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The great circle epidemic model

Ball, Frank and Neal, Peter John (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
Journal or Publication Title: Stochastic Processes and their Applications
Uncontrolled Keywords: Branching process ; Central limit theorems ; Coupling ; Epidemic process ; Small-world models ; Weak convergence
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 76931
Deposited By: ep_importer_pure
Deposited On: 30 Nov 2015 09:38
Refereed?: Yes
Published?: Published
Last Modified: 19 Nov 2017 12:56
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/76931

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