4.5 Article

A useful relationship between epidemiology and queueing theory: The distribution of the number of infectives at the moment of the first detection

期刊

MATHEMATICAL BIOSCIENCES
卷 219, 期 1, 页码 15-22

出版社

ELSEVIER SCIENCE INC
DOI: 10.1016/j.mbs.2009.02.001

关键词

Queueing theory; Epidemic; Branching processes; Detection; Infectious diseases

资金

  1. Netherlands Organization for Scientific Research [916.86.128]

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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 relation between the spread of 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 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. (C) 2009 Elsevier Inc. All rights reserved.

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