The great circle epidemic model

Ball, Frank and Neal, Peter (2003) The great circle epidemic model. Stochastic Processes and their Applications, 107 (2). pp. 233-268. ISSN 0304-4149

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Abstract

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→∞ is analysed. A branching process approximation for the early stages of an epidemic is described and made rigorous as n→∞ 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.

Item Type:	Article
Uncontrolled Keywords:	Branching process; Central limit theorems; Coupling; Epidemic process; Small-world models; Weak convergence
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 62 Statistics
Depositing User:	Ms Lucy van Russelt
Date Deposited:	18 Aug 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/550

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