  In this paper, we propose a two-group SIR epidemic model to simulate the
outcome of stay-at-home policy and wearing face masks during the first COVID-19
epidemic wave in the United States. Based on our proposed model, we further use
the optimal control approach (with the objective of minimizing total deaths) to
find the optimal dynamical distribution of face masks between the healthcare
workers and the general public. It is not surprising that all the face masks
should be solely reserved for the healthcare workers if the supply is short.
However, when the supply is indeed sufficient, our numerical study indicates
that the general public should share a large portion of face masks at the
beginning of an epidemic wave to dramatically reduce the death toll. This
interesting result partially contradicts with the guideline advised by the US
Surgeon General and the Centers for Disease Control and Prevention (CDC) in
March 2020. The optimality of this sounding CDC guideline highly depends on the
supply level of face masks that changes frequently, and hence it should be
adjusted according to the supply of face masks.
