Using a nonlinear curve fitting method we calculate the incidence of AIDS cases through a study of reported data on cumulative AIDS cases. The method allows one to estimate the expected value of the incubation time, which happens to be about 11 years, if the intervals of observation are sufficiently large (greater than or equal to 45 years). For smaller intervals of observation the mean observed incubation time will be much shorter in consequence of the overrepresentation of "quick runners". The model predicts a mean observed incubation time of 5.3 years for an infected cohort in the first seven years after infection.