In this talk I will discuss a relation between the spread of infectious diseases and the dynamics of so called M/G/1 queues with processor sharing service discipline. The relations between SIR epidemics and branching processes, which is well known in epidemiology, and the relation between /M/G/1 queues and birth death processes, which is well known in queueing theory, will be exploited. In particular, I will consider the number of infectious individuals in a standard SIR (Susceptible, Infectious, Removed) epidemic model at the moment of the first detection of the epidemic, where infectious individuals are detected at a constant per capita rate. I will use a result from the literature on queueing processes to show that this number of infectious individuals is geometrically distributed. This result has important consequences for statistical inference of infectious disease data, such as data on the spread of the hospital bacteria MRSA.
This talk is based on work with Martin Bootsma.