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On the number of recovered individuals in the \(SIS\) and \(SIR\) stochastic epidemic models. (English) Zbl 1200.92035
Summary: The basic models of infectious disease dynamics (the \(SIS\) and \(SIR\) models) are considered. Particular attention is paid to the number of infected individuals that recovered and its relationship with the final epidemic size. We investigate this descriptor both until the extinction of the epidemic and in the transient regime. Simple and efficient methods to obtain the distribution of the number of recovered individuals and its moments are proposed and discussed with respect to previous work. The methodology could also be extended to other stochastic epidemic models. The theory is illustrated by numerical experiments, which demonstrate that the proposed computational methods can be applied efficiently. In particular, we use the distribution of the number of individuals removed in the \(SIR\) model in conjunction with data of outbreaks of \(ESBL\) observed in the intensive care unit of a Spanish hospital.

MSC:
92D30 Epidemiology
65C50 Other computational problems in probability (MSC2010)
65C20 Probabilistic models, generic numerical methods in probability and statistics
Software:
MCQueue
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