  We analyze four models of epidemic spreading using a stochastic approach in
which the primary stochastic variables are the numbers of individuals in each
class. The stochastic approach is described by a master equation and the
transition rate for each process such as infection or recovery are set up by
using the law of mass action. We perform numerical simulations as well as
numerical integration of the evolution equations for the average number of each
class of individuals. The onset of the epidemic spreading is obtained by a
linear analysis of the disease free state, from which follows the initial
exponential increase of the infected and the frequency of new cases. The order
parameter and the variance in the number of individuals are also obtained
characterizing the onset of epidemic spreading as a critical phase transition.
