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The Final State of an Epidemic in a Large Heterogeneous Population with a Large Initial Number of Infectives

Published online by Cambridge University Press:  01 July 2016

Steven M. Butler
Steven M. Butler*
Affiliation:
University of Kentucky
*
* Postal address: Department of Statistics, 871 Patterson Office Tower, University of Kentucky, Lexington, KY 40506-0027, USA.
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Abstract

We describe some asymptotic properties of a general S–I–R epidemic process in a large heterogeneous population. We assume that the infectives behave independently, that each infective has a generally distributed random number of contacts with the others in the population, and that among the initial susceptibles there is an arbitrary initial distribution of susceptibility. For the case of a large number of initial infectives, we demonstrate the asymptotic normality of the final size distribution as well as convergence of the final distribution of susceptibility as the population size approaches infinity. The relationship between the mean of the limiting final size distribution and the initial heterogeneity of susceptibility is explored, for a parametric example.

Keywords

S–I–R EPIDEMICCOLLECTIVE REED–FROST MODEL

MSC classification

Primary: 92D30: Epidemiology
Secondary: 92D25: Population dynamics (general)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 3 , September 1994 , pp. 656 - 670
Copyright
Copyright © Applied Probability Trust 1994 

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