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Mixed Poisson approximation in the collective epidemic model

  • Lefèvre, Claude
  • Utev, Sergei
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    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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    File URL: http://www.sciencedirect.com/science/article/B6V1B-3SP2NRB-C/2/cefa1c701f087cb054bb1ef4e985d325
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    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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