Mixed Poisson approximation in the collective epidemic model

Claude Lefèvre and Sergei Utev

Stochastic Processes and their Applications, 1997, vol. 69, issue 2, 217-246

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.

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 (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (3)

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