Mathematical study for the phase-based transmissibility of a novel COVID-19 Coronavirus

Mathematical study for the phase-based transmissibility of a novel COVID-19 Coronavirus | 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 Mathematical study for the phase-based transmissibility of a novel COVID-19 Coronavirus Miled EL HAJJI, Sayed SAYARI, Abdelhamid ZAGHDANI This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-26318/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this paper, a mathematical dynamical system modeling a SEIRW model of infectious disease transmission for a transmissibility of a novel COVID-19 Coronavirus is studied. A qualitative analysis such as the local and global stability of equilibrium points is carried out. It is proved that if $\R \leq 1$, then the disease-free equilibrium is globally asymptotically stable and if $\R > 1$, then the disease-persistence equilibrium is globally asymptotically stable. Infectious Diseases Mathematical and Theoretical Biology COVID-19 Coronavirus SEIRW Model Local and Global Stability Direct Lyapunov Method Lasalle's Invariance Principle Figures Figure 1 Figure 2 Figure 3 Full Text Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version 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-26318","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":535246,"identity":"9844c0fe-6d10-4d19-91a7-44632c3f4bc0","order_by":1,"name":"Miled EL HAJJI","email":"","orcid":"https://orcid.org/0000-0002-4718-4463","institution":"ENIT-LAMSIN, BP. 37, 1002 Tunis-Belv\\'ed\\`ere, Tunis El Manar University, Tunisia \u0026 Higher Institute of Applied Science and Technology of Sousse, Sousse University, Cit\\'e Taffala, 4003 Sousse, Tunisia","correspondingAuthor":false,"prefix":"","firstName":"Miled","middleName":"EL","lastName":"HAJJI","suffix":""},{"id":535247,"identity":"04e31642-8616-4931-8e2c-19466bf330ca","order_by":2,"name":"Sayed SAYARI","email":"","orcid":"","institution":"Carthage University, Isteub, 2 Rue de l'Artisanat Charguia 2, 2035 Tunis, Tunisia","correspondingAuthor":false,"prefix":"","firstName":"Sayed","middleName":"","lastName":"SAYARI","suffix":""},{"id":535248,"identity":"47aa3160-9e16-456f-8dd4-274611b96be4","order_by":3,"name":"Abdelhamid ZAGHDANI","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABC0lEQVRIie3RsUrEMBjA8a8c1CVya4/iPUOOwolQFN8kH4VMdnLpWDjodHDriaKvEPEFvlLIYrFr4UTrfgcdndRW3KQttwnmD8kQ8iMJATCZ/mC8GcTAZzZkRCLyAZx23R8kcjq2NFZ1Ln+I7CfAIPMmi9ybXSXZMDk+eETaRiNUmuYuswtcXS/SCsRLJzlZhiq9yW1UOUmXsQ2un3XAQVx2X4xClR0mDFVJ2mXOBuPyYu5Y76KbFLuWOKhe3xKX8Se8awmIHlJ+n8K9SZyNZmtBzXGDZNe+RUzHoK2qpsC7L2XARR8pwod6G302X1nUhB+nR7dlkFZ1D/nVedzOewCAs302m0wm0//oCyHSaEu8a+DRAAAAAElFTkSuQmCC","orcid":"","institution":"University of Tunis, Boulevard du 9 Avril 1939 Tunis. Department of Mathematics, Ensit, Taha Hussein Avenue, Montfleury. Tunis, Tunisia.","correspondingAuthor":true,"prefix":"","firstName":"Abdelhamid","middleName":"","lastName":"ZAGHDANI","suffix":""}],"badges":[],"createdAt":"2020-04-30 23:13:55","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-26318/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-26318/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":1023908,"identity":"88535113-748e-46ae-8c87-886517cb802f","added_by":"auto","created_at":"2020-05-04 12:57:25","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":16606,"visible":true,"origin":"","legend":"Flowchart of the Reservoir-People transmission network model (SEIRW).","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-26318/v1/1.jpg"},{"id":1023910,"identity":"910b13b1-cd21-476a-8f54-31ccb8462eac","added_by":"auto","created_at":"2020-05-04 12:57:26","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":26712,"visible":true,"origin":"","legend":"(S(t),E(t), I(t),R(t),W(t)) behaviours for (left) n = 1000, m = 10, b1 = 1.5, b2 = 1, w = 1, g = 30, e = 1, R = 0.568 \u0014 1 and for (right) n = 10000, m = 10, b1 = 1.5, b2 = 1, w = 0.1, g = 30, e = 1, R = 0.619 \u0014 1.","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-26318/v1/2.jpg"},{"id":1023911,"identity":"9d96fb0d-c79d-40f3-b7f2-9849518556c5","added_by":"auto","created_at":"2020-05-04 12:57:26","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":25645,"visible":true,"origin":"","legend":"(S(t),E(t), I(t),R(t),W(t)) behaviours for (left) n = 1000, m = 10, b1 = 1.5, b2 = 1, w = 10, g = 30, e = 1, R = 3.125 \u003e 1 and for (right) n = 10000, m = 10, b1 = 1.5, b2 = 1, w = 1, g = 30, e = 1, R = 5.682 \u003e 1.","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-26318/v1/3.jpg"},{"id":1027766,"identity":"dad21861-3e7f-4c3b-a7b2-ac1877032e29","added_by":"auto","created_at":"2020-05-04 18:06:49","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":231040,"visible":true,"origin":"","legend":"","description":"","filename":"Covid1920.pdf","url":"https://assets-eu.researchsquare.com/files/rs-26318/v1_stamped.pdf"},{"id":1023909,"identity":"9eaf6304-62c0-4f81-ab2e-b887fb5bb100","added_by":"auto","created_at":"2020-05-04 12:57:26","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":288949,"visible":true,"origin":"","legend":"","description":"","filename":"Covid1920.pdf","url":"https://assets-eu.researchsquare.com/files/rs-26318/v1/Covid1920.pdf"},{"id":13501202,"identity":"9cfc3a25-6dc2-461b-8a5a-ad46924ae3c5","added_by":"auto","created_at":"2021-09-16 23:09:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":331124,"visible":true,"origin":"","legend":"","description":"","filename":"Covid1920.pdf","url":"https://assets-eu.researchsquare.com/files/rs-26318/v1_covered.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eMathematical study for the phase-based transmissibility of a novel COVID-19 Coronavirus\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"\u003cp\u003eThis preprint is available for \u003ca href='/article/rs-26318/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"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":"COVID-19, Coronavirus, SEIRW Model, Local and Global Stability, Direct Lyapunov Method, Lasalle's Invariance Principle","lastPublishedDoi":"10.21203/rs.3.rs-26318/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-26318/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, a mathematical dynamical system modeling a SEIRW model of infectious disease transmission for a transmissibility of a novel COVID-19 Coronavirus is studied. A qualitative analysis such as the local and global stability of equilibrium points is carried out.\u003c/p\u003e\u003cp\u003eIt is proved that if $\\R \\leq 1$, then the disease-free equilibrium is globally asymptotically stable and if $\\R \u0026gt; 1$, then the disease-persistence equilibrium is globally asymptotically stable.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","manuscriptTitle":"Mathematical study for the phase-based transmissibility of a novel COVID-19 Coronavirus","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2020-05-04 12:57:25","doi":"10.21203/rs.3.rs-26318/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":"9f57f491-919c-4f8c-a577-dac7b32561d0","owner":[],"postedDate":"May 4th, 2020","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":92284,"name":"Infectious Diseases"},{"id":92285,"name":"Mathematical and Theoretical Biology"}],"tags":[],"updatedAt":"2020-05-04T12:57:25+00:00","versionOfRecord":[],"versionCreatedAt":"2020-05-04 12:57:25","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-26318","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-26318","identity":"rs-26318","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}