Lancaster EPrints

Poisson approximations for epidemics with two levels of mixing

Ball, Frank and Neal, Peter John (2004) Poisson approximations for epidemics with two levels of mixing. Annals of Probability, 32 (1B). pp. 1168-1200. ISSN 0091-1798

Full text not available from this repository.

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 .

Item Type: Article
Journal or Publication Title: Annals of Probability
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 76930
Deposited By: ep_importer_pure
Deposited On: 30 Nov 2015 09:34
Refereed?: Yes
Published?: Published
Last Modified: 24 Nov 2017 06:27
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/76930

Actions (login required)

View Item