2020/07/19 by Marcelo Menezes Morato, Morato, Marcelo M., Igor M. L. Pataro +5
Mathematics · Psychology · #COVID-19 and Mental Health #COVID-19 epidemiological studies #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Mental Health Research Topics #Optimization and Control (math.OC) #Physics and Society (physics.soc-ph) #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.2007.09686
openalex publication_date 2020/07/19 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this paper, we formulate a Nonlinear Model Predictive Control (NMPC) to\nplan appropriate social distancing measures (and relaxations) in order to\nmitigate the COVID-19 pandemic effects, considering the contagion development\nin Brazil. The NMPC strategy is designed upon an adapted data-driven\nSusceptible-Infected-Recovered-Deceased (SIRD) contagion model, which takes\ninto account the effects of social distancing. Furthermore, the adapted SIRD\nmodel includes time-varying auto-regressive contagion parameters, which\ndynamically converge according to the stage of the pandemic. This new model is\nidentified through a three-layered procedures, with analytical regressions,\nLeast-Squares optimization runs and auto-regressive model fits. The data-driven\nmodel is validated and shown to adequately describe the contagion curves over\nlarge forecast horizons. In this model, control input is defined as finitely\nparametrized values for social distancing guidelines, which directly affect the\ntransmission and infection rates of the SARS-CoV-2 virus. The NMPC strategy\ngenerates piece-wise constant quarantine guidelines which can be\nrelaxed/strengthen as each week passes. The implementation of the method is\npursued through a search mechanism, since the control is finitely parametrized\nand, thus, there exist a finite number of possible control sequences.\nSimulation essays are shown to illustrate the results obtained with the\nproposed closed-loop NMPC strategy, which is able to mitigate the number of\ninfections and progressively loosen social distancing measures. With respect to\nan "open-loop"/no control condition, the number of deaths still could be\nreduced in up to 30 %. The forecast preview an infection peak to September 2nd,\n2020, which could lead to over 1.5 million deaths if no coordinate health\npolicy is enacted. The framework serves as guidelines for possible public\nhealth policies in Brazil.\n