2006.340: The great circle epidemic model

2006.340: Frank Ball and Peter Neal (2003) The great circle epidemic model. Stochastic Processes and their Applications, 107 (2). pp. 233-268. ISSN 0304-4149

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DOI: 10.1016/S0304-4149(03)00074-7

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.

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