Poisson approximations for epidemics with two levels of mixing

• 成果类型: Article
• 署名作者: Ball, F; Neal, P
• 署名单位: University of Nottingham; Lancaster University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2004
• 页码: 1168-1200
• 关键词: sir epidemics; final-size; transmission

摘要

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-i(n) = {nu(i, j,)(n) ; j = 1, 2,. . . n}, at the points of independent Poisson processes with rates gimel(G)(n) and gimel(L)(n), 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 --> infinity. 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 nu(i)(n) = nu((i-j)mod n)(n).