流行病学与排队论之间的有益关系
A useful relationship between epidemiology and queueing theory
摘要：
在本文中，我们建立了传染病的传播和所谓的M/G/1队列与处理器共享的动力学之间的关系。流行病学中众所周知的流行病的传播和分支过程之间的关系，并在排队论众所周知的M/G/1队列和出生死亡过程之间的关系将结合起来，提供一个框架，从排队论的结果可以在流行病学中使用，反之亦然。特别是，我们考虑了在一个标准的SIR流行病模型的传染病的个人的数量在第一次检测到的流行病，其中传染病的个人被检测到在一个恒定的人均率的时刻。我们使用的结果，从文献中的感染过程表明，这个数量的传染性个人是几何分布。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
