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

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          Abstract

          The SARS-CoV-2 virus was first registered in Brazil by the end of February 2020. Since then, the country counts over 150000 deaths due to COVID-19 and faces a profound social and economic crisis; there is also an ongoing health catastrophe, with the majority of hospital beds in many Brazilian cities currently occupied with COVID-19 patients. Thus, a Nonlinear Model Predictive Control (NMPC) scheme used to plan appropriate social distancing measures (and relaxations) in order to mitigate the effects of this pandemic is formulated in this paper. The strategy is designed upon an adapted data-driven Susceptible–Infected–Recovered–Deceased (SIRD) model, which includes time-varying auto-regressive immunological parameters. A novel identification procedure is proposed, composed of analytical regressions, Least-Squares optimization and auto-regressive model fits. The adapted SIRD model is validated with real data and able to adequately represent the contagion curves over large forecast horizons. The NMPC strategy is designed to generate piecewise constant quarantine guidelines, which can be reassessed (relaxed/strengthened) each week. Simulation results show that the proposed NMPC technique is able to mitigate the number of infections and progressively loosen social distancing measures. With respect to a “no-control” condition, the number of deaths could be reduced in up to 30% if the proposed NMPC coordinated health policy measures are enacted.

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          The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application

          Stephen A. Lauer, Kyra Grantz, Qifang Bi … (2020)
          Background: A novel human coronavirus, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), was identified in China in December 2019. There is limited support for many of its key epidemiologic features, including the incubation period for clinical disease (coronavirus disease 2019 [COVID-19]), which has important implications for surveillance and control activities. Objective: To estimate the length of the incubation period of COVID-19 and describe its public health implications. Design: Pooled analysis of confirmed COVID-19 cases reported between 4 January 2020 and 24 February 2020. Setting: News reports and press releases from 50 provinces, regions, and countries outside Wuhan, Hubei province, China. Participants: Persons with confirmed SARS-CoV-2 infection outside Hubei province, China. Measurements: Patient demographic characteristics and dates and times of possible exposure, symptom onset, fever onset, and hospitalization. Results: There were 181 confirmed cases with identifiable exposure and symptom onset windows to estimate the incubation period of COVID-19. The median incubation period was estimated to be 5.1 days (95% CI, 4.5 to 5.8 days), and 97.5% of those who develop symptoms will do so within 11.5 days (CI, 8.2 to 15.6 days) of infection. These estimates imply that, under conservative assumptions, 101 out of every 10 000 cases (99th percentile, 482) will develop symptoms after 14 days of active monitoring or quarantine. Limitation: Publicly reported cases may overrepresent severe cases, the incubation period for which may differ from that of mild cases. Conclusion: This work provides additional evidence for a median incubation period for COVID-19 of approximately 5 days, similar to SARS. Our results support current proposals for the length of quarantine or active monitoring of persons potentially exposed to SARS-CoV-2, although longer monitoring periods might be justified in extreme cases. Primary Funding Source: U.S. Centers for Disease Control and Prevention, National Institute of Allergy and Infectious Diseases, National Institute of General Medical Sciences, and Alexander von Humboldt Foundation.
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            Temporal dynamics in viral shedding and transmissibility of COVID-19

            Xi. He, Eric Lau, Peng Wu … (2020)
            We report temporal patterns of viral shedding in 94 patients with laboratory-confirmed COVID-19 and modeled COVID-19 infectiousness profiles from a separate sample of 77 infector-infectee transmission pairs. We observed the highest viral load in throat swabs at the time of symptom onset, and inferred that infectiousness peaked on or before symptom onset. We estimated that 44% (95% confidence interval, 25-69%) of secondary cases were infected during the index cases' presymptomatic stage, in settings with substantial household clustering, active case finding and quarantine outside the home. Disease control measures should be adjusted to account for probable substantial presymptomatic transmission.
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              Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts

              Joel Hellewell, Sam Abbott, Amy Gimma … (2020)
              Summary Background Isolation of cases and contact tracing is used to control outbreaks of infectious diseases, and has been used for coronavirus disease 2019 (COVID-19). Whether this strategy will achieve control depends on characteristics of both the pathogen and the response. Here we use a mathematical model to assess if isolation and contact tracing are able to control onwards transmission from imported cases of COVID-19. Methods We developed a stochastic transmission model, parameterised to the COVID-19 outbreak. We used the model to quantify the potential effectiveness of contact tracing and isolation of cases at controlling a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-like pathogen. We considered scenarios that varied in the number of initial cases, the basic reproduction number (R 0), the delay from symptom onset to isolation, the probability that contacts were traced, the proportion of transmission that occurred before symptom onset, and the proportion of subclinical infections. We assumed isolation prevented all further transmission in the model. Outbreaks were deemed controlled if transmission ended within 12 weeks or before 5000 cases in total. We measured the success of controlling outbreaks using isolation and contact tracing, and quantified the weekly maximum number of cases traced to measure feasibility of public health effort. Findings Simulated outbreaks starting with five initial cases, an R 0 of 1·5, and 0% transmission before symptom onset could be controlled even with low contact tracing probability; however, the probability of controlling an outbreak decreased with the number of initial cases, when R 0 was 2·5 or 3·5 and with more transmission before symptom onset. Across different initial numbers of cases, the majority of scenarios with an R 0 of 1·5 were controllable with less than 50% of contacts successfully traced. To control the majority of outbreaks, for R 0 of 2·5 more than 70% of contacts had to be traced, and for an R 0 of 3·5 more than 90% of contacts had to be traced. The delay between symptom onset and isolation had the largest role in determining whether an outbreak was controllable when R 0 was 1·5. For R 0 values of 2·5 or 3·5, if there were 40 initial cases, contact tracing and isolation were only potentially feasible when less than 1% of transmission occurred before symptom onset. Interpretation In most scenarios, highly effective contact tracing and case isolation is enough to control a new outbreak of COVID-19 within 3 months. The probability of control decreases with long delays from symptom onset to isolation, fewer cases ascertained by contact tracing, and increasing transmission before symptoms. This model can be modified to reflect updated transmission characteristics and more specific definitions of outbreak control to assess the potential success of local response efforts. Funding Wellcome Trust, Global Challenges Research Fund, and Health Data Research UK.
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                Author and article information

                Journal
                Journal ID (nlm-ta): ISA Trans
                Journal ID (iso-abbrev): ISA Trans
                Title: ISA Transactions
                Publisher: ISA. Published by Elsevier Ltd.
                ISSN (Print): 0019-0578
                ISSN (Electronic): 1879-2022
                Publication date PMC-release: 8 December 2020
                Publication date (Electronic): 8 December 2020
                Affiliations
                [a ]Renewable Energy Research Group (GPER), Department of Automation and Systems (DAS), Federal University of Santa Catarina (UFSC), Florianópolis, Brazil
                [b ]Department of Chemical Engineering (DEQ), Federal University of Bahia (UFBA), 02 Professor Aristides Novis St., Salvador, BA-40210910, Brazil
                [c ]CIESOL, Department of Informatics, University of Almería, Ctra. Sacramento s/n 04120, Almería, Spain
                Author notes
                [* ]Corresponding author.
                Article
                Publisher Item ID: S0019-0578(20)30531-0
                DOI: 10.1016/j.isatra.2020.12.012
                PMC ID: 7834916
                PubMed ID: 33309260
                SO-VID: 2848a644-2113-4406-ba61-2f19e83ce0b3
                Copyright © © 2020 ISA. Published by Elsevier Ltd. All rights reserved.
                License:

                Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.

                History
                Date received : 19 July 2020
                Date revision received : 4 December 2020
                Date accepted : 4 December 2020
                Categories
                Subject: Research Article

                Keywords: nonlinear model predictive control,covid-19,social isolation,sird model,system identification
                Data availability:
                Keywords: nonlinear model predictive control, covid-19, social isolation, sird model, system identification

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