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On the limiting behaviour of Downton's carrier epidemic in the case of a general infection mechanism

Published online by Cambridge University Press:  14 July 2016

James G. Booth
James G. Booth*
Affiliation:
University of Florida
*
∗Postal address: Department of Statistics, University of Florida, Gainesville, FL 32611, USA.
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Abstract

A generalization of Downton's (1968) carrier-borne epidemic process is considered in which the assumption of homogeneous mixing is replaced by a general infection mechanism. Using a method and notation similar to that of Gani and Purdue (1984), a recursive algorithm for the joint distribution of the total size and the total observed size of the epidemic is obtained.

Keywords

EPIDEMIC PROCESSMATRIX-GEOMETRIC METHODS
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 625 - 630
Copyright
Copyright © Applied Probability Trust 1989 

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References

Booth, J., Gani, J., Malice, M.-P., Mansouri, H. and Maravankin, G. (1986) A general solution for the epidemic with carriers. Statist. Prob. Letters 4, 9–15.CrossRefGoogle Scholar
Denton, G. M. (1972) On Downton's carrier-borne epidemic. Biometrika 59, 455–461.CrossRefGoogle Scholar
Downton, F. (1968) The ultimate size of carrier-borne epidemics. Biometrika 55, 277–289.CrossRefGoogle Scholar
Gani, J. and Purdue, P. (1984) Matrix-geometric methods for the general stochastic epidemic. IMA J. Math. Appl. Med. Biol. 1, 333–342.CrossRefGoogle ScholarPubMed
Weiss, G. H. (1965) On the spread of epidemics with carriers. Biometrics 21, 481–490.Google Scholar