Mixed Poisson approximation in the collective epidemic model
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.
Volume (Year): 69 (1997)
Issue (Month): 2 (September)
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