Effect of the mass vaccination duration on the spread of COVID-19 evaluated by a flexible compartment model

Effect of the mass vaccination duration on the spread of COVID-19 evaluated by a flexible compartment model | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Effect of the mass vaccination duration on the spread of COVID-19 evaluated by a flexible compartment model Hiroo Ohmori This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3705581/v3 This work is licensed under a CC BY 4.0 License Status: Posted Version 3 posted You are reading this latest preprint version Show more versions Abstract For COVID-19, infected individuals are isolated from the community when they become symptomatic, and when they become recovered individuals who have immunity, they return to the community. With an increase in the number of recovered individuals in the community, the contact rate between infected individuals and susceptible individuals decreases, resulting in a decrease in the number of infected individuals. Vaccination causes not only a decrease in the number of susceptible individuals in the community but also a reduction in the contact rate between infected individuals and susceptible individuals with an increase in the number of vaccinated individuals, as do the recovered individuals. From the viewpoint of herd immunity, the vaccination duration, which is the period between the start and the end of mass vaccination, must be examined because the number of vaccinated individuals actually increases gradually daily according to vaccination programs, and the total number of vaccinated individuals depends on the mass vaccination duration, controlling the spread of COVID-19. How long should we continue mass vaccination to contain the COVID-19 pandemic from a physical viewpoint? The number of infected individuals by different mass vaccination durations was calculated by a flexible compartment model specific to COVID-19. The model contains the vaccination rate as an independent variable in the calculation equations and, as the dependent variable, the number of isolated/recovered individuals and the population excluding the individuals kept in isolation, both of which affect the contact rate between infected individuals and susceptible individuals. The effect of the mass vaccination duration can be evaluated by comparing the total number of infected individuals among the cases with different mass vaccination durations for the cases with different start dates of vaccination, with different vaccination rates and with different symptomatic rates. The results show that since the contact rate decreases with an increase in the number of vaccinated individuals, the earlier the start date of vaccination is, the smaller the total number of infected individuals becomes, and the longer the mass vaccination duration is, the smaller the total number of infected individuals becomes. The results also showed that when vaccination is continued until the day when the sum of the number of recovered individuals and the number of vaccinated individuals exceeds an ‘expedient herd immunity threshold’, the total number of infected individuals is significantly reduced, and the duration of infection is also markedly shortened, as expected for the case with a sufficient mass vaccination duration. Immunology Infectious Diseases Statistical Epidemiology Virology Environmental Engineering Vaccine Development Hospital Medicine Computational Physics Applied Statistics Asymptomatic Compartment model COVID-19 Duration of infection Herd immunity Infected Infection during the latent period Isolation SIR model Recovered Susceptible Symptomatic rate Mass vaccination duration Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Full Text Additional Declarations The authors declare no competing interests. Supplementary Files EffectofMassvaccinationdurationtables162023Dec10.docx Effect of the mass vaccination duration on the spread of COVID-19 evaluated by a flexible compartment model Hiroo Ohfmori Tables 1-6 EffectofMassvaccinationdurationSupplApend12023Dec10.docx Supplementary Material Hiroo Ohmori Appendix 1: Explanations of independent variables and dependent variables used in the Excel file. EffectofMassvaccinationdurationSupplApend2Excel2023Dec10.docx Supple. Material 2; Appendix 2: Part of Excel for the simulation specific to COVID-19 H.Ohmori Cite Share Download PDF Status: Posted Version 3 posted You are reading this latest preprint version Show more versions Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3705581","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":258544235,"identity":"851205b7-bf7b-4b07-9708-8e3cf1472e07","order_by":0,"name":"Hiroo Ohmori","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCElEQVRIiWNgGAWjYDACCRBhYMPAcICBGSLCA5VhbMCrJQ2uRYJILQyHsWjBBfiluxMfVxScl+O7kcBswNjGUMfPc8bwAUONHQPzbOzWSM45u9nwjMFtY0mglgSgFgnJ3h5jA4ZjyQyMcw5g1WJwI3ebZIPB7cQNQC0HGNv+Sxic5zGTYGA7wMA4IwGflnP1UC0MUC3/CGo5kGAAc5jB2R4zCcY23FokZ+RuNmwwSDaceeZhs0HCOQbJmT3Hig0S+5J5cPmFXyJ348OGP3byfMeTD0t8KGPg5+dJ3vjgwzc7OUMcIYYEgFEHcQmHAYjBYziDkA4EYH8ApuQliNcyCkbBKBgFwxoAAFvfWcfI7W9AAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-5993-0996","institution":"Department of Natural Environmental Studies, Graduate School of Frontier Sciences, The University of Tokyo","correspondingAuthor":true,"prefix":"","firstName":"Hiroo","middleName":"","lastName":"Ohmori","suffix":""}],"badges":[],"createdAt":"2023-12-04 12:30:04","currentVersionCode":3,"declarations":{"humanSubjects":true,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-3705581/v3","doiUrl":"https://doi.org/10.21203/rs.3.rs-3705581/v3","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":49075018,"identity":"d2ebd80e-b7cf-46a3-a17d-1cd11e884825","added_by":"auto","created_at":"2024-01-02 18:12:52","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":85221,"visible":true,"origin":"","legend":"\u003cp\u003eFlow of individuals: ‘Susceptible; \u003cem\u003eRM\u003c/em\u003e, \u003cem\u003eNAP\u003c/em\u003e’, ‘Vaccinated; \u003cem\u003eV\u003c/em\u003e’, ‘Recovered; \u003cem\u003eRI\u003c/em\u003e, \u003cem\u003eRT\u003c/em\u003e, \u003cem\u003eRAS\u003c/em\u003e’, ‘Infected; \u003cem\u003eP\u003c/em\u003e(\u003cem\u003eI\u003c/em\u003e, \u003cem\u003ePI\u003c/em\u003e, \u003cem\u003eAS\u003c/em\u003e’), \u003cem\u003eUP\u003c/em\u003e’, ‘Isolated; \u003cem\u003eI\u003c/em\u003e, \u003cem\u003ePl\u003c/em\u003e and ‘Death; \u003cem\u003eDAS\u003c/em\u003e, \u003cem\u003eDTI\u003c/em\u003e, \u003cem\u003eDT\u003c/em\u003e’. (after Ohmori, 2022, 2023).\u003c/p\u003e","description":"","filename":"Fig1.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/65398c9883733809ce5f65f6.png"},{"id":49075120,"identity":"4c04ba77-ce02-4bf5-a1cd-c6cc079be3b5","added_by":"auto","created_at":"2024-01-02 18:20:52","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":17807,"visible":true,"origin":"","legend":"\u003cp\u003eChanges in the number of recovered individuals and contact rate for the cases with a vaccination rate of 0. \u003cem\u003eR\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e) is the number of recovered individuals. The value of \u003cem\u003eδ\u003c/em\u003e is 1. ‘\u003cem\u003esyr\u003c/em\u003e=0.8; \u003cem\u003ev\u003c/em\u003e0’ indicates that the symptomatic rate is 0.8, indicating that 80% of individuals newly infected a day become symptomatic and are isolated; the remaining 20% are asymptomatic and continue to stay in the community, for a vaccination rate of 0. The initial population, \u003cem\u003eTN \u003c/em\u003e(1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP \u003c/em\u003e(1), is 1; the potential (biological) infectious capacity of coronavirus,\u003cem\u003e pfc\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period,\u003cem\u003e lp\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig2.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/db3c60825a888c8c2d8af1e7.png"},{"id":49075032,"identity":"730d212f-9f67-4ff3-a9d7-90932afd6b5c","added_by":"auto","created_at":"2024-01-02 18:12:52","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":26889,"visible":true,"origin":"","legend":"\u003cp\u003eChanges in the sum of the number of recovered individuals and the number of vaccinated individuals, \u003cem\u003eR\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e)+\u003cem\u003e V\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e), and the change in the contact rate,\u003cem\u003e cr \u003c/em\u003e(\u003cem\u003en\u003c/em\u003e), by different start dates of vaccination. \u003cem\u003eR\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e) is the number of recovered individuals, and \u003cem\u003eV\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e) is the number of vaccinated individuals. ‘\u003cem\u003ev \u003c/em\u003e(101-)0.001’ indicates that vaccination with a vaccination rate of 0.001 starts on the 101\u003csup\u003est\u003c/sup\u003e and the vaccination rate increases by 0.001 a day to the end of simulation, indicating that the number of vaccinated individuals increases by 1,000 a day on and after the 101\u003csup\u003est\u003c/sup\u003e. The value of \u003cem\u003eδ\u003c/em\u003e is 1, that is, \u003cem\u003ealI\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e)=1 and \u003cem\u003ealV\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e)=1. The initial population, \u003cem\u003eTN \u003c/em\u003e(1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP \u003c/em\u003e(1), is 1; the potential (biological) infectious capacity of coronavirus,\u003cem\u003e pfc\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period,\u003cem\u003e lp\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig3.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/0b0b878fc6cf5723538388c1.png"},{"id":49076125,"identity":"945190d6-0b41-40a6-8deb-f0f124afadce","added_by":"auto","created_at":"2024-01-02 18:36:52","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":13574,"visible":true,"origin":"","legend":"\u003cp\u003eRelationships between the sum of the number of recovered individuals and the number of vaccinated individuals, \u003cem\u003eR\u003c/em\u003e(n)+ \u003cem\u003eV\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e), and the contact rate, \u003cem\u003ecr \u003c/em\u003e(\u003cem\u003en\u003c/em\u003e). ‘\u003cem\u003ev \u003c/em\u003e(101-)0.001’ indicates that vaccination with a vaccination rate of 0.001 starts on the 101\u003csup\u003est\u003c/sup\u003e and the vaccination rate increases by 0.001 a day to the end of simulation, indicating that the number of vaccinated individuals increases by 1,000 a day on and after the 101\u003csup\u003est\u003c/sup\u003e. The value of \u003cem\u003eδ \u003c/em\u003eis 1, that is, \u003cem\u003ealI\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e)=1 and \u003cem\u003ealV\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e)=1. The initial population, \u003cem\u003eTN \u003c/em\u003e(1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP \u003c/em\u003e(1), is 1; the potential (biological) infectious capacity of coronavirus,\u003cem\u003e pfc\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period,\u003cem\u003e lp\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig4.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/1af5506bfd67cfb039298e14.png"},{"id":49076637,"identity":"7a3018b1-3b03-41ae-9fdf-0508f8c5d637","added_by":"auto","created_at":"2024-01-02 18:44:52","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":22863,"visible":true,"origin":"","legend":"\u003cp\u003eChange in the number of individuals newly infected a day, \u003cem\u003eAP\u003c/em\u003e, the number of infected individuals, \u003cem\u003eP\u003c/em\u003e, the cumulative number of infected individuals, \u003cem\u003eCAP\u003c/em\u003e, and \u003cem\u003eSRT\u003c/em\u003e+\u003cem\u003eV\u003c/em\u003e. The '\u003cem\u003ev \u003c/em\u003e(51-136)0.01' means that vaccination with a vaccination rate of 0.01 starts on the 51\u003csup\u003est\u003c/sup\u003e and ends on the 136\u003csup\u003eth\u003c/sup\u003e. The symptomatic rate, \u003cem\u003esyr\u003c/em\u003e, is 0. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig5.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/6f7f43052e032fe23ec0c493.png"},{"id":49075313,"identity":"3e015759-5d30-4bef-8176-83e67a451dc7","added_by":"auto","created_at":"2024-01-02 18:28:52","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":24174,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the number of ‘Infected/day; \u003cem\u003eAP\u003c/em\u003e’, ‘Infected; \u003cem\u003eP\u003c/em\u003e’, and 'the cumulative number of infected individuals; \u003cem\u003eCAP\u003c/em\u003e' between two cases with different dates of the end of vaccination. The '\u003cem\u003ev \u003c/em\u003e(51-79)0.01' means that the vaccination with a vaccination rate of 0.01 starts on the 51\u003csup\u003est\u003c/sup\u003e and ends on the 79\u003csup\u003eth\u003c/sup\u003e. The symptomatic rate, \u003cem\u003esyr\u003c/em\u003e, is 0. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig6.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/d25f1d05ddde511c992c4bf5.png"},{"id":49075021,"identity":"caf066ec-9f8b-4256-a43b-afc65d6b68f7","added_by":"auto","created_at":"2024-01-02 18:12:52","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":16405,"visible":true,"origin":"","legend":"\u003cp\u003eChanges in the total number of infected individuals, \u003cem\u003eTI\u003c/em\u003e, and the date of the end of infection, ‘Date’, with a change in the date of the end of vaccination, ‘date xx: DEV’, for cases where vaccination with a vaccination rate of 0.01 starts on the 51\u003csup\u003est\u003c/sup\u003e. The symptomatic rate, \u003cem\u003esyr\u003c/em\u003e, is 0. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig7.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/618fe89009a78a673f71142b.png"},{"id":49076129,"identity":"627b01e7-c5d8-4048-ad5d-f51ebac09754","added_by":"auto","created_at":"2024-01-02 18:36:52","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":19962,"visible":true,"origin":"","legend":"\u003cp\u003eChanges in \u003cem\u003eSRT\u003c/em\u003e+\u003cem\u003eV\u003c/em\u003e and the total number of infected individuals, \u003cem\u003eTI\u003c/em\u003e, with a change in the date of the end of vaccination, ‘date xx: DEV’, for cases where vaccination with a vaccination rate of 0.01 starts on the 51\u003csup\u003est\u003c/sup\u003e. \u003cem\u003eSRT\u003c/em\u003e is the cumulative number of recovered individuals up to date xx, and \u003cem\u003eV\u003c/em\u003e is the cumulative number of vaccinated individuals up to date xx. The symptomatic rate, \u003cem\u003esyr\u003c/em\u003e, is 0. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig8.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/c0eca1ef3307e2c81cbe2e44.png"},{"id":49076126,"identity":"25a10a5e-7612-4955-a28e-e70ad06e143e","added_by":"auto","created_at":"2024-01-02 18:36:52","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":22325,"visible":true,"origin":"","legend":"\u003cp\u003eThe relationship between \u003cem\u003eSRT\u003c/em\u003e+\u003cem\u003eV \u003c/em\u003eand the increment of infected individuals a day (\u003cem\u003eΔInf\u003c/em\u003e/day), which indicates an incident rate, and between \u003cem\u003eSRT\u003c/em\u003e+\u003cem\u003eV\u003c/em\u003e and the increment (decrement) of the duration of infection a day (\u003cem\u003eΔ\u003c/em\u003eDur/day), by different dates of the end of vaccination, xx, for cases where vaccination with a vaccination rate of 0.01 starts on the 51\u003csup\u003est\u003c/sup\u003e. \u003cem\u003eSRT\u003c/em\u003e is the cumulative number of recovered individuals up to date xx, and \u003cem\u003eV\u003c/em\u003e is the cumulative number of vaccinated individuals up to date xx. \u003cem\u003eThe 'ΔInf\u003c/em\u003e/day: 79; 468' indicates that the date of the end of vaccination is 79 and the increment of infected individuals a day (\u003cem\u003eΔInf\u003c/em\u003e/day) during the period from the date of the end of infection of the 85\u003csup\u003eth\u003c/sup\u003e to that of the 79\u003csup\u003eth\u003c/sup\u003e, that is, 46 days from the 216\u003csup\u003eth\u003c/sup\u003e to the 262\u003csup\u003end\u003c/sup\u003e, is 468 (persons/day). The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig9.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/a30343d2e4c3bc0653fd18e0.png"},{"id":49075125,"identity":"31596308-1c08-4daf-a145-f763c0311556","added_by":"auto","created_at":"2024-01-02 18:20:52","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":26878,"visible":true,"origin":"","legend":"\u003cp\u003eChange in the number of individuals newly infected a day, \u003cem\u003eAP\u003c/em\u003e, in the number of infected individuals, \u003cem\u003eP\u003c/em\u003e, in the cumulative number of infected individuals, \u003cem\u003eCAP\u003c/em\u003e, and in \u003cem\u003eSRT\u003c/em\u003e+\u003cem\u003eV\u003c/em\u003e. '\u003cem\u003ev \u003c/em\u003e(101-250)0.001' means that the vaccination with a vaccination rate of 0.001 starts on the 101\u003csup\u003est\u003c/sup\u003e and ends on the 250\u003csup\u003eth\u003c/sup\u003e. The symptomatic rate, \u003cem\u003esyr\u003c/em\u003e, is 1. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig10.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/34e460ac4773ac43318b7943.png"},{"id":49075130,"identity":"b4f59bc4-304e-420e-816b-42ed16dd0af4","added_by":"auto","created_at":"2024-01-02 18:20:52","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":26866,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the number of ‘Infected/day; \u003cem\u003eAP\u003c/em\u003e’, ‘Infected; \u003cem\u003eP\u003c/em\u003e’, and 'the cumulative number of infected individuals; \u003cem\u003eCAP\u003c/em\u003e' between two cases with different dates of the end of vaccination. The '\u003cem\u003ev \u003c/em\u003e(101-250)0.001' means that the vaccination with a vaccination rate of 0.001 starts on the 101\u003csup\u003est\u003c/sup\u003e and ends on the 250\u003csup\u003eth\u003c/sup\u003e. The symptomatic rate, \u003cem\u003esyr\u003c/em\u003e, is 1. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig11.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/218d17c09a732d5c8002251f.png"},{"id":49075039,"identity":"12673a3b-ecee-4e69-9f20-66a845d7bf59","added_by":"auto","created_at":"2024-01-02 18:12:52","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":16463,"visible":true,"origin":"","legend":"\u003cp\u003eChange in the total number of infected individuals, \u003cem\u003eTI\u003c/em\u003e, and in the date of the end of infection, ‘Date’, with change in the date of the end of vaccination, ‘DEV’, for cases where vaccination with a vaccination rate of 0.001 starts on the 101\u003csup\u003est\u003c/sup\u003e. The symptomatic rate, \u003cem\u003esyr\u003c/em\u003e, is 1. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig12.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/f7c1f498e542beaff190b13c.png"},{"id":49075027,"identity":"4f06cecf-45ec-483c-8909-02830aa81a86","added_by":"auto","created_at":"2024-01-02 18:12:52","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":28056,"visible":true,"origin":"","legend":"\u003cp\u003eChange in the number of individuals newly infected a day, \u003cem\u003eAP\u003c/em\u003e, in the number of infected individuals, \u003cem\u003eP\u003c/em\u003e, in the cumulative number of infected individuals, \u003cem\u003eCAP\u003c/em\u003e, and in the sum of the number of recovered individuals and the number of vaccinated individuals, \u003cem\u003eSRT\u003c/em\u003e+\u003cem\u003eV\u003c/em\u003e. The ‘\u003cem\u003eAP\u003c/em\u003e; \u003cem\u003epfc\u003c/em\u003e1, \u003cem\u003esyr1\u003c/em\u003e; \u003cem\u003ev \u003c/em\u003e(51-200)0.001; 98-116; 18’ means that vaccination with a vaccination rate of 0.001 starts on the 51\u003csup\u003est\u003c/sup\u003e and ends on the 200\u003csup\u003eth\u003c/sup\u003e and that the number of individuals infected a day, \u003cem\u003eAP\u003c/em\u003e, is 18 at the peak from the 98\u003csup\u003eth\u003c/sup\u003e to the 116\u003csup\u003eth\u003c/sup\u003e. The symptomatic rate, \u003cem\u003esyr\u003c/em\u003e, is 1. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig13.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/a8a4527f435fa5cc9d968a7d.png"},{"id":49075037,"identity":"1bf06712-8e4c-4fbb-8cf3-c9dda086c0b7","added_by":"auto","created_at":"2024-01-02 18:12:52","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":25834,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the number of ‘Infected/day; \u003cem\u003eAP\u003c/em\u003e’, ‘Infected; \u003cem\u003eP\u003c/em\u003e’, and 'the cumulative number of infected individuals; \u003cem\u003eCAP\u003c/em\u003e' between two cases with different dates of the end of vaccination, ‘DEV’. The '\u003cem\u003ev \u003c/em\u003e(51-200)0.001' means that the vaccination with a vaccination rate of 0.001 starts on the 51\u003csup\u003est\u003c/sup\u003e and ends on the 200\u003csup\u003eth\u003c/sup\u003e. The symptomatic rate, syr, is 1. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig14.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/52275c43fb85dc5ccf48fcd8.png"},{"id":49637988,"identity":"a48d7b7a-c56e-4397-8238-955f7b61c42f","added_by":"auto","created_at":"2024-01-15 18:19:15","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":14361,"visible":true,"origin":"","legend":"\u003cp\u003eChange in the total number of infected individuals, \u003cem\u003eTI\u003c/em\u003e, and in the date of the end of infection, ‘Date’, with change in the date of the end of vaccination, ‘DEV’, for cases where vaccination with a vaccination rate of 0.001 starts on the 51st. The symptomatic rate is 1. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e(1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e(\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig15.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/a1a5a7c160557026a37f3a72.png"},{"id":49075316,"identity":"7e66cad4-ef15-4d26-b74f-c0b90eae989d","added_by":"auto","created_at":"2024-01-02 18:28:52","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":24190,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the number of ‘Infected/day; \u003cem\u003eAP\u003c/em\u003e’, ‘Infected; \u003cem\u003eP\u003c/em\u003e’, and 'the cumulative number of infected individuals; \u003cem\u003eCAP\u003c/em\u003e', and the cumulative number of vaccinated individuals, \u003cem\u003eV\u003c/em\u003e, between two cases with different dates of the end of vaccination. The '\u003cem\u003ev \u003c/em\u003e(201-300)0.001' means that the vaccination with a vaccination rate of 0.001 starts on the 201\u003csup\u003est\u003c/sup\u003e and ends on the 300\u003csup\u003eth\u003c/sup\u003e. The symptomatic rate, \u003cem\u003esyr\u003c/em\u003e, is 1. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig16.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/d3dc52a97ac341407917abbd.png"},{"id":49075040,"identity":"fef19a15-671e-49e4-887c-89393fb77d25","added_by":"auto","created_at":"2024-01-02 18:12:52","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":21164,"visible":true,"origin":"","legend":"\u003cp\u003eChange in the number of individuals newly infected a day, \u003cem\u003eAP\u003c/em\u003e; in the number of infected individuals, \u003cem\u003eP\u003c/em\u003e; and in the cumulative number of individuals, \u003cem\u003eCAP\u003c/em\u003e. The 'syr0.8; \u003cem\u003ev\u003c/em\u003e=0' means the case where the symptomatic rate is 0.8 and vaccination is not conducted. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig17.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/2363307707c5f6e32619aeb0.png"},{"id":49075323,"identity":"3596d37f-5273-4f81-97ae-834af5a892a7","added_by":"auto","created_at":"2024-01-02 18:28:52","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":27883,"visible":true,"origin":"","legend":"\u003cp\u003eChange in the number of individuals newly infected a day, \u003cem\u003eAP\u003c/em\u003e; in the number of infected individuals, \u003cem\u003eP\u003c/em\u003e; and in the cumulative number of infected individuals, \u003cem\u003eCAP\u003c/em\u003e. The '\u003cem\u003eP\u003c/em\u003e; \u003cem\u003esyr\u003c/em\u003e0.8; \u003cem\u003ev\u003c/em\u003e(101-230)0.001; 127; 60,392' represents the case with a symptomatic rate of 0.8, the vaccination with a vaccination rate of 0.001 starts on the 101\u003csup\u003est\u003c/sup\u003e and ends on the 230\u003csup\u003eth\u003c/sup\u003e, and the number of infected individuals, \u003cem\u003eP\u003c/em\u003e, is 60,392 at the peak on the 127\u003csup\u003eth\u003c/sup\u003e. From the 1\u003csup\u003est\u003c/sup\u003e to the 147\u003csup\u003eth\u003c/sup\u003e, the \u003cem\u003eCAP\u003c/em\u003e overcomes \u003cem\u003eSRT\u003c/em\u003e+\u003cem\u003eV\u003c/em\u003e. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig18.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/4c3a44f5aba8426d062b69cf.png"},{"id":49075318,"identity":"e89578a2-7d8b-4e91-8ab9-40efae46276a","added_by":"auto","created_at":"2024-01-02 18:28:52","extension":"png","order_by":19,"title":"Figure 19","display":"","copyAsset":false,"role":"figure","size":24851,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the number of individuals newly infected a day (\u003cem\u003eAP\u003c/em\u003e), the number of infected individuals (\u003cem\u003eP\u003c/em\u003e), and the cumulative number of infected individuals (\u003cem\u003eCAP\u003c/em\u003e) between two cases with different dates of the end of vaccination. The '\u003cem\u003ev \u003c/em\u003e(101-230)0.001; 127; 60,392; 227' means that the vaccination with a vaccination rate of 0.001 starts on the 101\u003csup\u003est\u003c/sup\u003e and ends on the 230\u003csup\u003eth\u003c/sup\u003e, the number of infected individuals, \u003cem\u003eP\u003c/em\u003e, is 60,392 at the peak on the 127\u003csup\u003eth\u003c/sup\u003e, and \u003cem\u003eP\u003c/em\u003e becomes 0 on the 227\u003csup\u003eth\u003c/sup\u003e. Since the dates when the infection ends are not significantly different between the two cases (approximately 2 weeks; 244-227=17 days), the differences are not clearly shown on the graph. The symptomatic rate, \u003cem\u003esyr\u003c/em\u003e, is 0.8. The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig19.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/8328f845180ae3f0cabf34cb.png"},{"id":49075134,"identity":"332d2005-dcb7-4e32-981e-3fd253fa5ec9","added_by":"auto","created_at":"2024-01-02 18:20:52","extension":"png","order_by":20,"title":"Figure 20","display":"","copyAsset":false,"role":"figure","size":22359,"visible":true,"origin":"","legend":"\u003cp\u003eRelationships between ‘Recovered +Vaccinated; \u003cem\u003eSRT\u003c/em\u003e+\u003cem\u003eV\u003c/em\u003e' and the increment of infected individuals a day (\u003cem\u003eΔInf\u003c/em\u003e/day), which indicates an incident rate, and between \u003cem\u003eSRT\u003c/em\u003e+\u003cem\u003eV\u003c/em\u003e and the increment (decrement) of the duration of infection a day (\u003cem\u003eΔ\u003c/em\u003eDur/day) by different dates of the end of vaccination, xx, for cases where vaccination with a vaccination rate of 0.001 starts on the 101\u003csup\u003est\u003c/sup\u003e. \u003cem\u003eSRT\u003c/em\u003e is the cumulative number of recovered individuals up to date xx, and \u003cem\u003eV\u003c/em\u003e is the cumulative number of vaccinated individuals up to date xx. The '\u003cem\u003eΔInf\u003c/em\u003e/day: 130; 1,164' indicates that the date of the end of vaccination is 130 and that the increment of infected individuals a day (\u003cem\u003eΔInf\u003c/em\u003e/day) during the period from the date of the end of duration of infection for the 130\u003csup\u003eth\u003c/sup\u003e to that for the 140\u003csup\u003eth\u003c/sup\u003e, that is, 4 days from the 244\u003csup\u003eth\u003c/sup\u003e to the 248\u003csup\u003eth\u003c/sup\u003e, is 1,164 (persons/day). The initial population, \u003cem\u003eTN\u003c/em\u003e (1), is 1,000,000; the initial number of infected individuals, \u003cem\u003eP\u003c/em\u003e (1), is 1; the potential (biological) infectious capacity of coronavirus, \u003cem\u003epfc\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 1.0; the latent period, \u003cem\u003elp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 5; and the recovery period, \u003cem\u003erp\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e), is 14.\u003c/p\u003e","description":"","filename":"Fig20.Massvaccination2023Dec4.png","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/5a97227c52fadf4df592525a.png"},{"id":49076123,"identity":"321546cd-61e4-447f-83cf-8c0e2ee8e0fd","added_by":"auto","created_at":"2024-01-02 18:36:52","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":125004,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEffect of the mass vaccination duration on the spread of COVID-19 evaluated by a flexible compartment model \u003c/strong\u003eHiroo Ohfmori\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTables 1-6\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"EffectofMassvaccinationdurationtables162023Dec10.docx","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/0355a1b30a0fc67446b448a3.docx"},{"id":49075116,"identity":"42daade2-bff2-4800-89df-51f202d7727b","added_by":"auto","created_at":"2024-01-02 18:20:52","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":117324,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSupplementary Material \u0026nbsp;\u003c/strong\u003eHiroo Ohmori\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAppendix 1: Explanations of independent variables and dependent variables used in the Excel file.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"EffectofMassvaccinationdurationSupplApend12023Dec10.docx","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/97966e45b2aa0c6e75ad7d54.docx"},{"id":49076636,"identity":"57a960b8-87f7-4a38-bae6-8378f5c0477c","added_by":"auto","created_at":"2024-01-02 18:44:52","extension":"docx","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":187170,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSupple. Material 2; Appendix 2: Part of Excel for the simulation specific to COVID-19\u003c/strong\u003e H.Ohmori\u003c/p\u003e","description":"","filename":"EffectofMassvaccinationdurationSupplApend2Excel2023Dec10.docx","url":"https://assets-eu.researchsquare.com/files/rs-3705581/v3/62113688c2e5914500ff6d68.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eEffect of the mass vaccination duration on the spread of COVID-19 evaluated by a flexible compartment model\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Tokyo","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Asymptomatic, Compartment model, COVID-19, Duration of infection, Herd immunity, Infected, Infection during the latent period, Isolation, SIR model, Recovered, Susceptible, Symptomatic rate, Mass vaccination duration","lastPublishedDoi":"10.21203/rs.3.rs-3705581/v3","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3705581/v3","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFor COVID-19, infected individuals are isolated from the community when they become symptomatic, and when they become recovered individuals who have immunity, they return to the community. With an increase in the number of recovered individuals in the community, the contact rate between infected individuals and susceptible individuals decreases, resulting in a decrease in the number of infected individuals. Vaccination causes not only a decrease in the number of susceptible individuals in the community but also a reduction in the contact rate between infected individuals and susceptible individuals with an increase in the number of vaccinated individuals, as do the recovered individuals. From the viewpoint of herd immunity, the vaccination duration, which is the period between the start and the end of mass vaccination, must be examined because the number of vaccinated individuals actually increases gradually daily according to vaccination programs, and the total number of vaccinated individuals depends on the mass vaccination duration, controlling the spread of COVID-19. How long should we continue mass vaccination to contain the COVID-19 pandemic from a physical viewpoint? The number of infected individuals by different mass vaccination durations was calculated by a flexible compartment model specific to COVID-19. The model contains the vaccination rate as an independent variable in the calculation equations and, as the dependent variable, the number of isolated/recovered individuals and the population excluding the individuals kept in isolation, both of which affect the contact rate between infected individuals and susceptible individuals. The effect of the mass vaccination duration can be evaluated by comparing the total number of infected individuals among the cases with different mass vaccination durations for the cases with different start dates of vaccination, with different vaccination rates and with different symptomatic rates. The results show that since the contact rate decreases with an increase in the number of vaccinated individuals, the earlier the start date of vaccination is, the smaller the total number of infected individuals becomes, and the longer the mass vaccination duration is, the smaller the total number of infected individuals becomes. The results also showed that when vaccination is continued until the day when the sum of the number of recovered individuals and the number of vaccinated individuals exceeds an \u0026lsquo;expedient herd immunity threshold\u0026rsquo;, the total number of infected individuals is significantly reduced, and the duration of infection is also markedly shortened, as expected for the case with a sufficient mass vaccination duration.\u003c/p\u003e","manuscriptTitle":"Effect of the mass vaccination duration on the spread of COVID-19 evaluated by a flexible compartment model","msid":"","msnumber":"","nonDraftVersions":[{"code":3,"date":"2024-01-02 18:12:47","doi":"10.21203/rs.3.rs-3705581/v3","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}},{"code":2,"date":"2023-12-11 19:45:21","doi":"10.21203/rs.3.rs-3705581/v2","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}},{"code":1,"date":"2023-12-06 01:31:15","doi":"10.21203/rs.3.rs-3705581/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ad8ee389-048f-42c8-9fba-172738b23e41","owner":[],"postedDate":"January 2nd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":27296833,"name":"Immunology"},{"id":27296834,"name":"Infectious Diseases"},{"id":27296835,"name":"Statistical Epidemiology"},{"id":27296836,"name":"Virology"},{"id":27296837,"name":"Environmental Engineering"},{"id":27296838,"name":"Vaccine Development"},{"id":27296839,"name":"Hospital Medicine"},{"id":27296840,"name":"Computational Physics"},{"id":27296841,"name":"Applied Statistics"}],"tags":[],"updatedAt":"2023-12-06T01:31:16+00:00","versionOfRecord":[],"versionCreatedAt":"2024-01-02 18:12:47","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v3","identity":"rs-3705581","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3705581","identity":"rs-3705581","version":["v3"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}