Dynamic optimal allocation of medical resources: a case study of face masks during the first COVID-19 epidemic wave in the United States

Jun Liu; Xiang-Sheng Wang; Jun Liu; Xiang-Sheng Wang

doi:10.3934/mbe.2023555

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 12472-12485. doi: 10.3934/mbe.2023555

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Dynamic optimal allocation of medical resources: a case study of face masks during the first COVID-19 epidemic wave in the United States

Jun Liu ¹,
Xiang-Sheng Wang ^{2
,
,}

1.
Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026, USA
2.
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70503, USA

Academic Editor: Jin Wang

Received: 07 April 2023 Revised: 18 May 2023 Accepted: 18 May 2023 Published: 24 May 2023

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.
- COVID-19,
- dynamic optimal control,
- pseudospectral method,
- face masks,
- healthcare workers
Citation: Jun Liu, Xiang-Sheng Wang. Dynamic optimal allocation of medical resources: a case study of face masks during the first COVID-19 epidemic wave in the United States[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 12472-12485. doi: 10.3934/mbe.2023555

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Abstract

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.

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