The great circle epidemic model

被引:13
作者
Ball, F
Neal, P
机构
[1] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England
[2] Univ Lancaster, Fylde Coll, Dept Math & Stat, Lancaster LA1 4YF, England
关键词
branching process; central limit theorems; coupling; epidemic process; small-world models; weak convergence;
D O I
10.1016/S0304-4149(03)00074-7
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 [统计学]; 070103 [概率论与数理统计]; 0714 [统计学];
摘要
We consider a stochastic model for the spread of an epidemic among a population of n individuals that are equally spaced around a circle. Throughout its infectious period, a typical infective, i say, makes global contacts, with individuals chosen independently and uniformly from the whole population, and local contacts, with individuals chosen independently and uniformly according to a contact distribution centred on i. The asymptotic situation in which the local contact distribution converges weakly as n --> infinity is analysed. A branching process approximation for the early stages of an epidemic is described and made rigorous as n --> infinity by using a coupling argument, yielding a threshold theorem for the model. A central limit theorem is derived for the final outcome of epidemics that take off, by using an embedding representation. The results are specialised to the case of a symmetric, nearest-neighbour local contact distribution. (C) 2003 Elsevier B.V. All rights reserved.
引用
收藏
页码:233 / 268
页数:36
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