Recent work on information survival in sensor and human P2P networks try to study the datum preservation or the virus spreading in a network under the dynamical system approach. Some interesting solutions propose to use non-linear dynamical systems and fixed point stability theorems, providing closed form formulas that depend on the largest eigenvalue of the dynamic system matrix. Given that in the Web there can be messages from one place to another, and that these messages can be, with some probability, new unclassified virus warning messages as well as worms or other kind of viruses, the sites can be infected very fast. The question to answer is how and when a network infection can become global and how it can be controlled or at least how to stabilize the spreading in such a way that it becomes confined below a fixed portion of the network. In this paper, we try to be a step ahead in this direction and apply classic results of the dynamical systems theory to model the behavior of a network where warning messages and viruses spread.