Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, V5A 1S6, BC, Canada.
Center for Health Evaluation and Outcome Sciences, 588 - 1081 Burrard Street St. Paul's Hospital, Vancouver, V6Z 1Y6, BC, Canada.
Health Care Manag Sci. 2023 Jun;26(2):200-216. doi: 10.1007/s10729-023-09632-9. Epub 2023 May 22.
We applied a queuing model to inform ventilator capacity planning during the first wave of the COVID-19 epidemic in the province of British Columbia (BC), Canada. The core of our framework is a multi-class Erlang loss model that represents ventilator use by both COVID-19 and non-COVID-19 patients. Input for the model includes COVID-19 case projections, and our analysis incorporates projections with different levels of transmission due to public health measures and social distancing. We incorporated data from the BC Intensive Care Unit Database to calibrate and validate the model. Using discrete event simulation, we projected ventilator access, including when capacity would be reached and how many patients would be unable to access a ventilator. Simulation results were compared with three numerical approximation methods, namely pointwise stationary approximation, modified offered load, and fixed point approximation. Using this comparison, we developed a hybrid optimization approach to efficiently identify required ventilator capacity to meet access targets. Model projections demonstrate that public health measures and social distancing potentially averted up to 50 deaths per day in BC, by ensuring that ventilator capacity was not reached during the first wave of COVID-19. Without these measures, an additional 173 ventilators would have been required to ensure that at least 95% of patients can access a ventilator immediately. Our model enables policy makers to estimate critical care utilization based on epidemic projections with different transmission levels, thereby providing a tool to quantify the interplay between public health measures, necessary critical care resources, and patient access indicators.
我们应用排队模型为不列颠哥伦比亚省（BC）加拿大 COVID-19 疫情第一波期间的呼吸机容量规划提供信息。我们框架的核心是一个多类 Erlang 损失模型，代表 COVID-19 和非 COVID-19 患者使用呼吸机的情况。模型的输入包括 COVID-19 病例预测，我们的分析结合了由于公共卫生措施和社会隔离而导致的不同传播水平的预测。我们整合了来自 BC 重症监护病房数据库的数据来校准和验证模型。通过离散事件模拟，我们预测了呼吸机的使用情况，包括何时达到容量以及有多少患者无法使用呼吸机。模拟结果与三种数值逼近方法进行了比较，即逐点平稳逼近、修正提供的负载和定点逼近。通过这种比较，我们开发了一种混合优化方法，以有效地确定满足准入目标所需的呼吸机容量。模型预测表明，公共卫生措施和社会隔离通过确保 COVID-19 第一波期间呼吸机容量不被达到，潜在地避免了每天多达 50 人死亡。如果没有这些措施，将需要额外的 173 台呼吸机，以确保至少 95%的患者可以立即使用呼吸机。我们的模型使决策者能够根据不同传播水平的疫情预测来估计重症监护的使用情况，从而提供了一种工具来量化公共卫生措施、必要的重症监护资源和患者准入指标之间的相互作用。
