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

Zimmerman, S.; Rutherford, A. R.; van der Waall, A.; Norena, M.; Dodek, P.

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.