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Accurate noise projection for reduced stochastic epidemic models

Chaos 19, 043110 (2009); doi:10.1063/1.3247350

Published 29 October 2009

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Eric Forgoston,1 Lora Billings,2 and Ira B. Schwartz1
1Nonlinear Dynamical Systems Section, Plasma Physics Division, U.S. Naval Research Laboratory, Code 6792, Washington, DC 20375, USA
2Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, New Jersey 07043, USA
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. ©2009 American Institute of Physics
History: Received 4 August 2009; accepted 23 September 2009; published 29 October 2009
Permalink: http://link.aip.org/link/?CHAOEH/19/043110/1
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KEYWORDS and PACS

Keywords
PACS
  • 87.10.Mn
    Stochastic modelling (biological/medical physics)
  • 02.50.Ga
    Markov processes
  • 87.23.Cc
    Population dynamics and ecological pattern formation
  • 87.19.X-
    Diseases
  • 02.50.Ey
    Stochastic processes
  • YEAR: 2009

PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (35)
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