{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T20:00:52Z","timestamp":1772136052785,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T00:00:00Z","timestamp":1624838400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T00:00:00Z","timestamp":1624838400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The SARS-CoV-2 pandemic triggered substantial economic and social disruptions. Mitigation policies varied across countries based on resources, political conditions, and human behavior. In the absence of widespread vaccination able to induce herd immunity, strategies to coexist with the virus while minimizing risks of surges are paramount, which should work in parallel with reopening societies. To support these strategies, we present a predictive control system coupled with a nonlinear model able to optimize the level of policies to stop epidemic growth. We applied this system to study the unfolding of COVID-19 in Bahia, Brazil, also assessing the effects of varying population compliance. We show the importance of finely tuning the levels of enforced measures to achieve SARS-CoV-2 containment, with periodic interventions emerging as an optimal control strategy in the long-term.<\/jats:p>","DOI":"10.1038\/s41598-021-92636-8","type":"journal-article","created":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T06:02:47Z","timestamp":1624860167000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["A control framework to optimize public health policies in the course of the COVID-19 pandemic"],"prefix":"10.1038","volume":"11","author":[{"given":"Igor M. L.","family":"Pataro","sequence":"first","affiliation":[]},{"given":"Juliane F.","family":"Oliveira","sequence":"additional","affiliation":[]},{"given":"Marcelo M.","family":"Morato","sequence":"additional","affiliation":[]},{"given":"Alan A. S.","family":"Amad","sequence":"additional","affiliation":[]},{"given":"Pablo I. P.","family":"Ramos","sequence":"additional","affiliation":[]},{"given":"Felipe A. C.","family":"Pereira","sequence":"additional","affiliation":[]},{"given":"Mateus S.","family":"Silva","sequence":"additional","affiliation":[]},{"given":"Daniel C. P.","family":"Jorge","sequence":"additional","affiliation":[]},{"given":"Roberto F. S.","family":"Andrade","sequence":"additional","affiliation":[]},{"given":"Mauricio L.","family":"Barreto","sequence":"additional","affiliation":[]},{"given":"Marcus Americano da","family":"Costa","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,6,28]]},"reference":[{"key":"92636_CR1","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1038\/s41586-020-2404-8","volume":"584","author":"S Hsiang","year":"2020","unstructured":"Hsiang, S. et al. The effect of large-scale anti-contagion policies on the COVID-19 pandemic. Nature 584, 262 (2020).","journal-title":"Nature"},{"key":"92636_CR2","doi-asserted-by":"crossref","unstructured":"Haug, N. et al. Ranking the effectiveness of worldwide COVID-19 government interventions. Nat. Hum. Behav. 1\u201310 (2020).","DOI":"10.1101\/2020.07.06.20147199"},{"key":"92636_CR3","doi-asserted-by":"publisher","first-page":"1535","DOI":"10.1057\/s41287-020-00314-8","volume":"32","author":"G Valensisi","year":"2020","unstructured":"Valensisi, G. Covid-19 and global poverty: are LDCs being left behind? Eur. J. Dev. Res. 32, 1535\u20131557 (2020).","journal-title":"Eur. J. Dev. Res."},{"key":"92636_CR4","unstructured":"Laborde, D., Will, M., & Vos, R. COVID-19 and global food security. J.\u00a0Swinnen, J.\u00a0McDermott, eds. (International Food Policy Research Institute\u2013IFPRI, 2020), vol.\u00a032, chap.\u00a02, pp. 16\u201319. Washington, DC."},{"key":"92636_CR5","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1016\/S1473-3099(20)30120-1","volume":"20","author":"E Dong","year":"2020","unstructured":"Dong, E., Du, H. & Gardner, L. An interactive web-based dashboard to track COVID-19 in real time. Lancet Infect. Dis. 20, 533 (2020).","journal-title":"Lancet Infect. Dis."},{"key":"92636_CR6","doi-asserted-by":"publisher","first-page":"2423","DOI":"10.1590\/1413-81232020256.1.10502020","volume":"25","author":"EM Aquino","year":"2020","unstructured":"Aquino, E. M., Silveira, I. H., Pescarini, J. M., Aquino, R. & Souza-Filho, J. . A. . d. Medidas de distanciamento social no controle da pandemia de COVID-19: potenciais impactos e desafios no Brasil. Ci\u00eancia & Sa\u00fade Coletiva 25, 2423 (2020).","journal-title":"Ci\u00eancia &amp; Sa\u00fade Coletiva"},{"key":"92636_CR7","doi-asserted-by":"crossref","unstructured":"Jorge, D. C. P. et\u00a0al. Assessing the nationwide impact of COVID-19 mitigation policies on the transmission rate of SARS-CoV-2 in Brazil. Epidemics 35, (2020).","DOI":"10.1016\/j.epidem.2021.100465"},{"key":"92636_CR8","doi-asserted-by":"publisher","first-page":"1255","DOI":"10.1126\/science.abd2161","volume":"369","author":"DS Candido","year":"2020","unstructured":"Candido, D. S. et\u00a0al. Evolution and epidemic spread of SARS-CoV-2 in Brazil. Science (New York, N.Y.) 369, 1255\u20131260 (2020).","journal-title":"Science"},{"key":"92636_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41467-020-20314-w","volume":"12","author":"J Oliveira","year":"2021","unstructured":"Oliveira, J. et al. (2021) Mathematical modeling of COVID-19 in 14.8 million individuals in Bahia, Brazil. Nat. Commun. 12, 1 (2021).","journal-title":"Nat. Commun."},{"key":"92636_CR10","doi-asserted-by":"crossref","unstructured":"Costa, G. S., Cota, W., Ferreira, S. C. Outbreak diversity in epidemic waves propagating through distinct geographical scales. Phys. Rev. Research 2, (2020).","DOI":"10.1103\/PhysRevResearch.2.043306"},{"key":"92636_CR11","doi-asserted-by":"crossref","unstructured":"Melo, C. M. D., Silva, G. A., Melo, A. R. & Freitas, A. C. COVID-19 pandemic outbreak: the Brazilian reality from the first case to the collapse of health services. Anais da Academia Brasileira de Ci\u00eancias 92, (2020).","DOI":"10.1590\/0001-3765202020200709"},{"key":"92636_CR12","unstructured":"Morato, M. M., Pataro, I. M. L., Americano da Costa, M. V., Normey-Rico, J. E. A parametrized nonlinear predictive control strategy for relaxing COVID-19 social distancing measures in Brazil. ISA Trans. (2020)."},{"key":"92636_CR13","doi-asserted-by":"crossref","unstructured":"Buss, L. F. et al. Three-quarters attack rate of SARS-CoV-2 in the Brazilian amazon during a largely unmitigated epidemic. Science 371, (2020).","DOI":"10.1126\/science.abe9728"},{"key":"92636_CR14","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1038\/s41577-020-00451-5","volume":"20","author":"A Fontanet","year":"2020","unstructured":"Fontanet, A. & Cauchemez, S. COVID-19 herd immunity: where are we?. Nat. Rev. Immunol. 20, 583 (2020).","journal-title":"Nat. Rev. Immunol."},{"key":"92636_CR15","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1126\/science.abf7921","volume":"371","author":"D Sridhar","year":"2021","unstructured":"Sridhar, D. & Gurdasani, D. Herd immunity by infection is not an option. Science 371, 230 (2021).","journal-title":"Science"},{"key":"92636_CR16","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1038\/s41586-020-2405-7","volume":"584","author":"S Flaxman","year":"2020","unstructured":"Flaxman, S. et al. Estimating the effects of non-pharmaceutical interventions on COVID-19 in europe. Nature 584, 257 (2020).","journal-title":"Nature"},{"key":"92636_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2020.07.005","volume":"869","author":"E Estrada","year":"2020","unstructured":"Estrada, E. Covid-19 and SARS-CoV-2. Modeling the present, looking at the future. Phys. Rep. 869, 1 (2020).","journal-title":"Phys. Rep."},{"key":"92636_CR18","doi-asserted-by":"publisher","first-page":"1465","DOI":"10.1126\/science.abc5096","volume":"369","author":"NW Ruktanonchai","year":"2020","unstructured":"Ruktanonchai, N. W. et al. Assessing the impact of coordinated COVID-19 exit strategies across Europe. Science 369, 1465 (2020).","journal-title":"Science"},{"key":"92636_CR19","doi-asserted-by":"crossref","unstructured":"Dehning, J. et al. Inferring change points in the spread of COVID-19 reveals the effectiveness of interventions. Science 369, (2020).","DOI":"10.1126\/science.abb9789"},{"key":"92636_CR20","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1126\/science.aba9757","volume":"368","author":"M Chinazzi","year":"2020","unstructured":"Chinazzi, M. et al. The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak. Science 368, 395 (2020).","journal-title":"Science"},{"key":"92636_CR21","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.ijid.2015.10.024","volume":"42","author":"GM Knight","year":"2016","unstructured":"Knight, G. M. et al. Bridging the gap between evidence and policy for infectious diseases: How models can aid public health decision-making. Int. J. Infect. Dis. 42, 17 (2016).","journal-title":"Int. J. Infect. Dis."},{"key":"92636_CR22","doi-asserted-by":"crossref","unstructured":"Djidjou-Demasse, R. et al. Optimal COVID-19 epidemic control until vaccine deployment. medRxiv (2020).","DOI":"10.1101\/2020.04.02.20049189"},{"key":"92636_CR23","doi-asserted-by":"crossref","unstructured":"K\u00f6hler, J. et al. Robust and optimal predictive control of the COVID-19 outbreak. Annual Reviews in Control (2020).","DOI":"10.1016\/j.arcontrol.2020.11.002"},{"key":"92636_CR24","doi-asserted-by":"publisher","first-page":"10711","DOI":"10.1038\/s41598-020-67459-8","volume":"10","author":"C Tsay","year":"2020","unstructured":"Tsay, C., Lejarza, F., Stadtherr, M. & Baldea, M. Modeling, state estimation, and optimal control for the us COVID-19 outbreak. Sci. Rep. 10, 10711 (2020).","journal-title":"Sci. Rep."},{"key":"92636_CR25","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1016\/j.arcontrol.2020.07.001","volume":"50","author":"MM Morato","year":"2020","unstructured":"Morato, M. M., Bastos, S. B., Cajueiro, D. O. & Normey-Rico, J. E. An optimal predictive control strategy for COVID-19 (SARS-CoV-2) social distancing policies in Brazil. Ann. Rev. Control 50, 417 (2020).","journal-title":"Ann. Rev. Control"},{"key":"92636_CR26","doi-asserted-by":"publisher","first-page":"27087","DOI":"10.1073\/pnas.2010836117","volume":"117","author":"C Xiong","year":"2020","unstructured":"Xiong, C., Hu, S., Yang, M., Luo, W. & Zhang, L. Mobile device data reveal the dynamics in a positive relationship between human mobility and COVID-19 infections. Proc. Natl. Acad. Sci. 117, 27087 (2020).","journal-title":"Proc. Natl. Acad. Sci."},{"key":"92636_CR27","first-page":"1","volume":"14","author":"PJ Hotez","year":"2020","unstructured":"Hotez, P. J., Huete-Perez, J. A. & Bottazzi, M. E. COVID-19 in the Americas and the erosion of human rights for the poor. PLOS Neglect. Trop. Dis. 14, 1 (2020).","journal-title":"PLOS Neglect. Trop. Dis."},{"key":"92636_CR28","unstructured":"Materials and methods are available as supplementary materials at the Nature Scientific Reports website."},{"key":"92636_CR29","unstructured":"InLoco, Social isolation map COVID-19 (in portuguese) (2020). https:\/\/mapabrasileirodacovid.inloco.com.br\/pt. Accessed Jan 22, 2021."},{"key":"92636_CR30","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1590\/0034-761220200549","volume":"55","author":"LG Barberia","year":"2021","unstructured":"Barberia, L. G., Cantarelli, L. G. R., de Faria Oliveira, M. L. C., de Paula Moreira, N. & Rosa, I. S. C. The effect of state-level social distancing policy stringency on mobility in the states of Brazil. Revista de Administra\u00e7\u00e3o P\u00fablica [online] 55, 27 (2021).","journal-title":"Revista de Administra\u00e7\u00e3o P\u00fablica [online]"},{"key":"92636_CR31","doi-asserted-by":"publisher","first-page":"4363","DOI":"10.1016\/j.aej.2021.03.004","volume":"60","author":"SB Bastos","year":"2021","unstructured":"Bastos, S. B., Morato, M. M., Cajueiro, D. O. & Normey-Rico, J. E. The COVID-19 (SARS-CoV-2) uncertainty tripod in Brazil: assessments on model-based predictions with large under-reporting. Alexandria Eng. J. 60, 4363 (2021).","journal-title":"Alexandria Eng. J."},{"key":"92636_CR32","unstructured":"Scottish Government, Coronavirus (COVID-19): local protection levels (2020). https:\/\/www.gov.scot\/publications\/coronavirus-covid-19-stay-at-home-guidance. Accessed Jan 10, 2021."},{"key":"92636_CR33","unstructured":"The White House, Guidelines: opening up America again (2020). https:\/\/www.whitehouse.gov\/openingamerica. Accessed Jun 1, 2020."},{"key":"92636_CR34","unstructured":"State Government of S\u00e3o Paulo, Brazil, S\u00e3o Paulo plan: conscious resuming (Plano S\u00e3o Paulo: retomada consciente) (2021). https:\/\/www.saopaulo.sp.gov.br\/planosp. Accessed Jan 10, 2021."},{"key":"92636_CR35","unstructured":"Government of Ireland, Resilience and Recovery 2020-2021: Plan for Living with COVID-19 (2021). https:\/\/www.gov.ie\/en\/campaigns\/resilience-recovery-2020-2021-plan-for-living-with-covid-19. Accessed Jan 10, 2021."},{"key":"92636_CR36","unstructured":"North Carolina state government, Staying Ahead of the Curve (2021). https:\/\/www.nc.gov\/covid-19\/staying-ahead-curve. Accessed Jan 10, 2021."},{"key":"92636_CR37","doi-asserted-by":"crossref","unstructured":"Larrosa, J. M. C. SARS-CoV-2 in Argentina: lockdown, mobility, and contagion. J. Med. Virol. (2020).","DOI":"10.1101\/2020.10.03.20203232"},{"key":"92636_CR38","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/s10654-020-00649-w","volume":"35","author":"R Chowdhury","year":"2020","unstructured":"Chowdhury, R. et al. Dynamic interventions to control COVID-19 pandemic: a multivariate prediction modelling study comparing 16 worldwide countries. Eur. J. Epidemiol. 35, 389 (2020).","journal-title":"Eur. J. Epidemiol."},{"key":"92636_CR39","doi-asserted-by":"publisher","first-page":"860","DOI":"10.1126\/science.abb5793","volume":"368","author":"SM Kissler","year":"2020","unstructured":"Kissler, S. M., Tedijanto, C., Goldstein, E., Grad, Y. H. & Lipsitch, M. Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period. Science 368, 860 (2020).","journal-title":"Science"},{"key":"92636_CR40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pone.0244706","volume":"16","author":"J Hindes","year":"2021","unstructured":"Hindes, J., Bianco, S. & Schwartz, I. B. Optimal periodic closure for minimizing risk in emerging disease outbreaks. PLoS One 16, 1 (2021).","journal-title":"PLoS One"},{"key":"92636_CR41","doi-asserted-by":"publisher","first-page":"1","DOI":"10.7189\/jogh.10.020375","volume":"10","author":"O Aiyewumi","year":"2020","unstructured":"Aiyewumi, O. & Okeke, M. I. The myth that Nigerians are immune to SARS-CoV-2 and that COVID-19 is a hoax are putting lives at risk. J. Glob. Health 10, 1 (2020).","journal-title":"J. Glob. Health"},{"key":"92636_CR42","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.3389\/fphar.2020.01205","volume":"11","author":"OO Ogunleye","year":"2020","unstructured":"Ogunleye, O. O. et al. Response to the novel corona virus (COVID-19) pandemic across Africa: successes, challenges, and implications for the future. Front. Pharmacol. 11, 1205 (2020).","journal-title":"Front. Pharmacol."},{"key":"92636_CR43","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1126\/science.abb6105","volume":"368","author":"H Tian","year":"2020","unstructured":"Tian, H. et al. An investigation of transmission control measures during the first 50 days of the COVID-19 epidemic in China. Science 368, 638 (2020).","journal-title":"Science"},{"key":"92636_CR44","doi-asserted-by":"crossref","unstructured":"Chan, D. K., Zhang, C.-Q., & Josefsson, K.\u00a0W. Why people failed to adhere to COVID-19 preventive behaviors? perspectives from an integrated behavior change model. Infect. Control Hosp. Epidemiol. 1\u20136 (2020).","DOI":"10.1017\/ice.2020.245"},{"key":"92636_CR45","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1007\/s10865-014-9616-z","volume":"38","author":"DK-C Chan","year":"2015","unstructured":"Chan, D.K.-C. et al. Preventing the spread of H1N1 influenza infection during a pandemic: autonomy-supportive advice versus controlling instruction. J. Behav. Med. 38, 416 (2015).","journal-title":"J. Behav. Med."},{"key":"92636_CR46","unstructured":"Hale, T. et al. Oxford COVID-19 Government Response Tracker (2020). https:\/\/covidtracker.bsg.ox.ac.uk\/. Accessed Dec 15, 2020"},{"key":"92636_CR47","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/j.ifacol.2018.11.029","volume":"51","author":"KMM Rathai","year":"2018","unstructured":"Rathai, K. M. M., Alamir, M., Sename, O. & Tang, R. A parameterized NMPC scheme for embedded control of semi-active suspension system. IFAC-PapersOnLine 51, 301 (2018).","journal-title":"IFAC-PapersOnLine"}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-92636-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-92636-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-92636-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,3]],"date-time":"2022-12-03T05:24:18Z","timestamp":1670045058000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-92636-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,28]]},"references-count":47,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["92636"],"URL":"https:\/\/doi.org\/10.1038\/s41598-021-92636-8","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2021.01.28.21250692","asserted-by":"object"}]},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,28]]},"assertion":[{"value":"17 March 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 June 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 June 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"13403"}}