Accurate noise projection for reduced stochastic epidemic models

Eric Forgoston, Lora Billings, Ira B. Schwartz

Research output: Contribution to journalArticleResearchpeer-review

16 Citations (Scopus)

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.

Original languageEnglish
Article number043110
JournalChaos
Volume19
Issue number4
DOIs
StatePublished - 1 Jan 2009

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Stochastic Epidemic Models
Center Manifold
Stochastic models
projection
Projection
Stochastic Dynamical Systems
Epidemiological Model
Stochastic Evolution Equations
Time Series Prediction
Stochastic systems
Finite Population
Langevin Equation
Relaxation Time
Stochastic Systems
Relaxation time
Markov Process
Markov processes
Normal Form
Time series
Dynamical systems

Cite this

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Accurate noise projection for reduced stochastic epidemic models. / Forgoston, Eric; Billings, Lora; Schwartz, Ira B.

In: Chaos, Vol. 19, No. 4, 043110, 01.01.2009.

Research output: Contribution to journalArticleResearchpeer-review

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