A useful relationship between epidemiology and queueing theory

TL;DR

This paper establishes a novel link between epidemiology and queueing theory by relating the number of infectious individuals at epidemic detection to queueing models, enabling cross-disciplinary insights and analysis.

Contribution

It introduces a framework connecting epidemic spread and queueing processes, specifically relating infectious counts to M/G/1 queue dynamics.

Findings

Number of infectious individuals at detection is geometrically distributed.

Provides a new analytical approach for epidemic modeling using queueing theory.

Bridges concepts between epidemiology and queueing processes.

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.