  We present a Monte Carlo simulation of the transmission of measles within a
population sample during its growing and equilibrium states by introducing two
different vaccination schedules of one and two doses. We study the effects of
the contact rate per unit time $\xi $ as well as the initial conditions on the
persistence of the disease. We found a weak effect of the initial conditions
while the disease persists when $\xi $ lies in the range 1/L-10/L ($L$ being
the latent period). Further comparison with existing data, prediction of future
epidemics and other estimations of the vaccination efficiency are provided.
  Finally, we compare our approach to the models using the mass action
principle in the first and another epidemic region and found the incidence
independent of the number of susceptibles after the epidemic peak while it
strongly fluctuates in its growing region. This method can be easily applied to
other human, animals and vegetable diseases and includes more complicated
parameters.
