Accurate Noise Projection for Reduced Stochastic Epidemic Models

TL;DR

This paper introduces a novel analytical method using a normal form coordinate transform to accurately project noise onto the center manifold of a stochastic SEIR epidemic model, enabling improved long-term predictions of infectious cases.

Contribution

The paper develops an analytical approach to derive the stochastic center manifold and reduced equations, accurately capturing noise effects in epidemic modeling.

Findings

Reduced stochastic system matches original system over long timescales

Method improves prediction accuracy of infectious case numbers

Applicable to both infinite and finite population models

Abstract

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.