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A non-standard family of polynomials and the final size distribution of Reed-Frost epidemic processes

Published online by Cambridge University Press:  01 July 2016

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

This paper provides a global treatment of the final size distribution of Reed–Frost epidemic processes. Exact and asymptotic results are derived for both single and multipopulation situations. The key tool is a non-standard family of polynomials, introduced initially by Gontcharoff (1937) for one variable, revisited and extended here for several variables. The attractiveness of these polynomials will be enhanced in forthcoming works in the epidemic context as well as in other fields.

Keywords

MARTINGALELIMIT THEOREMS
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 1 , March 1990 , pp. 25 - 48
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

Research partially supported by NATO Grant n° 0757/87.

Research partially supported by the Institut National de la Santé et de la Recherche Médicale under contract n° 878020

References

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