Accurate Noise Projection for Reduced Stochastic Epidemic Models

Details Accurate Noise Projection for Reduced Stochastic Epidemic Models Accurate Noise Projection for Reduced Stochastic Epidemic Models

2009-03-05

arxiv.org/abs/0903.1038v2

Nonlinear Sciences

Adaptation and Self-Organizing Systems

38 pages, 10 figures, new title, Final revision to appear in Chaos

Scientific paper

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.

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