Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico, 87131, USA.
Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico, 87131, USA.
Sci Rep. 2021 Mar 22;11(1):6525. doi: 10.1038/s41598-021-85496-9.
Optimizing the impact on the economy of control strategies aiming at containing the spread of COVID-19 is a critical challenge. We use daily new case counts of COVID-19 patients reported by local health administrations from different Metropolitan Statistical Areas (MSAs) within the US to parametrize a model that well describes the propagation of the disease in each area. We then introduce a time-varying control input that represents the level of social distancing imposed on the population of a given area and solve an optimal control problem with the goal of minimizing the impact of social distancing on the economy in the presence of relevant constraints, such as a desired level of suppression for the epidemics at a terminal time. We find that with the exception of the initial time and of the final time, the optimal control input is well approximated by a constant, specific to each area, which contrasts with the implemented system of reopening 'in phases'. For all the areas considered, this optimal level corresponds to stricter social distancing than the level estimated from data. Proper selection of the time period for application of the control action optimally is important: depending on the particular MSA this period should be either short or long or intermediate. We also consider the case that the transmissibility increases in time (due e.g. to increasingly colder weather), for which we find that the optimal control solution yields progressively stricter measures of social distancing. We finally compute the optimal control solution for a model modified to incorporate the effects of vaccinations on the population and we see that depending on a number of factors, social distancing measures could be optimally reduced during the period over which vaccines are administered to the population.
优化旨在控制 COVID-19 传播的控制策略对经济的影响是一个关键挑战。我们使用美国不同大都市区（MSA）的地方卫生部门报告的 COVID-19 患者每日新增病例数来参数化一个模型，该模型很好地描述了疾病在每个地区的传播。然后，我们引入一个时变控制输入，该输入代表对特定地区人口实施的社交距离水平，并解决一个最优控制问题，目标是在存在相关约束的情况下最小化社交距离对经济的影响，例如在终端时间对流行病的期望抑制水平。我们发现，除了初始时间和最终时间外，最优控制输入很好地近似为每个区域特有的常数，这与分阶段重新开放的实施系统形成对比。对于所有考虑的区域，这个最佳水平对应于比从数据估计的水平更严格的社交距离。最优应用控制措施的时间段的正确选择很重要：具体取决于特定的 MSA，这段时间应该是短、长还是中间。我们还考虑了传染性随时间增加的情况（例如由于天气越来越冷），对于这种情况，我们发现最优控制解会产生越来越严格的社交距离措施。我们最后为考虑到疫苗对人群影响的模型计算最优控制解，并发现根据许多因素，在向人群接种疫苗的期间，社交距离措施可以最优地减少。
