Poisson approximations for epidemics with two levels of mixing.
type: Item
instance of: scholarly article
title: Poisson approximations for epidemics with two levels of mixing.
zbMATH Open document ID: 1060.92050
author: Frank Ball
author: Peter Neal
published in: The Annals of Probability
publication date: 2004-09-15T00:00:00Z
review text: The authors consider rather general models of epidemic spread in heterogeneous populations, where individuals make random contacts both locally and, at a reduced rate, globally. They derive a sufficient condition under which the distribution of the number of individuals who survive the epidemic converges weakly to a Poisson distribution as the population size tends to infinity; see also \textit{H. E. Daniels} [Proc. 5\,th Berkeley Symp. Math. Stat. Probab. 4, 281--293 (1967)]. The result is specialized to a households model, to an overlapping groups model, and to the great circle model.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 2100745
zbMATH Keywords: epidemic models
zbMATH Keywords: local and global mixing
zbMATH Keywords: Poisson convergence
zbMATH Keywords: random graph
zbMATH Keywords: positively related
zbMATH Keywords: coupling
reviewed by: A. D. Barbour
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1079021475
OpenAlex ID: W1989607057
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DOI: 10.1214/AOP/1079021475
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description: scientific article; zbMATH DE number 2100745