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arXiv · 0812.4135

A useful relationship between epidemiology and queueing theory

Pieter Trapman·Martin Bootsma
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Abstract

In this paper we establish a relation between the spread of infectious diseases and the dynamics of so called M/G/1 queues with processor sharing. The in epidemiology well known relation between the spread of epidemics and branching processes and the in queueing theory well known relation between M/G/1 queues and birth death processes will be combined to provide a framework in which results from queueing theory can be used in epidemiology and vice versa. In particular, we consider the number of infectious individuals in a standard SIR epidemic model at the moment of the first detection of the epidemic, where infectious individuals are detected at a constant per capita rate. We use a result from the literature on queueing processes to show that this number of infectious individuals is geometrically distributed.

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Pieter Trapman, Martin Bootsma. 2008-12-22. A useful relationship between epidemiology and queueing theory. https://arxiv.org/abs/0812.4135

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