A useful relationship between epidemiology and queueing theory: The distribution of the number of infectives at the moment of the first detection
A useful relationship between epidemiology and queueing theory: The distribution of the number of infectives at the moment of the first detection
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DOI：
10.1016/j.mbs.2009.02.001
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发表时间：
2009-05-01
影响因子：
4.3
通讯作者：
Bootsma, Martinus Christoffel Jozef
中科院分区：
文献类型：
--
作者：
Trapman, Pieter;Bootsma, Martinus Christoffel Jozef
本文建立了传染病传播与具有处理器共享的M/G/1队列动力学之间的关系。流行病的传播和分支过程之间的关系（这在流行病学中是众所周知的）以及M/G/1队列和出生死亡过程之间的关系（这在排队理论中是众所周知的）将被结合起来，以提供一个框架，在这个框架中，排队理论的结果可以用于流行病学，反之亦然。特别是，我们考虑了在第一次发现流行病时标准SIR流行病模型中感染个体的数量，其中感染个体以恒定的人均率被发现。我们使用关于排队过程的文献结果来表明这种感染个体的数量呈几何分布。(C) 2009爱思唯尔公司版权所有。
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.