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A note on the total size distribution of carrier-borne epidemic models

Published online by Cambridge University Press:  14 July 2016

Frank Ball
Frank Ball*
Affiliation:
University of Nottingham
*
∗ Postal address: Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
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Abstract

The coupling method of Ball (1986) is extended to carrier-borne epidemics, thus providing a new proof of a result of Daniels (1972) concerning the total size distribution of Downton's stochastic carrier-borne epidemic. The generalization to multipopulation carrier-borne epidemics is immediate.

Keywords

COUPLINGMULTIPOPULATION EPIDEMIC
Type
Short Communication
Information
Journal of Applied Probability , Volume 27 , Issue 4 , December 1990 , pp. 908 - 912
Copyright
Copyright © Applied Probability Trust 1990 

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References

Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases and its Applications, 2nd edn. Griffin, London.Google Scholar
Ball, F. G. (1986) A note on the total size distribution of epidemic models. J. Appl. Prob. 23, 832–836.CrossRefGoogle Scholar
Daniels, H. E. (1967) The distribution of the total size of an epidemic. Proc. 5th Berkeley Symp. Math. Statist. Prob. 4, 281–293.Google Scholar
Daniels, H. E. (1972) An exact relation in the theory of carrier-borne epidemics. Biometrika 59, 211–213.Google Scholar
Downton, F. (1967) A note on the ultimate size of a general stochastic epidemic. Biometrika 54, 314–316.Google Scholar
Downton, F. (1968) The ultimate size of carrier-borne epidemics. Biometrika 55, 277–289.Google Scholar
Picard, P. (1980) Applications of martingale theory to some epidemic models. J. Appl. Prob. 17, 583–599.Google Scholar
Watson, R. K. (1980) On the size distribution of some epidemic models. J. Appl. Prob. 17, 912–921.CrossRefGoogle Scholar
Weiss, G. H. (1965) On the spread of epidemics by carriers. Biometrics 21, 481–491.CrossRefGoogle ScholarPubMed