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An introduction to stochastic epidemic models. (English) Zbl 1206.92022
Bauer, Fred (ed.) et al., Mathematical epidemiology. Berlin: Springer (ISBN 978-3-540-78910-9/pbk). Lecture Notes in Mathematics 1945. Mathematical Biosciences Subseries, 81-130 (2008).
Summary: 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).
For the entire collection see [Zbl 1159.92034].

MSC:
92D30 Epidemiology
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
92C60 Medical epidemiology
92-04 Software, source code, etc. for problems pertaining to biology
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