We have demonstrated that the normal form coordinate transform method reduces the Langevin system so that both the noise and dynamics are accurately projected onto the lower-dimensional manifold. It is natural to consider ͑a͒ the replacement of the stochastic term by a deterministic period drive of small amplitude and ͑b͒ the extension to finite populations. These cases are discussed, respectively, in Secs. VI A and VI B. . 6 . ͑Color online͒ Histogram of probability density p SI of the S and I values found using ͑a͒ the complete stochastic system of transformed equations for the SEIR model with mortality ͓Eqs. ͑20a͒-͑20c͔͒ and ͑b͒ the reduced system of equations of the SEIR model with mortality that is found using the stochastic normal form coordinate transform ͓Eqs. ͑29a͒, ͑29b͒, ͑B1a͒, and ͑B1b͔͒. The histograms are created using 100 years worth of time series ͑starting with year 40͒ for 500 realizations, and the color-bar values have been normalized by 10 −3 . Cross correlation between time series found using the original stochastic system of transformed equations and the reduced system of equations based on the deterministic center manifold ͑"circle" markers͒ and cross correlation between time series found using the original stochastic system of transformed equations and the reduced system of equations based on the stochastic normal form coordinate transform ͑"square" markers͒. The cross correlation is computed using time series from t = 800 to t = 1000.