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Accurate noise projection for reduced stochastic epidemic models

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 transfo...

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Detalles Bibliográficos
Autores principales: Forgoston, Eric, Billings, Lora, Schwartz, Ira B.
Formato: Texto
Lenguaje:English
Publicado: American Institute of Physics 2009
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2780467/
https://www.ncbi.nlm.nih.gov/pubmed/20059206
http://dx.doi.org/10.1063/1.3247350
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author Forgoston, Eric
Billings, Lora
Schwartz, Ira B.
author_facet Forgoston, Eric
Billings, Lora
Schwartz, Ira B.
author_sort Forgoston, Eric
collection PubMed
description 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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spelling pubmed-27804672010-12-01 Accurate noise projection for reduced stochastic epidemic models Forgoston, Eric Billings, Lora Schwartz, Ira B. Chaos Regular Articles 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. American Institute of Physics 2009-12 2009-10-29 /pmc/articles/PMC2780467/ /pubmed/20059206 http://dx.doi.org/10.1063/1.3247350 Text en Copyright © 2009 American Institute of Physics
spellingShingle Regular Articles
Forgoston, Eric
Billings, Lora
Schwartz, Ira B.
Accurate noise projection for reduced stochastic epidemic models
title Accurate noise projection for reduced stochastic epidemic models
title_full Accurate noise projection for reduced stochastic epidemic models
title_fullStr Accurate noise projection for reduced stochastic epidemic models
title_full_unstemmed Accurate noise projection for reduced stochastic epidemic models
title_short Accurate noise projection for reduced stochastic epidemic models
title_sort accurate noise projection for reduced stochastic epidemic models
topic Regular Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2780467/
https://www.ncbi.nlm.nih.gov/pubmed/20059206
http://dx.doi.org/10.1063/1.3247350
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