  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.
