An Introduction to Stochastic Epidemic Models

  • Linda J. S. Allen
Part of the Lecture Notes in Mathematics book series (LNM, volume 1945)

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).


Sample Path Epidemic Model Basic Reproduction Number High Order Moment Continuous Time Markov Chain 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Linda J. S. Allen
    • 1
  1. 1.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA

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