Abstract
We consider a model that distinguishes susceptible; infected, but not yet infectious; pre-symptomatic, symptomatic, asymptomatic, and hospitalized infectious; recovered and dead members of two groups: healthcare workers (HCW) and members of the community that they serve. Because of the frequency or duration of their exposures to SARS-CoV-2, a greater fraction of HCW would experience severe COVID-19 symptoms that require medical care, which reduces mortality rates, absent personal protective equipment (PPE). While N95 masks (and, possibly, other scarce medical resources) are available to members of both groups, they do not use them equally well (i.e. efficacy and compliance differ). We investigated the optimal allocation of potentially scarce medical resources between these groups to control the pandemic and reduce overall infections and mortality via derivation and analysis of expressions for the reproduction numbers and final size. We also simulated prevalence and cumulative incidence, quantities relevant to surge capacity and population immunity, respectively. We found that, under realistic conditions, the optimal allocation is virtually or entirely to HCW, but that allocation of surplus masks and other medical resources to members of the general community also reduces infections and deaths.