Literature data, respective to kinetics of infectivities due to prion diseases, have been here reconsidered. The autocatalytic phenomenon of prion replication and the process of advancement of the infection are also considered. A model describing the interconversion from "normal" into "pathogenic" prions, and the subsequent growth of the infection, is proposed. This model takes into account the existence of two different steps: the first, slower, in which the interaction between the two different prions, with the transformation of normal prions into the pathogen ones, takes place. The second one, very fast, in which the degree of advancement of the infection assumes the form of an irreversible, rapid trend.