Ideally, no one would have to wait for access to a life-saving device, such as a ventilator. But during the coronavirus disease 2019 (COVID-19) crisis, many hospitals have run short of ventilators — as well as respiratory therapists (RTs) who are trained to operate them — while other facilities scramble to prepare for the coming demand surge. Any patient who needs a ventilator might not be able to get one, imperiling their survival. Mathematically, the delay that a patient may experience depends on the number of ventilators at the hospital, the number of patients who need them, and the average time that patients spend on them. COVID-19 increases the arrival rate of ventilator patients at hospitals, and these patients have longer lengths of stay, resulting in the sharp rise in demand for ventilators. Hospitals need to estimate how many ventilators they will need to respond to this crisis, accounting for increased uncertain arrival rates and lengths of stay. At the same time, regional coordinators want to know which hospitals have the greatest need for the next spare ventilator or available capacity for the next ventilator patient.
To address the ventilator allocation problem at both of these levels, the authors of this Perspective designed a model that can be used to calculate the number of ventilators and RTs needed to achieve a target wait time — the average delay for a ventilator experienced by a new patient. The target wait time corresponds with a probability that any wait is experienced: If the average wait is small, most patients would in fact experience no wait at all. At the regional level, planners can use this model to assess needs and allocate patients or resources efficiently across hospitals in order to minimize patient wait time.