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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...
Autores principales: | , , |
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Formato: | Texto |
Lenguaje: | English |
Publicado: |
American Institute of Physics
2009
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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. |
format | Text |
id | pubmed-2780467 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2009 |
publisher | American Institute of Physics |
record_format | MEDLINE/PubMed |
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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