A Parametrized Nonlinear Predictive Control Strategy for Relaxing COVID-19 Social Distancing Measures in Brazil

Abstract: In this paper, we formulate a Nonlinear Model Predictive Control (NMPC) to plan appropriate social distancing measures (and relaxations) in order to mitigate the COVID-19 pandemic effects, considering the contagion development in Brazil. The NMPC strategy is designed upon an adapted data-driven Susceptible-Infected-Recovered-Deceased (SIRD) contagion model, which takes into account the effects of social distancing. Furthermore, the adapted SIRD model includes time-varying auto-regressive contagion parameters, which dynamically converge according to the stage of the pandemic. This new model is identified through a three-layered procedures, with analytical regressions, Least-Squares optimization runs and auto-regressive model fits. The data-driven model is validated and shown to adequately describe the contagion curves over large forecast horizons. In this model, control input is defined as finitely parametrized values for social distancing guidelines, which directly affect the transmission and infection rates of the SARS-CoV-2 virus. The NMPC strategy generates piece-wise constant quarantine guidelines which can be relaxed/strengthen as each week passes. The implementation of the method is pursued through a search mechanism, since the control is finitely parametrized and, thus, there exist a finite number of possible control sequences. Simulation essays are shown to illustrate the results obtained with the proposed closed-loop NMPC strategy, which is able to mitigate the number of infections and progressively loosen social distancing measures. With respect to an "open-loop"/no control condition, the number of deaths still could be reduced in up to 30 %. The forecast preview an infection peak to September 2nd, 2020, which could lead to over 1.5 million deaths if no coordinate health policy is enacted. The framework serves as guidelines for possible public health policies in Brazil.