{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T13:10:20Z","timestamp":1790601020816,"version":"4.1.0"},"reference-count":56,"publisher":"National Academy of Sciences","issue":"10","license":[{"start":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T00:00:00Z","timestamp":1677456000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee","doi-asserted-by":"publisher","award":["HKU C7123-20G"],"award-info":[{"award-number":["HKU C7123-20G"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee","doi-asserted-by":"publisher","award":["HKU C7123-20G"],"award-info":[{"award-number":["HKU C7123-20G"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]},{"name":"RiFood","award":["RiFood 1-CD52"],"award-info":[{"award-number":["RiFood 1-CD52"]}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2023,3,7]]},"abstract":"<jats:p>\n                    The two nearby Amazonian cities of Iquitos and Manaus endured explosive COVID-19 epidemics and may well have suffered the world\u2019s highest infection and death rates over 2020, the first year of the pandemic. State-of-the-art epidemiological and modeling studies estimated that the populations of both cities came close to attaining herd immunity (&gt;70% infected) at the termination of the first wave and were thus protected. This makes it difficult to explain the more deadly second wave of COVID-19 that struck again in Manaus just months later, simultaneous with the appearance of a new P.1 variant of concern, creating a catastrophe for the unprepared population. It was suggested that the second wave was driven by reinfections, but the episode has become controversial and an enigma in the history of the pandemic. We present a data-driven model of epidemic dynamics in Iquitos, which we also use to explain and model events in Manaus. By reverse engineering the multiple epidemic waves over 2 y in these two cities, the partially observed Markov process model inferred that the first wave left Manaus with a highly susceptible and vulnerable population (\u224840% infected) open to invasion by P.1, in contrast to Iquitos (\u224872% infected). The model reconstructed the full epidemic outbreak dynamics from mortality data by fitting a flexible time-varying reproductive number\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:msub>\n                            <mml:mi>R<\/mml:mi>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:mfenced close=\")\" open=\"(\">\n                            <mml:mi>t<\/mml:mi>\n                          <\/mml:mfenced>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    while estimating reinfection and impulsive immune evasion. The approach is currently highly relevant given the lack of tools available to assess these factors as new SARS-CoV-2 virus variants appear with different degrees of immune evasion.\n                  <\/jats:p>","DOI":"10.1073\/pnas.2211422120","type":"journal-article","created":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T15:17:27Z","timestamp":1677511047000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":17,"title":["Resolving the enigma of Iquitos and Manaus: A modeling analysis of multiple COVID-19 epidemic waves in two Amazonian cities"],"prefix":"10.1073","volume":"120","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3253-654X","authenticated-orcid":false,"given":"Daihai","family":"He","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China"},{"name":"Research Institute for Future Food, The Hong Kong Polytechnic University, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8339-5965","authenticated-orcid":false,"given":"Lixin","family":"Lin","sequence":"additional","affiliation":[{"name":"Mathematical Sciences, School of Science, Royal Melbourne Institute of Technology (RMIT) University, Melbourne, Victoria 3000, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yael","family":"Artzy-Randrup","sequence":"additional","affiliation":[{"name":"Department of Theoretical and Computational Ecology, Institute for Biodiversity and Ecosystem Dynamics (IBED), University of Amsterdam, 1090 GE, Amsterdam, Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8565-4710","authenticated-orcid":false,"given":"Haydar","family":"Demirhan","sequence":"additional","affiliation":[{"name":"Mathematical Sciences, School of Science, Royal Melbourne Institute of Technology (RMIT) University, Melbourne, Victoria 3000, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6297-7154","authenticated-orcid":false,"given":"Benjamin J.","family":"Cowling","sequence":"additional","affiliation":[{"name":"World Health Organization (WHO) Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong SAR, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6465-579X","authenticated-orcid":false,"given":"Lewi","family":"Stone","sequence":"additional","affiliation":[{"name":"Mathematical Sciences, School of Science, Royal Melbourne Institute of Technology (RMIT) University, Melbourne, Victoria 3000, Australia"},{"name":"Biomathematics Unit, School of Zoology, Faculty of Life Sciences, Tel Aviv University, Ramat Aviv 69978, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2023,2,27]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/S2214-109X(21)00173-X"},{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.abe9728"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40615-021-01148-8"},{"key":"e_1_3_4_4_2","doi-asserted-by":"crossref","unstructured":"D. He The unexpected dynamics of COVID-19 in Manaus Brazil: Was herd immunity achieved? medRxiv [Preprint] (2021). https:\/\/doi.org\/10.1101\/2021.02.18.21251809.","DOI":"10.1101\/2021.02.18.21251809"},{"key":"e_1_3_4_5_2","unstructured":"Anonymous Brazil Minist\u00e9rio da Sa\u00fade Opendatasus SRAG 2020 in Opendatasus (Brazil) (2020)."},{"key":"e_1_3_4_6_2","unstructured":"Anonymous \u201cPlataforma Ncional de Datos Abiertos\u201d 1 February 2022. https:\/\/www.datosabiertos.gob.pe\/group\/ministerio-de-salud."},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41591-021-01378-7"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0140-6736(21)00183-5"},{"key":"e_1_3_4_9_2","article-title":"Attack rate and the price of SARS-CoV-2 herd immunity in Brazil","author":"Rocha Filho T.","year":"2021","unstructured":"T. Rocha Filho , Attack rate and the price of SARS-CoV-2 herd immunity in Brazil. Res. Sq., 10.21203\/rs.3.rs-659187\/v2 (2021).","journal-title":"Res. Sq."},{"key":"e_1_3_4_10_2","article-title":"Covid-19: Seroprevalencia en la ciudad de Iquitos es de 75 por ciento","author":"Anonymous","unstructured":"Anonymous, Covid-19: Seroprevalencia en la ciudad de Iquitos es de 75 por ciento. Andina, 6 April 2022. https:\/\/andina.pe\/agencia\/noticia-covid19-seroprevalencia-la-ciudad-iquitos-es-75-ciento-815197.aspx.","journal-title":"Andina"},{"key":"e_1_3_4_11_2","article-title":"Director Regional de Salud Loreto: No podemos decir que Iquitos tiene inmunidad de reba\u00f1o","author":"Anonymous","unstructured":"Anonymous, Director Regional de Salud Loreto: No podemos decir que Iquitos tiene inmunidad de reba\u00f1o. CanalN, 6 April 2022. https:\/\/canaln.pe\/actualidad\/director-regional-salud-loreto-no-podemos-decir-que-iquitos-tiene-inmunidad-rebano-n420928.","journal-title":"CanalN"},{"key":"e_1_3_4_12_2","unstructured":"Anonymous A Brazilian city thought it had herd immunity. It was wrong. The Economist 4 April 2022. https:\/\/www.economist.com\/the-americas\/2021\/01\/23\/a-brazilian-city-thought-it-had-herd-immunity-it-was-wrong."},{"key":"e_1_3_4_13_2","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.abc0927"},{"key":"e_1_3_4_14_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature05638"},{"key":"e_1_3_4_15_2","doi-asserted-by":"publisher","DOI":"10.3201\/eid2809.212226"},{"key":"e_1_3_4_16_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pgph.0001211"},{"key":"e_1_3_4_17_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1321656111"},{"key":"e_1_3_4_18_2","doi-asserted-by":"publisher","DOI":"10.35663\/amp.2020.373.1050"},{"key":"e_1_3_4_19_2","doi-asserted-by":"publisher","DOI":"10.1128\/mSphere.00685-21"},{"key":"e_1_3_4_20_2","doi-asserted-by":"publisher","DOI":"10.1136\/bmjgh-2022-008477"},{"key":"e_1_3_4_21_2","first-page":"100112","article-title":"SARS-CoV-2 Lambda and Gamma variants competition in Peru, a country with high seroprevalence","volume":"6","author":"Vargas-Herrera N.","year":"2022","unstructured":"N. Vargas-Herrera , SARS-CoV-2 Lambda and Gamma variants competition in Peru, a country with high seroprevalence. Lancet Reg. Health Am. 6, 100112 (2022).","journal-title":"Lancet Reg. Health Am."},{"key":"e_1_3_4_22_2","doi-asserted-by":"publisher","DOI":"10.11145\/j.biomath.2021.03.087"},{"key":"e_1_3_4_23_2","unstructured":"N. Brazeau \u201cReport 34: COVID-19 infection fatality ratio: estimates from seroprevalence\u201d (Report 34 Imperial College London London UK Jan 1 2022). https:\/\/www.imperial.ac.uk\/mrc-global-infectious-disease-analysis\/covid-19\/report-34-ifr\/."},{"key":"e_1_3_4_24_2","doi-asserted-by":"publisher","DOI":"10.3201\/eid2803.211993"},{"key":"e_1_3_4_25_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.abh2644"},{"key":"e_1_3_4_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijid.2021.07.017"},{"key":"e_1_3_4_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/S2214-109X(20)30387-9"},{"key":"e_1_3_4_28_2","doi-asserted-by":"publisher","DOI":"10.1056\/NEJMc2108120"},{"key":"e_1_3_4_29_2","doi-asserted-by":"publisher","DOI":"10.1128\/Spectrum.00087-21"},{"key":"e_1_3_4_30_2","article-title":"Risk of SARS-CoV-2 reinfection 18 months after primary infection: Population-level observational study","author":"Flacco M. E.","year":"2022","unstructured":"M. E. Flacco , Risk of SARS-CoV-2 reinfection 18 months after primary infection: Population-level observational study. medRxiv [Preprint] (2022). https:\/\/doi.org\/10.1101\/2022.02.19.22271221.","journal-title":"medRxiv [Preprint]"},{"key":"e_1_3_4_31_2","doi-asserted-by":"publisher","DOI":"10.1056\/NEJMc2203985"},{"key":"e_1_3_4_32_2","doi-asserted-by":"publisher","DOI":"10.3201\/eid2801.211817"},{"key":"e_1_3_4_33_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-020-19652-6"},{"key":"e_1_3_4_34_2","doi-asserted-by":"publisher","DOI":"10.1080\/08898480009525471"},{"key":"e_1_3_4_35_2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9876.00187"},{"key":"e_1_3_4_36_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0603181103"},{"key":"e_1_3_4_37_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-27603-y"},{"key":"e_1_3_4_38_2","doi-asserted-by":"publisher","DOI":"10.1177\/0049124104268644"},{"key":"e_1_3_4_39_2","unstructured":"S. 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R.","year":"2021","unstructured":"A. R. R. Freitas , The emergence of novel SARS-CoV-2 variant P. 1 in Amazonas (Brazil) was temporally associated with a change in the age and sex profile of COVID-19 mortality: A population based ecological study. Lancet Reg. Health Am. 1, 100021 (2021).","journal-title":"Lancet Reg. Health Am."},{"key":"e_1_3_4_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/S2214-109X(21)00355-7"},{"key":"e_1_3_4_46_2","unstructured":"S. Kadelka Science 2021: An alternative empirically-supported adjustment for sero-reversion yields a 10 percentage point lower estimate of the cumulative incidence of SARS-CoV-2 in Manaus by October 2020. arXiv [Preprint] (2021). https:\/\/doi.org\/10.48550\/arXiv.2103.13951."},{"key":"e_1_3_4_47_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41562-020-0928-4"},{"key":"e_1_3_4_48_2","unstructured":"Anonymous \u201cAmazonas and Manaus daily COVID-19 confirmed death data\u201d 1 February 2022. http:\/\/www.amazonas.am.gov.br\/content\/uploads\/2021\/01\/20_01_21_BOLETIM_DIARIO_DE_CASOS_COVID-19-12.pdf."},{"key":"e_1_3_4_49_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2009.0151"},{"key":"e_1_3_4_50_2","unstructured":"A. A. King \u201cWorking with ordinary differential equations in pomp\u201d 1 February 2022. https:\/\/kingaa.github.io\/clim-dis\/parest\/odes.html."},{"key":"e_1_3_4_51_2","doi-asserted-by":"publisher","DOI":"10.1126\/scitranslmed.aan5325"},{"key":"e_1_3_4_52_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0600816103"},{"key":"e_1_3_4_53_2","doi-asserted-by":"publisher","DOI":"10.1136\/bmjopen-2020-040263"},{"key":"e_1_3_4_54_2","doi-asserted-by":"publisher","DOI":"10.1093\/jtm\/taaa115"},{"key":"e_1_3_4_55_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2020.0596"},{"key":"e_1_3_4_56_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41591-020-0962-9"}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.2211422120","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,21]],"date-time":"2023-09-21T08:58:29Z","timestamp":1695286709000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/10.1073\/pnas.2211422120"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,27]]},"references-count":56,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2023,3,7]]}},"alternative-id":["10.1073\/pnas.2211422120"],"URL":"https:\/\/doi.org\/10.1073\/pnas.2211422120","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,27]]},"assertion":[{"value":"2022-07-06","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-01-17","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-02-27","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e2211422120"}}