After performing a Markov simulation of Eq. ͑C3͒ with a population size of N =10ϫ 10 6 , we can compare the dynamics of the transformed system with the dynamics of the original system by transforming the Y i variables in the time series back to the original s, e, and i variables. Dividing by N yields S, E, and I. Figure 10͑a͒ shows a time series, after the transients have decayed, of the fraction of the population that is infected with a disease I. The mean and the frequency agree with those found from the Markov simulation of the original system. We have performed the simulation for 500 realizations, and a histogram representing the probability density p SI is shown in Fig. 10͑b͒ . The color-bar values in Fig. 10͑b͒ have been normalized by 10 −4 . One can see in Fig.  10͑a͒ that the relative fluctuations of the I component have nearly doubled. While the fluctuation size was 0.152 for the original system, it is 0.310 for the transformed system. Additionally, the two histograms shown in Figs. 9͑b͒ and 10͑b͒ have a relative entropy of d KL = 0.9519, which means they are not in agreement. Because the simulation of the stochastic dynamics in the complete system of transformed variables does not qualitatively ͑or quantitatively͒ resemble the original stochastic system, we cannot expect that the reduced system will agree with either the original or the transformed systems. Therefore, much care should be exercised when extending the model reduction results ͑which show outstanding agreement͒ derived for a specific type of noise in the limit of infinite population to finite populations with a more general type of noise.