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:
Journal Article
Journal or Publication Title:
Stochastic Processes and their Applications
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
ID Code:
76931
Deposited By:
Deposited On:
30 Nov 2015 09:38
Refereed?:
Yes
Published?:
Published
Last Modified:
29 Jan 2020 02:52