Accurate fluctuation prediction in epidemics using stochastic model reduction

We consider a large-scale dynamical system with stochastic forcing and outline a general theory to reduce the dimension of the stochastic system. The general procedure employs a stochastic normal form coordinate transform and allows one to analytically derive both the stochastic center manifold and the reduced set of stochastic evolution equations. The transformation correctly projects both the dynamics and the noise onto the center manifold. We have applied the theory to a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model. When compared with the original model, the reduced dynamical system accurately predicts fluctuations of disease outbreaks both in amplitude and phase.