The solutions of the complete stochastic system of transformed equations as well as the reduced system of equations were computed numerically. We have shown that the individual time series does not agree because the noise has not been correctly projected onto the stochastic center manifold. However, by comparing histograms of the probability density p SI of the S and I values, we saw that there was a very good agreement. This is caused by the fact that although the two solutions are out of phase with one another, their range of amplitude values is similar. The phase difference is not represented in the two histograms. This is a real drawback when trying to predict the timing of outbreaks and leads to potential problems when considering epidemic control, such as the enhancement of disease extinction through random vaccine control. 35 To accurately project the noise onto the manifold, we derived a stochastic normal form coordinate transform for the complete stochastic system of transformed equations. The numerical solution to this reduced system was compared with the solution to the original system, and we showed that there was an excellent agreement both qualitatively and quantitatively. As with the first method, the histograms of the probability density p SI of the S and I values agree very well.