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Stochastic Epidemic Modeling

In: Mathematical and Statistical Estimation Approaches in Epidemiology

Author

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  • Priscilla E. Greenwood

    (Arizona State University, Department of Mathematics and Statistics)

  • Luis F. Gordillo

    (University of Puerto Rico-RUM, Department of Mathematics)

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.

Suggested Citation

  • Priscilla E. Greenwood & Luis F. Gordillo, 2009. "Stochastic Epidemic Modeling," Springer Books, in: Gerardo Chowell & James M. Hyman & Luís M. A. Bettencourt & Carlos Castillo-Chavez (ed.), Mathematical and Statistical Estimation Approaches in Epidemiology, pages 31-52, Springer.
    • Handle: RePEc:spr:sprchp:978-90-481-2313-1_2
    DOI: 10.1007/978-90-481-2313-1_2
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