一个评估大流行期间服务设施传播风险的风险理论框架
A Queueing-Theoretic Framework for Evaluating Transmission Risks in Service Facilities During a Pandemic
摘要：
我们提出了一个新的模型框架，用于评估大流行期间疾病传播的风险，在小规模环境中，由到达和服务过程中的随机性驱动，即，易发生火灾的有限空间服务设施，如杂货店。我们提出了一个新的度量（$R_0^{\mathsf{sys}}$）的启发$R_0$，“基本繁殖数”的概念，从流行病学，衡量传染病的传播。我们得到的$R_0^{\mathsf{sys}}$度量各种排队模型的服务设施，利用一种新的排队理论的概念：逗留时间重叠。我们展示了我们的指标如何用于探索旨在遏制服务设施内疾病传播的各种干预措施的有效性。具体而言，我们专注于COVID-19疫情期间采用的一些普遍干预措施：限制服务设施的占用率、保护高风险客户（通过优先级或指定时间窗）以及提高服务速度（或限制乘客持续时间）。我们讨论了各种方向，以适应我们的传播模型，将一些更细微的疾病传播的功能，包括在人口免疫水平的异质性，口罩使用的不同水平，在疾病传播的空间考虑。
英文摘要：
We propose a new modeling framework for evaluating the risk of disease transmission during a pandemic in small-scale settings driven by stochasticity in the arrival and service processes, i.e., congestion-prone confined-space service facilities, such as grocery stores. We propose a novel metric ($R_0^{\mathsf{sys}}$) inspired by $R_0$, the "basic reproduction number" concept from epidemiology, which measures the transmissibility of infectious diseases. We derive the $R_0^{\mathsf{sys}}$ metric for various queueing models of service facilities by leveraging a novel queueing-theoretic notion: sojourn time overlaps. We showcase how our metric can be used to explore the efficacy of a variety of interventions aimed at curbing the spread of disease inside service facilities. Specifically, we focus on some prevalent interventions employed during the COVID-19 pandemic: limiting the occupancy of service facilities, protecting high-risk customers (via prioritization or designated time windows), and increasing the service speed (or limiting patronage duration). We discuss a variety of directions for adapting our transmission model to incorporate some more nuanced features of disease transmission, including heterogeneity in the population immunity level, varying levels of mask usage, and spatial considerations in disease transmission.
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