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The final state of an epidemic in a large heterogeneous population with a large initial number of infectives. (English) Zbl 0827.92022

Summary: We describe some asymptotic properties of a general S-I-R epidemic process in a large heterogeneous population. We assume that the infectives behave independently, that each infective has a generally distributed random number of contacts with the others in the population, and that among the initial susceptibles there is an arbitrary initial distribution of susceptibility. For the case of a large number of initial infectives, we demonstrate the asymptotic normality of the final size distribution as well as convergence of the final distribution of susceptibility as the population size approaches infinity. The relationship between the mean of the limiting final size distribution and the initial heterogeneity of susceptibility is explored for a parametric example.

MSC:

92D30 Epidemiology
92D25 Population dynamics (general)
60K99 Special processes

Citations:

Zbl 0827.92023
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