An optimal predictive control strategy for COVID-19 (SARS-CoV-2) social distancing policies in Brazil

Abstract

This paper formulates a Model Predictive Control (MPC) policy to mitigate the COVID-19 contagion in Brazil, designed as optimal On-Off social isolation strategy. The proposed optimization algorithm is able to determine the time and duration of social distancing policies in the country. The achieved results are based on data from the period between March and May of 2020, regarding the cumulative number of infections and deaths due to the SARS-CoV-2 virus. This dataset is assumably largely sub-notified due to the absence of mass testing in Brazil. Thus, the MPC is based on a SIR model which is identified using an uncertainty-weighted Least-Squares criterion. Furthermore, this model includes an additional dynamic variable that mimics the response of the population to the social distancing policies determined by the government, which affect the COVID-19 transmission rate. The proposed control method is set within a mixed-logical formalism, since the decision variable is forcefully binary (existence or the absence of social distance policy). A dwell-time constraint is included to avoid too frequent shifts between these two inputs. The achieved simulation results illustrate how such optimal control method would operate in practice, pointing out that no social distancing should be relaxed before mid August 2020. If relaxations are necessary, they should not be performed before this date and should be in small periods, no longer than 25 days. This paradigm would proceed roughly until January/2021. The results also indicate a possible second peak of infections, which has a forecast to the beginning of October. This peak can be reduced if the periods of days with relaxed social isolation measures are shortened.

A parametrized nonlinear predictive control strategy for relaxing COVID-19 social distancing measures in Brazil

“…COVID-19 cases and deaths. The expectations disclosed on the recent literature suggest catastrophic scenarios for the coming months, which may last until mid- , or even later [8] , [9] , [10] .…”

“…The approach considers that the control input directly affects the infection and transmission rates (parameters of the SIRD model); Alleman et al [20] consider the application of a NMPC algorithm regarding the data from Belgium. The control input is the actual isolation parameter which attenuates the transmission factor in the SIRD model; Morato et al [10] consider an optimal On–Off MPC design, which is formulated as mixed-integer problem with dwell-time constraints. Furthermore, the response of the population to social isolation rules is modeled with an additional dynamic variable, which is incorporated to the SIRD dynamics.…”

“…Morato et al [10] consider an optimal On–Off MPC design, which is formulated as mixed-integer problem with dwell-time constraints. Furthermore, the response of the population to social isolation rules is modeled with an additional dynamic variable, which is incorporated to the SIRD dynamics.…”

DeepSOCIAL: Social Distancing Monitoring and Infection Risk Assessment in COVID-19 Pandemic

“…Therefore, it is important all individuals maintain controlled behaviours and observe social distancing. Many research works such as [5][6][7] have proved social-distancing as an effective non-pharmacological approach and an important inhibitor for limiting the transmission of contagious diseases such as H1N1, SARS, and COVID-19. Figure 2 demonstrates the effect of following appropriate social distancing guidelines to reduce the rate of infection transmission among individuals [8,9].…”

DeepSOCIAL: Social Distancing Monitoring and Infection Risk Assessment in COVID-19 Pandemic

“…Many research works such as [5], [6], [7] have proved social-distancing as an effective non-pharmacological approach and an important inhibitor for limiting the transmission of contagious diseases such as H1N1, SARS, and COVID-19. Figure 2 demonstrates the effect of following appropriate social distancing guideline to reduce the rate of infection transmission among individuals [8], [9].…”