The paper offers a mathematical interpretation of a complex phenomenon such as the development of the Internet, by means of a simple epidemic diffusion model with a time-varying population. The results, and in particular the trends of potentials users, allow to individuate different historical phases, that are driven by fundamental technology evolutions of the Net. The analysis highlights the growth of the Internet potential users is changed recently from an exponential to a linear trend, but it do not point out any signal that the saturation is approaching. In the last five years the explosion of the number of the effective users seems to be due to the introduction of mass applications based on the web, and to the unfolding of network effects. However, the growth of the effective body of users could be difficult to keep at the present rate; moreover, not only technological but also normative and regulatory drivers could be at stake.