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We show\u2014as proof of concept grounded on rigorous mathematical evidence\u2014that periodic, high-frequency alternation of into, and out-of, lockdown effectively mitigates second-wave effects, while allowing continued, albeit reduced, economic activity. Periodicity confers (i) predictability, which is essential for economic sustainability, and (ii) robustness, since lockdown periods are not activated by uncertain measurements over short time scales. In turn\u2014while not eliminating the virus\u2014this fast switching policy is sustainable over time, and it mitigates the infection until a vaccine or treatment becomes available, while alleviating the social costs associated with long lockdowns. Typically, the policy might be in the form of 1-day of work followed by 6-days of lockdown every week (or perhaps 2 days working, 5 days off) and it can be modified at a slow-rate based on measurements filtered over longer time scales. Our results highlight the potential efficacy of high frequency switching interventions in post lockdown mitigation. All code is available on Github at <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"https:\/\/github.com\/V4p1d\/FPSP_Covid19\" xlink:type=\"simple\">https:\/\/github.com\/V4p1d\/FPSP_Covid19<\/jats:ext-link>. A software tool has also been developed so that interested parties can explore the proof-of-concept system.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1008604","type":"journal-article","created":{"date-parts":[[2021,1,21]],"date-time":"2021-01-21T18:26:53Z","timestamp":1611253613000},"page":"e1008604","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":45,"title":["Post-lockdown abatement of COVID-19 by fast periodic switching"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2645-1064","authenticated-orcid":true,"given":"Michelangelo","family":"Bin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8236-1816","authenticated-orcid":true,"given":"Peter Y. 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The timing of one-shot interventions for epidemic control. MedRxiv [Preprint]. 2020. Available from: https:\/\/www.medrxiv.org\/content\/10.1101\/2020.03.02.20030007v2","DOI":"10.1101\/2020.03.02.20030007"},{"key":"pcbi.1008604.ref004","unstructured":"Gopinath G. The great lockdown: worst economic downturn since the great depression. In: IMFBlog. 2020. Available from: https:\/\/blogs.imf.org\/2020\/04\/14\/the-great-lockdown-worst-economic-downturn-since-the-great-depression\/."},{"key":"pcbi.1008604.ref005","doi-asserted-by":"crossref","unstructured":"Peng L, Yang W, Zhang D, Zhuge C, Hong L. Epidemic analysis of COVID-19 in China by dynamical modeling. MedRxiv [Preprint]. 2020. Available from: https:\/\/www.medrxiv.org\/content\/10.1101\/2020.02.16.20023465v1","DOI":"10.1101\/2020.02.16.20023465"},{"key":"pcbi.1008604.ref006","doi-asserted-by":"crossref","first-page":"860","DOI":"10.1126\/science.abb5793","article-title":"Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period","volume":"368","author":"SM Kissler","year":"2020","journal-title":"Science"},{"key":"pcbi.1008604.ref007","unstructured":"Parisini T, Shorten R, Stone L. The new science of lockdowns. In: Scientific American Observations [Internet]. 2020. Available from: https:\/\/blogs.scientificamerican.com\/observations\/the-new-science-of-lockdowns\/."},{"key":"pcbi.1008604.ref008","doi-asserted-by":"crossref","unstructured":"Eichenbaum MS, Rebelo S, Trabandt M. The macroeconomics of epidemics. National Bureau of Economic Research, NBER Working Paper No. 26882. 2020. Available from: https:\/\/www.nber.org\/papers\/w26882","DOI":"10.3386\/w26882"},{"key":"pcbi.1008604.ref009","doi-asserted-by":"crossref","first-page":"1595","DOI":"10.1016\/S0140-6736(20)31034-5","article-title":"COVID-19 immunity passports and vaccination certificates: scientific, equitable, and legal challenges","volume":"395","author":"AL Phelan","year":"2020","journal-title":"The Lancet"},{"key":"pcbi.1008604.ref010","unstructured":"Flaxman S, Mishra S, Gandy A, Unwin HJT, Coupland H, Mellan TA, et al. Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand. [Technical Report]. 2020. Available from: https:\/\/www.imperial.ac.uk\/media\/imperial-college\/medicine\/mrc-gida\/2020-03-30-COVID19-Report-13.pdf"},{"key":"pcbi.1008604.ref011","unstructured":"Leicester lockdown tightened as coronavirus cases rise. BBC News. 2020 June 30. Available from: https:\/\/www.bbc.co.uk\/news\/uk-england-leicestershire-53229371"},{"key":"pcbi.1008604.ref012","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/S0167-2789(00)00187-1","article-title":"Seasonally forced disease dynamics explored as switching between attractors","volume":"148","author":"MJ Keeling","year":"2001","journal-title":"Physica D: Nonlinear Phenomena"},{"key":"pcbi.1008604.ref013","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/nature05638","article-title":"Seasonal dynamics of recurrent epidemics","volume":"446","author":"L Stone","year":"2007","journal-title":"Nature"},{"key":"pcbi.1008604.ref014","doi-asserted-by":"crossref","first-page":"20190202","DOI":"10.1098\/rsif.2019.0202","article-title":"Invariant predictions of epidemic patterns from radically different forms of seasonal forcing","volume":"16","author":"I Papst","year":"2019","journal-title":"Journal of the Royal Society Interface"},{"key":"pcbi.1008604.ref015","unstructured":"Zhu L, Zhou Y. The dynamics of an SIQS epidemic model with pulse quarantine. Proc. 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On fast multi-shot epidemic interventions for post lock-down mitigation: implications for simple COVID-19 models. arXiv [Preprint] 2020 March 22. Available from: https:\/\/arxiv.org\/abs\/2003.09930"},{"key":"pcbi.1008604.ref025","unstructured":"Karin O, Y. Bar-On YM, Milo T, Katzir I, Mayo A, Korem Y, et al. Cyclic exit strategies to suppress COVID-19 and allow economic activity. MedRxiv [Preprint]. 2020 April 28. Available from: https:\/\/doi.org\/10.1101\/2020.04.04.200535792"},{"key":"pcbi.1008604.ref026","unstructured":"Meidan D, Schulmann N, Cohen R, Haber S, Yaniv E, Sarid R, et al. Alternating quarantine for sustainable mitigation of COVID-19. arXiv [Preprint] 2020 April 3. Available from: https:\/\/arxiv.org\/abs\/2004.01453."},{"key":"pcbi.1008604.ref027","doi-asserted-by":"crossref","first-page":"e0236857","DOI":"10.1371\/journal.pone.0236857","article-title":"Feasibility study of mitigation and suppression strategies for controlling COVID-19 outbreaks in London and Wuhan","volume":"15","author":"P Yang","year":"2020","journal-title":"PLOS ONE"},{"key":"pcbi.1008604.ref028","article-title":"The positive impact of lockdown in Wuhan on containing the COVID-19 outbreak in China","volume":"27","author":"H Lau","year":"2020","journal-title":"Journal of Travel Medicine"},{"key":"pcbi.1008604.ref029","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1186\/s12916-020-01597-8","article-title":"Quantifying the impact of physical distance measures on the transmission of COVID-19 in the UK","volume":"18","author":"CMMID COVID-19 working group","year":"2020","journal-title":"BMC Medicine"},{"key":"pcbi.1008604.ref030","doi-asserted-by":"crossref","first-page":"138539","DOI":"10.1016\/j.scitotenv.2020.138539","article-title":"Evaluation of the lockdowns for the SARS-CoV-2 epidemic in Italy and Spain after one month follow up","volume":"725","author":"A Tob\u00ecas","year":"2020","journal-title":"Science of The Total Environment"},{"key":"pcbi.1008604.ref031","unstructured":"The employment situation\u2014November 2020. News Release Bureau of Labor Statistics. 2020; USDL-20-2184. Available from: https:\/\/www.bls.gov\/news.release\/pdf\/empsit.pdf"},{"key":"pcbi.1008604.ref032","unstructured":"Eurostat News Release. 2020; 74. 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