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Poisson approximations for epidemics with two levels of mixing

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>2004
<mark>Journal</mark>Annals of Probability
Issue number1B
Volume32
Number of pages33
Pages (from-to)1168-1200
Publication StatusPublished
<mark>Original language</mark>English

Abstract

This paper is concerned with a stochastic model for the spread of an epidemic among a population of n individuals, labeled 1,2,…,n , in which a typical infected individual, i say, makes global contacts, with individuals chosen independently and uniformly from the whole population, and local contacts, with individuals chosen independently according to the contact distribution V n i ={v n i,j ;j=1,2,…,n} , at the points of independent Poisson processes with rates λ n G and λ n L , respectively, throughout an infectious period that follows an arbitrary but specified distribution. The population initially comprises m n infectives and n−m n susceptibles. A sufficient condition is derived for the number of individuals who survive the epidemic to converge weakly to a Poisson distribution as n→∞ . The result is specialized to the households model, in which the population is partitioned into households and local contacts are chosen uniformly within an infective's household; the overlapping groups model, in which the population is partitioned in several ways and local mixing is uniform within the elements of the partitions; and the great circle model, in which v n i,j =v n (i−j) modn .