The global COVID-19 pandemic (SARS-CoV-2 virus) is the defining health crisis of our century. Due to the absence of vaccines and drugs that can help to fight it, the world solution to control the spread has been to consider public social distance measures that avoids the saturation of the health system. In this context, we investigate a Model Predictive Control (MPC) framework to determine the time and duration of social distancing policies. We use Brazilian data in the period from March to May of 2020. The available data regarding the number of infected individuals and deaths suffers from sub-notification due to the absence of mass tests and the relevant presence of the asymptomatic individuals. We estimate variations of the SIR model using an uncertainty-weighted Least-Squares criterion that considers both nominal and inconsistent-data conditions. Moreover, we add to our versions of the SIR model an additional dynamic state variable to mimic the response of the population to the social distancing policies determined by the government that affects the speed of COVID-19 transmission. Our control framework is within a mixed-logical formalism, since the decision variable is forcefully binary (the existence or the absence of social distance policy). A dwell-time constraint is included to avoid harsh shifting between these two states. Finally, we present simulation results to illustrate how such optimal control policy would operate. These results point out that no social distancing should be relaxed before mid August 2020. If relaxations are necessary, they should not be performed before the beginning this date and should be in small periods, no longer than 25 days. This paradigm would proceed roughly until January/2021. The second peak of infections, which has a forecast to the beginning of October, can be reduced if the periods of no-isolation days are shortened.

中文翻译：

---

巴西 COVID-19 (SARS-CoV-2) 社会疏远政策的最佳预测控制策略

全球 COVID-19 大流行（SARS-CoV-2 病毒）是本世纪决定性的健康危机。由于缺乏可以帮助对抗它的疫苗和药物，控制传播的世界解决方案是考虑采取公共社交距离措施，以避免卫生系统饱和。在这种情况下，我们研究了模型预测控制 (MPC) 框架，以确定社会疏远政策的时间和持续时间。我们使用的是 2020 年 3 月至 5 月期间的巴西数据。由于没有进行大规模检测以及相关无症状个体的存在，有关感染人数和死亡人数的可用数据受到了子通知的影响。我们使用不确定性加权最小二乘标准来估计 SIR 模型的变化，该标准考虑了名义数据和不一致数据条件。此外，我们在 SIR 模型的版本中添加了一个额外的动态状态变量，以模拟人口对政府确定的影响 COVID-19 传播速度的社会疏远政策的反应。我们的控制框架属于混合逻辑形式，因为决策变量是强制二元的（社会距离政策的存在或不存在）。包含停留时间约束以避免在这两种状态之间剧烈转换。最后，我们展示了模拟结果来说明这种最优控制策略将如何运作。这些结果指出，在 2020 年 8 月中旬之前，不应放松社交距离。如果需要放松，则不应在此日期开始之前进行，并且应在短时间内进行，不超过 25 天。这种范式将大致持续到 2021 年 1 月。如果缩短非隔离天数，第二次感染高峰预计会在 10 月初出现。