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Mathematical and Statistical Estimation Approaches in Epidemiology pp 31–52Cite as

Stochastic Epidemic Modeling

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Abstract

We review the topic of stochastic epidemic modeling with emphasis on compartmental stochastic models. A main theme is the usefulness of the correspondence between these and their large population deterministic limits, which describe dynamical systems. The dynamics of an ODE system informs us of the deterministic skeleton upon which the behavior of corresponding stochastic systems are built. In this chapter we present a number of examples, mostly in the context of susceptible-infected-removed (SIR) models, and point out how this way of thinking may be useful in understanding other stochastic models. In particular we discuss the distribution of final epidemic size, the effect of different patterns of infectiousness, and the quantification of stochastically sustained oscillations.

Keywords

  • Epidemic modeling
  • Stochastic SIR
  • Final size distribution
  • Vaccination
  • Stochastically sustained oscillations
  • Variable infectiousness

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, USA

    Priscilla E. Greenwood

  2. Department of Mathematics, University of Puerto Rico-RUM, Mayaguez, PR 00681-9018, USA

    Luis F. Gordillo

Authors
  1. Priscilla E. Greenwood
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  2. Luis F. Gordillo
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Editor information

Editors and Affiliations

  1. Arizona State University School of Human Evolution & Social Change, Tempe, AZ 85287-2402, USA

    Dr. Gerardo Chowell

  2. Los Alamos National Laboratory, Mail Stop B284, Los Alamos, NM 87545, USA

    Dr. James M. Hyman & Dr. Luís M. A. Bettencourt & 

  3. Dept. Mathematics & Statistics, Arizona State University, P.O.Box 871804, Tempe, AZ 85287, USA

    Carlos Castillo-Chavez

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Greenwood, P.E., Gordillo, L.F. (2009). Stochastic Epidemic Modeling. In: Chowell, G., Hyman, J.M., Bettencourt, L.M.A., Castillo-Chavez, C. (eds) Mathematical and Statistical Estimation Approaches in Epidemiology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2313-1_2

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