  We study the persistent recoverable prevalence and the extinction of computer
viruses via e-mails on a growing scale-free network with new users, which
structure is estimated form real data. The typical phenomenon is simulated in a
realistic model with the probabilistic execution and detection of viruses.
Moreover, the conditions of extinction by random and targeted immunizations for
hubs are derived through bifurcation analysis for simpler models by using a
mean-field approximation without the connectivity correlations. We can
qualitatively understand the mechanisms of the spread in linearly growing
scale-free networks.
