Using the same numerical scheme previously described, we numerically integrate the complete stochastic system of transformed equations of the SEIR model ͓Eqs. ͑20a͒-͑20c͔͒ along with the reduced system of equations that is based on the deterministic center manifold with a replacement of the noise terms ͓Eqs. ͑22a͒ and ͑22b͔͒. The complete system is solved for U, V, and W, while the reduced system is solved for V and W. In the latter case, U is computed using the center manifold equation given by Eq. ͑17͒. Once the values of U, V, and W are known, we compute the values of S, Ē , and Ī using the transformation given by Eqs. ͑7a͒-͑7c͒. We shift S, Ē , and Ī, respectively, by S 0 , E 0 , and I 0 to find the values of S, E, and I. Figures 3͑a͒ and 3͑b͒ compare the time series of the fraction of the population that is infected with a disease I, computed using the complete stochastic system of transformed equations of the SEIR model ͓Eqs. ͑20a͒-͑20c͔͒ with the time series of I computed using the reduced system of equations of the SEIR model that is based on the deterministic center manifold with a replacement of the noise terms ͓Eqs. ͑22a͒ and ͑22b͔͒. Figure 3͑a͒ shows the initial transients, while Fig. 3͑b͒ shows the time series after the transients have decayed. One can see that the solution computed using the reduced system quickly becomes out of phase with the solution of the complete system. Use of this reduced system would lead to an incorrect prediction of the initial disease outbreak. Additionally, the predicted amplitude of the initial outbreak would be incorrect. The poor agreement, both in phase and amplitude, between the two solutions con-tinues for long periods of time, as seen in Fig. 3͑b͒ . We also have computed the cross correlation of the two time series shown in Figs. 3͑a͒ and 3͑b͒ to be approximately 0.34. Since the cross correlation measures the similarity between the two time series, this low value quantitatively suggests a poor agreement between the two solutions.