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Mixed Poisson approximation in the collective epidemic model

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  • Lefèvre, Claude
  • Utev, Sergei
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    Abstract

    The collective epidemic model is a quite flexible model that describes the spread of an infectious disease of the Susceptible-Infected-Removed type in a closed population. A statistic of great interest is the final number of susceptibles who survive the disease. In the present paper, a necessary and sufficient condition is derived that guarantees the weak convergence of the law of this variable to a mixed Poisson distribution when the initial susceptible population tends to infinity, provided that the outbreak is severe in a certain sense. New ideas in the proof are the exploitation of a stochastic convex order relation and the use of a weak convergence theorem for products of i.i.d. random variables.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 69 (1997)
    Issue (Month): 2 (September)
    Pages: 217-246

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    Handle: RePEc:eee:spapps:v:69:y:1997:i:2:p:217-246

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    Related research

    Keywords: Collective epidemic model Final susceptible state Generalized epidemic model Mixed Poisson approximation Infinitely divisible distribution Branching process Stochastic convex order Weak convergence of products of i.i.d. r.v.'s;

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    Cited by:
    1. Denuit, Michel & Lefevre, Claude & Utev, Sergey, 2002. "Measuring the impact of dependence between claims occurrences," Insurance: Mathematics and Economics, Elsevier, vol. 30(1), pages 1-19, February.

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