We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR)
epidemiological model. Through the use of a normal form coordinate transform,
we are able to analytically derive the stochastic center manifold along with
the associated, reduced set of stochastic evolution equations. The
transformation correctly projects both the dynamics and the noise onto the
center manifold. Therefore, the solution of this reduced stochastic dynamical
system yields excellent agreement, both in amplitude and phase, with the
solution of the original stochastic system for a temporal scale that is orders
of magnitude longer than the typical relaxation time. This new method allows
for improved time series prediction of the number of infectious cases when
modeling the spread of disease in a population. Numerical solutions of the
fluctuations of the SEIR model are considered in the infinite population limit
using a Langevin equation approach, as well as in a finite population simulated
as a Markov process.Comment: 38 pages, 10 figures, new title, Final revision to appear in Chao