A Queuing Model for Ventilator Capacity Management during the COVID-19 Pandemic

Abstract

We present a queue model to inform ventilator capacity management under different COVID-19 pandemic scenarios. Our model was used to support ventilator capacity planning during the first wave of the COVID-19 epidemic in British Columbia (BC), Canada. The core of our framework is an extended Erlang loss model, which incorporates COVID-19 case projections, along with the proportion of cases requiring a ventilator, the delay from symptom onset to ventilation, non-COVID-19 ventilator demand, and ventilation time. We implemented our model using discrete event simulation to forecast ventilator utilization. The results predict when capacity would be reached and the rate at which patients would be unable to access a ventilator. We further determined the number of ventilators required to meet a performance indicator target for ventilator access. We applied our model to BC by calibrating to the BC Intensive Care Unit Database and by using local epidemic projections. Epidemic scenarios with and without reduced transmission, due to social distancing and other behavioral changes, were used to link public health interventions to operational impacts on ventilator utilization. The results predict that reduced transmission could potentially avert up to 50 deaths per day by ensuring that ventilator capacity would likely not be reached. Without reduced transmission, an additional 181 ventilators would be required to meet our performance indicator target that 95% of patients can access a ventilator immediately. Our model provides a tool for policy makers to quantify the interplay between public health interventions, necessary critical care resources, and performance indicators for patient access.

Strength and Limitation of Biological Paradigm during Pandemic of Covid-19: An Application of Queueing Theory

“…They showed that the patient waiting time in the order of consultation, detection or cure of COVID-19 in case of inequalities within the organization improves globally according to the logarithm rule. Zimmerman et al [14] performed a queueing model to report ventilation capacity management in different COVID-19 epidemic scenarios. The model was used to organize ventilation capacity during the first wave of COVID-19 in British Columbia, Canada.…”

Panel on Simulation Modeling for Covid-19

“…We have been developing queue network and discrete event simulation (DES) models of patient flow within the acute care system. Our first project was to develop a generalized Erlang loss queue model for access to mechanical ventilators during the first wave of the pandemic (Zimmerman et al 2021). Case project input for the model was provided twice per week by the British Columbia Centre for Disease Control (BC CDC) and a report on model output was sent to the Ministry of Health to inform planning during the early stages of the pandemic.…”