{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T07:33:49Z","timestamp":1771659229740,"version":"3.50.1"},"reference-count":48,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MBE"],"published-print":{"date-parts":[[2023]]},"abstract":"<jats:p xml:lang=\"fr\">&lt;abstract&gt;&lt;p&gt;COVID-19 has been spreading widely since January 2020, prompting the implementation of non-pharmaceutical interventions and vaccinations to prevent overwhelming the healthcare system. Our study models four waves of the epidemic in Munich over two years using a deterministic, biology-based mathematical model of SEIR type that incorporates both non-pharmaceutical interventions and vaccinations. We analyzed incidence and hospitalization data from Munich hospitals and used a two-step approach to fit the model parameters: first, we modeled incidence without hospitalization, and then we extended the model to include hospitalization compartments using the previous estimates as a starting point. For the first two waves, changes in key parameters, such as contact reduction and increasing vaccinations, were enough to represent the data. For wave three, the introduction of vaccination compartments was essential. In wave four, reducing contacts and increasing vaccinations were critical parameters for controlling infections. The importance of hospitalization data was highlighted, as it should have been included as a crucial parameter from the outset, along with incidence, to avoid miscommunication with the public. The emergence of milder variants like Omicron and a significant proportion of vaccinated people has made this fact even more evident.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/mbe.2023452","type":"journal-article","created":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T10:13:03Z","timestamp":1680343983000},"page":"10304-10338","source":"Crossref","is-referenced-by-count":3,"title":["Data suggested hospitalization as critical indicator of the severity of the COVID-19 pandemic, even at its early stages"],"prefix":"10.3934","volume":"20","author":[{"given":"Stefanie","family":"Fuderer","sequence":"first","affiliation":[{"name":"Department of Mathematics, Technical University of Munich, Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christina","family":"Kuttler","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Technical University of Munich, Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Hoelscher","sequence":"additional","affiliation":[{"name":"Division of Infectious Diseases and Tropical Medicine, Medical Center of the University of Munich, Munich, Germany"},{"name":"German Center for Infection Research (DZIF), partner site Munich, Munich, Germany"},{"name":"Center for International Health (CIH), University Hospital, Munich, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ludwig Christian","family":"Hinske","sequence":"additional","affiliation":[{"name":"Department of Anesthesiology, University Hospital, Munich, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Noemi","family":"Castelletti","sequence":"additional","affiliation":[{"name":"Division of Infectious Diseases and Tropical Medicine, Medical Center of the University of Munich, Munich, Germany"},{"name":"Institute of Radiation Medicine, Helmholtz Zentrum M\u00fcnchen, Neuherberg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"key-10.3934\/mbe.2023452-1","doi-asserted-by":"publisher","unstructured":"B. Ganesh, T. Rajakumar, M. Malathi, N. Manikandan, J. Nagaraj, A. Santhakumar, et al., Epidemiology and pathobiology of SARS-CoV-2 (COVID-19) in comparison with SARS, MERS: An updated overview of current knowledge and future perspectives, <i>Clin. Epidemiol. Glob. Health<\/i>, <b>10<\/b> (2021), 100694. https:\/\/doi.org\/10.1016\/j.cegh.2020.100694","DOI":"10.1016\/j.cegh.2020.100694"},{"key":"key-10.3934\/mbe.2023452-2","unstructured":"World Health Organization, WHO Director-General's Opening Remarks at the Media Briefing on COVID-19-11 March 2020, 2020. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.who.int\/director-general\/speeches\/detail\/who-director-general-s-opening-remarks-at-the-media-briefing-on-covid-19---11-march-2020\">https:\/\/www.who.int\/director-general\/speeches\/detail\/who-director-general-s-opening-remarks-at-the-media-briefing-on-covid-19---11-march-2020<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-3","unstructured":"World Health Organization, WHO Coronavirus (COVID-19) Dashboard, 2022. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/covid19.who.int\/\">https:\/\/covid19.who.int\/<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-4","unstructured":"Robert Koch-Institute (RKI), Table showing current Covid-19 infections per day as time series, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/npgeo-corona-npgeo-de.hub.arcgis.com\/datasets\/dd4580c810204019a7b8eb3e0b329dd6_0\/explore\">https:\/\/npgeo-corona-npgeo-de.hub.arcgis.com\/datasets\/dd4580c810204019a7b8eb3e0b329dd6_0\/explore<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-5","unstructured":"Robert Koch-Institute (RKI), Kontaktpersonen-Nachverfolgung bei SARS-CoV-2-Infektionen, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.rki.de\/DE\/Content\/InfAZ\/N\/Neuartiges_Coronavirus\/Kontaktperson\/Management.html; jsessionid = 78E4E999E14B2E6A3E8F02E5957D2C97.internet121?nn = 13490888#doc13516162bodyText14\">https:\/\/www.rki.de\/DE\/Content\/InfAZ\/N\/Neuartiges_Coronavirus\/Kontaktperson\/Management.html; jsessionid = 78E4E999E14B2E6A3E8F02E5957D2C97.internet121?nn = 13490888#doc13516162bodyText14<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-6","unstructured":"Robert Koch-Institute (RKI), Tabelle mit den gemeldeten Impfungen nach Bundesl\u00e4ndern und Impfquoten nach Altersgruppen, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.rki.de\/DE\/Content\/InfAZ\/N\/Neuartiges_Coronavirus\/Daten\/Impfquotenmonitoring\">https:\/\/www.rki.de\/DE\/Content\/InfAZ\/N\/Neuartiges_Coronavirus\/Daten\/Impfquotenmonitoring<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-7","unstructured":"Robert Koch-Institute (RKI), Kurz und Knapp: Faktenbl\u00e4tter zum Impfen - COVID-19 Impfung, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.rki.de\/DE\/Content\/Infekt\/Impfen\/Materialien\/Faktenblaetter\/Faktenblaetter_inhalt.html\">https:\/\/www.rki.de\/DE\/Content\/Infekt\/Impfen\/Materialien\/Faktenblaetter\/Faktenblaetter_inhalt.html<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-8","doi-asserted-by":"publisher","unstructured":"J. Schilling, A. Lehfeld, D. Schumacher, M. Diercke, S. Buda, W. Haas, et al., Krankheitsschwere der ersten COVID-19-Welle in Deutschland basierend auf den Meldungen gem\u00e4\u00df Infektionsschutzgesetz, <i>J. Health Monit.<\/i>, <b>5<\/b> (2020), 2\u201320. https:\/\/doi.org\/10.25646\/7169","DOI":"10.25646\/7169"},{"key":"key-10.3934\/mbe.2023452-9","unstructured":"Centers for Disease Control and Prevention (CDC), National Center for Immunization and Respiratory Diseases (NCIRD), Disease Burden of Flu, 2022. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.cdc.gov\/flu\/about\/burden\/index.html\/\">https:\/\/www.cdc.gov\/flu\/about\/burden\/index.html\/<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-10","unstructured":"Robert Koch-Institute (RKI), Coronavirus SARS-CoV-2: Fallzahlen und Meldungen, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.rki.de\/SharedDocs\/FAQ\/NCOV2019\/FAQ_Liste_Fallzahlen_Meldungen.html\">https:\/\/www.rki.de\/SharedDocs\/FAQ\/NCOV2019\/FAQ_Liste_Fallzahlen_Meldungen.html<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-11","unstructured":"R. M. Anderson, The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS, <i>J. Acquir. Immune Defic. Syndr.<\/i>, <b>1<\/b> (1988), 241\u2013256."},{"key":"key-10.3934\/mbe.2023452-12","doi-asserted-by":"crossref","unstructured":"F. Brauer, C. Castillo-Chavez, <i>Mathematical Models in Population Biology and Epidemiology<\/i>, Springer, New York, 2012.","DOI":"10.1007\/978-1-4614-1686-9"},{"key":"key-10.3934\/mbe.2023452-13","doi-asserted-by":"publisher","unstructured":"D. Chumachenko, I. Meniailov, K. Bazilevych, T. Chumachenko, S. Yakovlev, Investigation of statistical machine learning models for COVID-19 epidemic process simulation: Random Forest, K-Nearest Neighbors, Gradient Boosting, <i>Computation<\/i>, <b>10<\/b> (2022), 2079\u20133197. https:\/\/doi.org\/10.3390\/computation10060086","DOI":"10.3390\/computation10060086"},{"key":"key-10.3934\/mbe.2023452-14","doi-asserted-by":"publisher","unstructured":"F. Ying, N. O'Clery, Modelling COVID-19 transmission in supermarkets using an agent-based model, <i>PLoS One<\/i>, <b>16<\/b> (2021), 0249821. https:\/\/doi.org\/10.1371\/journal.pone.0249821","DOI":"10.1371\/journal.pone.0249821"},{"key":"key-10.3934\/mbe.2023452-15","doi-asserted-by":"publisher","unstructured":"R. Nistal, M. de la Sen, J. Gabirondo, S. Alonso-Quesada, A. J. Garrido, I. Garrido, A Study on COVID-19 incidence in Europe through two SEIR epidemic models which consider mixed contagions from asymptomatic and symptomatic individuals, <i>Appl. Sci.<\/i>, <b>11<\/b> (2021), 2076\u20133417. https:\/\/doi.org\/10.3390\/app11146266","DOI":"10.3390\/app11146266}"},{"key":"key-10.3934\/mbe.2023452-16","doi-asserted-by":"publisher","unstructured":"R. Nistal, M. de la Sen, J. Gabirondo, S. Alonso-Quesada, A. J. Garrido, I. Garrido, A Modelization of the Propagation of COVID-19 in regions of Spain and Italy with evaluation of the transmission rates related to the intervention measures, <i>Biology<\/i>, <b>10<\/b> (2021), 121. https:\/\/doi.org\/10.3390\/biology10020121","DOI":"10.3390\/biology10020121"},{"key":"key-10.3934\/mbe.2023452-17","doi-asserted-by":"publisher","unstructured":"J. Ozaki, Y. Shida, H. Takayasu, M. Takayasu, Direct modelling from GPS data reveals daily-activity-dependency of effective reproduction number in COVID-19 pandemic, <i>Sci Rep.<\/i>, <b>12<\/b>, (2022), 17888. https:\/\/doi.org\/10.1038\/s41598-022-22420-9","DOI":"10.1038\/s41598-022-22420-9"},{"key":"key-10.3934\/mbe.2023452-18","doi-asserted-by":"publisher","unstructured":"D. Okuonghae, A. Omame, Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria, <i>Chaos, Solitons Fractals<\/i>, <b>139<\/b> (2020), 110032. https:\/\/doi.org\/10.1016\/j.chaos.2020.110032","DOI":"10.1016\/j.chaos.2020.110032"},{"key":"key-10.3934\/mbe.2023452-19","doi-asserted-by":"publisher","unstructured":"M. V. Barbarossa, J. Fuhrmann, J. H. Meinke, S. Krieg, H. V. Varma, N. Castelletti, et al., Modeling the spread of COVID-19 in Germany: Early assessment and possible scenarios, <i>PLoS ONE<\/i>, <b>15<\/b>, (2020). https:\/\/doi.org\/10.1371\/journal.pone.0238559","DOI":"10.1371\/journal.pone.0238559"},{"key":"key-10.3934\/mbe.2023452-20","unstructured":"S\u00fcddeutsche Zeitung, Coronavirus-Pandemie in Bayern: R\u00fcckblick April 2020, <i>S\u00fcddeutsche Zeitung<\/i>, 2020. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.sueddeutsche.de\/bayern\/coronavirus-bayern-rueckblick-april-1.4873340\">https:\/\/www.sueddeutsche.de\/bayern\/coronavirus-bayern-rueckblick-april-1.4873340<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-21","unstructured":"Norddeutscher Rundfunk, Corona-Chronologie: November 2020, 2020. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.ndr.de\/nachrichten\/info\/Corona-Chronologie-November-2020, coronachronologie128.html\">https:\/\/www.ndr.de\/nachrichten\/info\/Corona-Chronologie-November-2020, coronachronologie128.html<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-22","unstructured":"Norddeutscher Rundfunk, Corona-Chronologie: Dezember 2020. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.ndr.de\/nachrichten\/info\/Corona-Chronologie-Dezember-2020, coronachronologie130.html\">https:\/\/www.ndr.de\/nachrichten\/info\/Corona-Chronologie-Dezember-2020, coronachronologie130.html<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-23","unstructured":"Norddeutscher Rundfunk, Corona-Chronologie: Januar 2021, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.ndr.de\/nachrichten\/info\/Corona-Chronologie-Januar-2021, coronachronologie134.html\">https:\/\/www.ndr.de\/nachrichten\/info\/Corona-Chronologie-Januar-2021, coronachronologie134.html<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-24","unstructured":"S\u00fcddeutsche Zeitung, Was in M\u00fcnchen ab heute gilt, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.sueddeutsche.de\/muenchen\/muenchen-corona-notbremse-mittwoch-1.5263849\">https:\/\/www.sueddeutsche.de\/muenchen\/muenchen-corona-notbremse-mittwoch-1.5263849<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-25","unstructured":"S\u00fcddeutsche Zeitung, Diese Corona-Regeln gelten nun in M\u00fcnchen, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.sueddeutsche.de\/muenchen\/muenchen-corona-lockerungen-gastronomie-ausgangssperre-1.5288681\">https:\/\/www.sueddeutsche.de\/muenchen\/muenchen-corona-lockerungen-gastronomie-ausgangssperre-1.5288681<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-26","unstructured":"Bayerische Staatsregierung, Pressemitteilungen: Bericht aus der Kabinettssitzung vom 4. Juni 2021, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.bayern.de\/bericht-aus-der-kabinettssitzung-vom-4-juni-2021\/\">https:\/\/www.bayern.de\/bericht-aus-der-kabinettssitzung-vom-4-juni-2021\/<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-27","unstructured":"Deutsche Akademie der Naturforscher Leopoldina, Ad-hoc-Stellungnahmen zur Coronavirus-Pandemie: Zusammenfassung der Stellungnahmen zur Coronavirus-Pandemie, 2020."},{"key":"key-10.3934\/mbe.2023452-28","doi-asserted-by":"publisher","unstructured":"H. Panknin, S. Schr\u00f6der, Konsequente Schutzma\u00dfnahmen gegen Ansteckung, <i>Procare<\/i>, <b>25<\/b>, (2020), 20\u201322. https:\/\/doi.org\/10.1007\/s00735-020-1261-x","DOI":"10.1007\/s00735-020-1261-x"},{"key":"key-10.3934\/mbe.2023452-29","unstructured":"Robert Koch-Institute (RKI), \u00dcbersicht zu besorgniserregenden SARS-CoV-2-Virusvarianten (VOC), 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.rki.de\/DE\/Content\/InfAZ\/N\/Neuartiges_Coronavirus\/Virusvariante.html\">https:\/\/www.rki.de\/DE\/Content\/InfAZ\/N\/Neuartiges_Coronavirus\/Virusvariante.html<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-30","unstructured":"Robert Koch-Institute (RKI), Berichte zu Virusvarianten von SARS-CoV-2 in Deutschland, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.rki.de\/DE\/Content\/InfAZ\/N\/Neuartiges_Coronavirus\/DESH\/Berichte-VOC-tab.html\">https:\/\/www.rki.de\/DE\/Content\/InfAZ\/N\/Neuartiges_Coronavirus\/DESH\/Berichte-VOC-tab.html<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-31","unstructured":"Robert Koch-Institute (RKI), SARS-CoV-2: Virologische Basisdaten sowie Virusvarianten, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.rki.de\/DE\/Content\/InfAZ\/N\/Neuartiges_Coronavirus\/Virologische_Basisdaten.html; jsessionid = A1752CE0733B8B43969A64CD80B9B253.internet082?nn = 13490888\">https:\/\/www.rki.de\/DE\/Content\/InfAZ\/N\/Neuartiges_Coronavirus\/Virologische_Basisdaten.html; jsessionid = A1752CE0733B8B43969A64CD80B9B253.internet082?nn = 13490888<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-32","unstructured":"Landeshauptstadt M\u00fcnchen-Das offizielle Stadtportal, Coronavirus-F\u00e4lle in M\u00fcnchen: Aktuelle Zahlen, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.muenchen.de\/rathaus\/Stadtinfos\/Coronavirus-Fallzahlen.html\">https:\/\/www.muenchen.de\/rathaus\/Stadtinfos\/Coronavirus-Fallzahlen.html<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-33","doi-asserted-by":"publisher","unstructured":"E. Callaway, Delta coronavirus variant: scientists brace for impact, <i>Nature<\/i>, (2021), 17\u201318. https:\/\/doi.org\/10.1038\/d41586-021-01696-3","DOI":"10.1038\/d41586-021-01696-3"},{"key":"key-10.3934\/mbe.2023452-34","unstructured":"BR24, Corona-Regeln: Was aktuell in Bayern gilt, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.br.de\/nachrichten\/bayern\/corona-regeln-in-bayern-was-gilt, Sbtbuu0\">https:\/\/www.br.de\/nachrichten\/bayern\/corona-regeln-in-bayern-was-gilt, Sbtbuu0<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-35","unstructured":"S\u00fcddeutsche Zeitung, Corona in Bayern: Newsblog vom 5. bis zum 26. Juli 2021, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.sueddeutsche.de\/bayern\/corona-bayern-archiv-1.5342370\">https:\/\/www.sueddeutsche.de\/bayern\/corona-bayern-archiv-1.5342370<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-36","unstructured":"S\u00fcddeutsche Zeitung, Corona-Regeln Bayern: Welche Regeln aktuell in Bayern gelten, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.sueddeutsche.de\/bayern\/bayern-corona-regeln-2g-3g-maskenpflicht-1.4878824\">https:\/\/www.sueddeutsche.de\/bayern\/bayern-corona-regeln-2g-3g-maskenpflicht-1.4878824<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-37","doi-asserted-by":"crossref","unstructured":"C. Walter, F. Fischer, Interdisciplinary Supply Proof (IVENA): Improving Emergency Care through E-Health?, <i>NOTARZT<\/i>, <b>33<\/b>, (2017), 50.","DOI":"10.1055\/s-0043-105634"},{"key":"key-10.3934\/mbe.2023452-38","unstructured":"Robert Koch-Institute (RKI), Epidemiologischer Steckbrief zu SARS-CoV-2 und COVID-19, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.rki.de\/DE\/Content\/InfAZ\/N\/Neuartiges_Coronavirus\/Steckbrief.html; jsessionid = 1E68F40DA18BE45CC49EE51EA8FA8CC8.internet051?nn = 2386228\">https:\/\/www.rki.de\/DE\/Content\/InfAZ\/N\/Neuartiges_Coronavirus\/Steckbrief.html; jsessionid = 1E68F40DA18BE45CC49EE51EA8FA8CC8.internet051?nn = 2386228<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-39","doi-asserted-by":"publisher","unstructured":"S. Amit, G. Regev-Yochay, A. Afek, Y. Kreiss, E. Leshem, Early rate reductions of SARS-CoV-2 infection and COVID-19 in BNT162b2 vaccine recipients, <i>Lancet<\/i>, <b>397<\/b>, (2021), 875\u2013877. https:\/\/doi.org\/10.1016\/s0140-6736(21)00448-7","DOI":"10.1016\/s0140-6736(21)00448-7"},{"key":"key-10.3934\/mbe.2023452-40","doi-asserted-by":"publisher","unstructured":"H. Xin, Y. Li, P. Wu, Z. Li, E. H. Y. Lau, Y. Qin, et al., Estimating the latent period of coronavirus disease 2019 (COVID-19), <i>Clin. Infect. Dis.<\/i>, <b>74<\/b> (2022), 1678\u20131681. https:\/\/doi.org\/10.1093\/cid\/ciab746","DOI":"10.1093\/cid\/ciab746"},{"key":"key-10.3934\/mbe.2023452-41","doi-asserted-by":"publisher","unstructured":"D. Buitrago-Garcia, D. Egli-Gany, M. J. Counotte, S. Hossmann, H. Imeri, A. M. Ipekci, et al., Occurrence and transmission potential of asymptomatic and presymptomatic SARS-CoV-2 infections: A living systematic review and meta-analysis, <i>PLoS Med.<\/i>, <b>17<\/b>, (2020). https:\/\/doi.org\/10.1371\/journal.pmed.1003346","DOI":"10.1371\/journal.pmed.1003346"},{"key":"key-10.3934\/mbe.2023452-42","unstructured":"Bayerisches Landesamt f\u00fcr Statistik, Die Datenbank des Bayerischen Landesamtes f\u00fcr Statistik, 2023. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.statistikdaten.bayern.de\/genesis\/online; jsessionid%3D6CB3363574391F9435FD661D9125B699?sequenz%3DtabelleErgebnis%26selectionname%3D12411-001\">https:\/\/www.statistikdaten.bayern.de\/genesis\/online; jsessionid%3D6CB3363574391F9435FD661D9125B699?sequenz%3DtabelleErgebnis%26selectionname%3D12411-001<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-43","doi-asserted-by":"publisher","unstructured":"N. Potere, E. Valeriani, M. Candeloro, M. Tana, E. Porreca, A. Abbate, et al., Acute complications and mortality in hospitalized patients with coronavirus disease 2019: A systematic review and meta-analysis, <i>Crit. Care<\/i>, <b>24<\/b> (2020), 1\u201312. https:\/\/doi.org\/10.1186\/s13054-020-03022-1","DOI":"10.1186\/s13054-020-03022-1"},{"key":"key-10.3934\/mbe.2023452-44","doi-asserted-by":"crossref","unstructured":"M. Martcheva, <i>An Introduction to Mathematical Epidemiology<\/i>, Springer, New York, 2015.","DOI":"10.1007\/978-1-4899-7612-3"},{"key":"key-10.3934\/mbe.2023452-45","doi-asserted-by":"publisher","unstructured":"Y. Goldberg, M. Mandel, Y. M. Bar-On, O. Bodenheimer, L. S. Freedman, E. Haas, et al., Waning immunity of the BNT162b2 vaccine: A nationwide study from Israel, <i>New Engl. J. Med.<\/i>, (2021). https:\/\/doi.org\/10.1056\/nejmoa2114228","DOI":"10.1056\/nejmoa2114228"},{"key":"key-10.3934\/mbe.2023452-46","unstructured":"BR24, Covid-19 in den Kliniken: Die Welle der Ungeimpften, 2021. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.br.de\/nachrichten\/bayern\/covid-19-in-den-kliniken-die-welle-der-ungeimpften, SjYWL3B\">https:\/\/www.br.de\/nachrichten\/bayern\/covid-19-in-den-kliniken-die-welle-der-ungeimpften, SjYWL3B<\/ext-link>"},{"key":"key-10.3934\/mbe.2023452-47","unstructured":"K. P. Burnham, D. R. Anderson, <i>Model Selection and Multimodel Inference<\/i>, Springer, New York, 2002."},{"key":"key-10.3934\/mbe.2023452-48","doi-asserted-by":"crossref","unstructured":"M. L. Gavrilova, O. Gervasi, V. Kumar, C. J. K. Tan, D. Taniar, A. Lagan\u00e0, et al., Computational science and its applications-ICCSA 2006: international conference, Glasgow, in <i>ICCSA: International Conference on Computational Science and Its Applications<\/i>, <b>3982<\/b> (2006).","DOI":"10.1007\/11751595"}],"container-title":["Mathematical Biosciences and Engineering"],"original-title":[],"link":[{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/mbe.2023452?viewType=html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T10:13:36Z","timestamp":1680344016000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/mbe.2023452"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"references-count":48,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023]]}},"URL":"https:\/\/doi.org\/10.3934\/mbe.2023452","relation":{},"ISSN":["1551-0018"],"issn-type":[{"value":"1551-0018","type":"print"}],"subject":[],"published":{"date-parts":[[2023]]}}}