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In this paper we establish a relation between the spread of infectiousdiseases and the dynamics of so called M/G/1 queues with processor sharing. Thein epidemiology well known relation between the spread of epidemics andbranching processes and the in queueing theory well known relation betweenM/G/1 queues and birth death processes will be combined to provide a frameworkin which results from queueing theory can be used in epidemiology and viceversa.  In particular, we consider the number of infectious individuals in a standardSIR epidemic model at the moment of the first detection of the epidemic, whereinfectious individuals are detected at a constant per capita rate. We use aresult from the literature on queueing processes to show that this number ofinfectious individuals is geometrically distributed.

A useful relationship between epidemiology and queueing theory