Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026, USA.
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70503, USA.
Math Biosci Eng. 2023 May 24;20(7):12472-12485. doi: 10.3934/mbe.2023555.
In this paper, we propose a two-group SIR epidemic model to simulate the outcome of the stay-at-home policy and the imposed face mask policy during the first COVID-19 epidemic wave in the United States. Then, we use a dynamic optimal control approach (with the objective of minimizing total deaths) to find the optimal dynamical distribution of face masks between healthcare workers and the general public. It is not surprising that all face masks should be solely reserved for 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 the epidemic wave to dramatically reduce the death toll. This interesting result partially contradicts 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, which changes frequently; hence, it should be adjusted according to the supply of face masks.
在本文中，我们提出了一个两群组 SIR 传染病模型，以模拟美国第一次 COVID-19 疫情期间的居家隔离政策和强制佩戴口罩政策的结果。然后，我们使用动态最优控制方法（以最小化总死亡人数为目标）来寻找医护人员和公众之间口罩的最优动态分配。如果供应短缺，所有口罩都应该专门留给医护人员，这并不奇怪。然而，当供应确实充足时，我们的数值研究表明，在疫情初期，公众应该共享大量口罩，以显著降低死亡人数。这一有趣的结果部分与美国外科医生总干事和疾病控制与预防中心（CDC）在 2020 年 3 月建议的指南相矛盾。该 CDC 指南的最优性高度取决于口罩的供应水平，而口罩的供应水平经常变化；因此，应根据口罩的供应情况进行调整。
