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Asymptotic final size distribution of the multitype Reed–Frost process

Published online by Cambridge University Press:  14 July 2016

Gianpaolo Scalia-Tomba
Gianpaolo Scalia-Tomba*
Affiliation:
University of Stockholm
*
∗Postal address: Dept of Mathematical Statistics, University of Stockholm, Box 6701, S-113 85 Stockholm, Sweden.
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Abstract

The asymptotic final size distribution of a multitype Reed–Frost process, a chain-binomial model for the spread of an infectious disease in a finite, closed multitype population, is derived, as the total population size grows large. When all subgroups are of comparable size, the infection pattern irreducible and the epidemic started by a small number of initial infectives, the classical threshold behaviour is obtained, depending on the basic reproduction rate of the disease in the population, and the asymptotic distributions for small and large outbreaks can be found. The same techniques can then be used to study other asymptotic situations, e.g. small groups in an otherwise large population, large numbers of initial infectives and reducible infection patterns.

Keywords

CHAIN-BINOMIAL PROCESSFINAL EPIDEMIC SIZEASYMPTOTIC DISTRIBUTIONMULTITYPE EPIDEMIC MODEL
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 563 - 584
Copyright
Copyright © Applied Probability Trust 1986 

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