where 4 4 , 5 5 , and 6 6 are given by Eqs. ͑21a͒-͑21c͒. Using Eqs. ͑30a͒-͑30c͒ or some other similar deterministic drive, the solution computed using the reduced system based on the deterministic center manifold analysis will agree perfectly with the solution computed using the complete system of equations. On the other hand, since the reduced system based on the normal form analysis was derived specifically for white noise, the transient solution found using this reduced system will not agree with the solution found using the complete system. It is possible to find a normal form coordinate transform for periodic forcing, but the normal form will be different than the one derived in this article for white noise. Figures 8͑a͒ and 8͑b͒ compare the time series of the fraction of the population that is infected with a disease I, computed using the complete 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 found using the stochastic normal form coordinate transform ͓Eqs. ͑29a͒, ͑29b͒, ͑B1a͒, and ͑B1b͔͒, but where the stochastic terms of both systems have been replaced by the deterministic terms given by Eqs. ͑30a͒-͑30c͒. Figure 8͑a͒ shows the initial transients, while Fig. 8͑b͒ shows a piece of the time series after the transients have decayed. One can see in Figs. 8͑a͒ and 8͑b͒ that although the two solutions eventually become relatively synchronized with one another, there is a poor agreement, both in phase and amplitude, throughout the transient.