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Mixed Poisson approximation in the collective epidemic model

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  • Lefèvre, Claude
  • Utev, Sergei

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.

Suggested Citation

  • Lefèvre, Claude & Utev, Sergei, 1997. "Mixed Poisson approximation in the collective epidemic model," Stochastic Processes and their Applications, Elsevier, vol. 69(2), pages 217-246, September.
    • Handle: RePEc:eee:spapps:v:69:y:1997:i:2:p:217-246
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    Citations

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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.
    2. Claude Lefèvre & Sergey Utev, 1998. "On Order-Preserving Properties of Probability Metrics," Journal of Theoretical Probability, Springer, vol. 11(4), pages 907-920, October.
    3. Claude Lefe`vre & Sergey Utev, 1999. "Branching Approximation for the Collective Epidemic Model," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 211-228, September.

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