analyzes the spread of computer viruses on scale-free networks, which are networks where the probability of a node having k connections follows a power-law distribution $ P(k) \sim k^{-\gamma} $, with $ \gamma $ between 2 and 3. The authors find that scale-free networks lack an epidemic threshold, meaning that infections can persist regardless of the spreading rate. This is a significant departure from traditional epidemic models, which assume a threshold for an epidemic to occur. The study uses real data from computer virus infections to show that the average lifetime and prevalence of viral strains on the Internet are consistent with the properties of scale-free networks. The authors also perform simulations of the susceptible-infected-susceptible (SIS) model on scale-free networks and find that the prevalence of infections decays exponentially with decreasing spreading rate. The results suggest that the persistence of infections is more related to the implementation of prophylactic safety measures than to the availability of specific anti-virus software. The study also shows that the spreading of infections on scale-free networks follows an algebraic form, which is consistent with real data. The authors conclude that the topology of scale-free networks plays a crucial role in epidemic modeling and that the absence of an epidemic threshold in these networks has important implications for understanding the spread of infections in complex systems. The results also have implications for other fields, such as epidemiology and pollution control. The study is supported by grants from the European Network Contract and the CICYT grant.