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A unified analysis of the final size and severity distribution in collective Reed-Frost epidemic processes

Published online by Cambridge University Press:  01 July 2016

Philippe Picard  and
Claude Lefevre
Philippe Picard*
Affiliation:
Université de Lyon 1
Claude Lefevre*
Affiliation:
Université Libre de Bruxelles
*
∗Postal address: Mathématiques Appliquées, Université de Lyon 1, 43 Boulevard du 11 Novembre 1918, F-69622 Villeurbanne, France.
∗∗Postal address: Institut de Statistique C. P. 210, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050 Bruxelles, Belgique.
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Abstract

An extended version, called collective, of the randomized Reed-Frost processes is considered where each infective during his survival time fails to transmit the infection within any given set of susceptibles with a probability depending only on the size of that set. Our purpose is to provide a unified analysis of the distribution of the final size and severity, the two main components of the cost generated by the infection process. The method developed relies on the construction of a family of martingales and the use of a family of polynomials studied recently by the authors (Lefèvre and Picard (1990)). The results generalize a number of earlier ones and are derived in a more direct and systematic way than before.

Keywords

MARTINGALESFAMILY OF POLYNOMIALS
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 2 , June 1990 , pp. 269 - 294
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

Research supported by the Institut National de la Santé et de la Recherche Médicale under contract n° 898014.

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