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Asymptotic analysis of the general stochastic epidemic with variable infectious periods. (English) Zbl 1004.92032

Summary: A generalisation of the classical general stochastic epidemic within a closed, homogeneously mixing population is considered, in which the infectious periods of infectives follow i.i.d. random variables having an arbitrary but specified distribution. The asymptotic behaviour of the total size distribution for the epidemic as the initial numbers of susceptibles and infectives tend to infinity is investigated by generalising the construction of T. Sellke [J. Appl. Probab. 20, 390-394 (1983; Zbl 0526.92024)] and reducing the problem to a boundary crossing problem for sums of independent random variables.

MSC:

92D30 Epidemiology
60F17 Functional limit theorems; invariance principles
60G35 Signal detection and filtering (aspects of stochastic processes)

Citations:

Zbl 0526.92024
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