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-Remov ed type in a closed population. A statistic of great interest is the f inal number of susceptibles who survive the disease. In the present pa per, a necessary and sufficient condition is derived that guarantees t he weak convergence of the law of this variable to a mixed Poisson dis tribution when the initial susceptible population tends to infinity, p rovided that the outbreak is severe in a certain sense. New ideas in t he proof are the exploitation of a stochastic convex order relation an d the use of a weak convergence theorem for products of i.i.d. random variables. (C) 1997 Elsevier Science B.V.