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The area under the trajectory of carriers in a carrier-borne epidemic

Published online by Cambridge University Press:  14 July 2016

Claude Lefèvre
Claude Lefèvre*
Affiliation:
Université Libre de Bruxelles
*
∗Postal address: Institut de Statistique, Université Libre de Bruxelles, Campus Plaine, Boulevard du Triomphe, B–1050, Bruxelles, Belgium.
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Abstract

This paper is concerned with the area under the trajectory of carriers in the Downton carrier-borne epidemic (1968). Its Laplace–Stieltjes transform is studied, and a recursive equation derived for it. Its mean is examined in some detail and the solution obtained is expressed as a power series in π, the proportion of the infected susceptibles becoming carriers.

Keywords

CARRIER-BORNE EPIDEMICSEXPECTED NUMBER OF SURVIVORSAREA UNDER THE TRAJECTORY OF CARRIERS
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 231 - 241
Copyright
Copyright © Applied Probability Trust 1979 

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References

Abakuks, A. (1974) A note on supercritical carrier-borne epidemics. Biometrika 61, 271–275.Google Scholar
Bailey, N. T. J. (1957) The Mathematical Theory of Epidemics. Griffin, London.Google Scholar
Downton, F. (1968) The ultimate size of carrier-borne epidemics. Biometrika 55, 277–289.CrossRefGoogle Scholar
Downton, F. (1972) The area under the infectives trajectory of the general stochastic epidemic. J. Appl. Prob. 9, 414–417. Correction J. Appl. Prob. 9, 873–876.CrossRefGoogle Scholar
Gani, J. and Jerwood, D. (1972) The cost of a general stochastic epidemic. J. Appl. Prob. 9, 257–269.Google Scholar
Jerwood, D. (1974) The cost of a carrier-borne epidemic. J. Appl. Prob. 11, 642–651.Google Scholar
Kryscio, R. J. and Saunders, R. (1976) A note on the cost of carrier-borne, right-shift, epidemic models. J. Appl. Prob. 13, 652–661.CrossRefGoogle Scholar
Lefevre, C. (1978) The expected ultimate size of a carrier-borne epidemic. J. Appl. Prob. 15, 414–419.Google Scholar
Mcneil, D. R. (1970) Integral functionals of birth and death processes and related limiting distributions. Ann. Math. Statist. 41, 480–485.Google Scholar
Saunders, R., Lefevre, C. and Kryscio, R. J. (1979) A note on the expected number of survivors in supercritical carrier-borne epidemics. J. Appl. Prob. 16, (3).Google Scholar
Weiss, G. M. (1965) On the spread of epidemics by carriers. Biometrics 21, 481–490.Google Scholar