It should be noted that the use of these two reduction methods is not constrained to problems in epidemiology, but rather may be used for many types of physical problems. For some generic systems, such as the singularly perturbed, damped Duffing oscillator, either reduction method can be used since the terms in the normal form coordinate transform which lead to the average stochastic center manifold being different from the deterministic center manifold occur at very high order. 17 In other words, the average stochastic center manifold and deterministic center manifold are virtually identical. For the SEIR model considered in this article, there are terms at low order in the normal form transform, which cause a significant difference between the average stochastic center manifold and the deterministic manifold. Therefore, as we have demonstrated, when working with the SEIR model, one must use the normal form coordinate transform method to correctly project the noise onto the center manifold.