An introduction to stochastic epidemic models

Linda J.S. Allen

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

243 Scopus citations


A brief introduction to the formulation of various types of stochastic epidemic models is presented based on the well-known deterministic SIS and SIR epidemic models. Three different types of stochastic model formulations are discussed: discrete time Markov chain, continuous time Markov chain and stochastic differential equations. Properties unique to the stochastic models are presented: probability of disease extinction, probability of disease outbreak, quasistationary probability distribution, final size distribution, and expected duration of an epidemic. The chapter ends with a discussion of two stochastic formulations that cannot be directly related to the SIS and SIR epidemic models. They are discrete time Markov chain formulations applied in the study of epidemics within households (chain binomial models) and in the prediction of the initial spread of an epidemic (branching processes).

Original languageEnglish
Title of host publicationMathematical Epidemiology
Number of pages50
ISBN (Print)9783540789109
StatePublished - 2008

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434


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