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The time of occurence of the maximum of a closed epidemic

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Stochastic Processes in Epidemic Theory

Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 86))

Abstract

This paper may seem a somewhat theoretical exercise when so many practical problems relating to epidemics are urgently awaiting solution. However, it often happens in our subject that study of the behaviour of an oversimplified model can lead to insights mto essential features of more realistic but complicated models. Here we consider the classical closed epidemic with x susceptibles and y infectives at time t, and examine the statistical behaviour of the maximum number of infectives in a particular epidemic and the time at which it is attained. The rather counterintuitive behaviour which is revealed may be relevant in more realistic situations.

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References

  • Barbour A.D., A note on the maximum size of a closed epidemic, J. Roy. Statist. Soc. B 37 (1975), 459-460.

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  • Daniels H.E., The maximum size of a closed epidemic, Adv. Appl. Prob. 6 (1974), 607-621.

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  • Daniels H.E., The maximum of a Gaussian process whose mean path has a maximum, with an application to the strength of bundles of fibres, Adv. App. Prob. 21 (1989), 315-333.

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  • Daniels H.E. and Skyrme T.H.R., The maximum of a random walk whose mean path has a maximum, Adv. Appl. Prob. 17 (1985), 85-99.

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Author information

Authors and Affiliations

  1. Statistical Laboratory, Dept. of Pure Math, University of Cambridge, CB2 1SB, Cambridge, England

    Henry E. Daniels

Authors
  1. Henry E. Daniels
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Editor information

Editors and Affiliations

  1. Institut de Mathématiques, Université de Fribourg, CH-1700, Fribourg, Schweiz

    Jean-Pierre Gabriel

  2. Institut de Statistique C.P. 210, Université Libre de Bruxelles, B-1050, Bruxelles, Belgien

    Claude Lefèvre

  3. Lab. de Calcul des Probabilités et Statistique, Université de Lyon I, F-69622, Villeurbanne Cedex, Frankreich

    Philippe Picard

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© 1990 Springer-Verlag Berlin Heidelberg

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Daniels, H.E. (1990). The time of occurence of the maximum of a closed epidemic. In: Gabriel, JP., Lefèvre, C., Picard, P. (eds) Stochastic Processes in Epidemic Theory. Lecture Notes in Biomathematics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10067-7_12

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  • DOI: https://doi.org/10.1007/978-3-662-10067-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52571-4

  • Online ISBN: 978-3-662-10067-7

  • eBook Packages: Springer Book Archive

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