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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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: Journal Article
Journal or Publication Title: Stochastic Processes and their Applications
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: 11 Jun 2019 02:49

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