Optimal age- and sex-based management of the queue to ventilators during the Covid-19 crisis

Abstract

Triage protocols for intensive care units are based on priorities assigned to presents, but ignore patients about to arrive, so a priority newcomer may not find a ventilator and its associated nursing staff available because they are occupied by a lower-priority patient who however was present at the moment of assignment. Conversely, waiting too long leads to losing elderly patients who could have been saved by ventilators. As age and sex are major determinants of mortality by Covid-19 and have the merit, in contrast to other priority criteria, of being immediately available to health professionals, the criterion is the minimization of the mean mortality rate weighted by age- and sex-specific life expectancies. The dynamics is a queuing process involving mortality and return home flows and competition between ages. The result is the determination of an optimal threshold age that can guide triage.

Keywords: Covid-19; Intensive care unit; M/M/c; Queueing theory; Triage.

Fig. 1

Compartments in the queue at hospital of patients in demand of ventilators.

Fig. 2

Estimated distribution of hospital inflows ${\hat{\lambda }}_a∕{\sum }_{a=20}^{100+}{\hat{\lambda }}_a$ by age for the whole of France from 18 March to 1 May 2020.

Fig. 3

Mean mortality rate weighted by life expectancies, for ${\hat{\mu }}_1$, ${\hat{g}}_1$, ${\hat{\mu }}_2$, ${\hat{g}}_2$, and comparison of the cases $\xi =1$ (mortality and return home rates constant in age) and $\xi =1.5$ taken as example for ${\mu }_i\left(a\right)={\hat{\mu }}_i{\xi }^{(a-70)∕30}$ and $g_i\left(a\right)={\hat{g}}_i{\xi }^{-(a-70)∕30}$, age $a$ in years.