A Mathematical Model for the Transmission Dynamics of Yellow Fever with Vaccination and Vector Control

A Mathematical Model for the Transmission Dynamics of Yellow Fever with Vaccination and Vector Control | 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 A Mathematical Model for the Transmission Dynamics of Yellow Fever with Vaccination and Vector Control Isaac Adesola Olopade, Musleh Anas Ibrahim, Abdul Kareem Adamu, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7372710/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 Yellow fever, a mosquito borne viral hemorrhagic disease endemic in sub Saharan Africa, remains a significant public health challenge due to insufficient vaccination coverage and inadequate vector control. This study proposes a deterministic model for the transmission dynamics of yellow fever, explicitly incorporating the effect of vaccination alongside vector control as intervention strategies. The model categorized the human population into susceptible, exposed, infectious, and recovered classes, while the vector population is partitioned into susceptible, exposed and infectious compartments, capturing the human-mosquito-human transmission pathway. The model's mathematical wellposedness is established by proving the positivity, boundedness, and uniqueness of solutions. Equilibrium analysis reveals the existence of both disease free and endemic steady states. The effective reproduction number , is derived using the next generation matrix method. Local stability of the disease free equilibrium is examined by linearizing the Jacobian matrix at the disease free state, while the endemic equilibrium is analyzed using the Routh Hurwitz criterion. Global stability results are established via the Castillo Chavez theorem for the disease free equilibrium and an appropriate Lyapunov function for the endemic equilibrium. Sensitivity analysis identifies key parameters influencing , with vaccination coverage and vector control exhibiting strong negative impacts on transmission. Numerical simulations demonstrate that increasing vaccination rates and intensifying mosquito control efforts can reduce below unity, thereby preventing outbreaks. This study emphasizes the importance of combined vaccination and vector control strategies in reducing the burden of yellow fever. Yellow fever Vaccination Vector control Mathematical modeling Effective reproduction number Stability analysis Sensitivity analysis Numerical simulation Full Text Additional Declarations No competing interests reported. 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7372710","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":501802901,"identity":"b47e7752-9192-4e03-825a-d10d2d9c9621","order_by":0,"name":"Isaac Adesola Olopade","email":"","orcid":"","institution":"Federal University Wukari","correspondingAuthor":false,"prefix":"","firstName":"Isaac","middleName":"Adesola","lastName":"Olopade","suffix":""},{"id":501802902,"identity":"a7a5be86-beca-43d4-919b-85b20e6cebf5","order_by":1,"name":"Musleh Anas Ibrahim","email":"data:image/png;base64,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","orcid":"","institution":"Federal University Wukari","correspondingAuthor":true,"prefix":"","firstName":"Musleh","middleName":"Anas","lastName":"Ibrahim","suffix":""},{"id":501802903,"identity":"bf20ac5a-7397-4f19-a3a7-eb548ee95109","order_by":2,"name":"Abdul Kareem Adamu","email":"","orcid":"","institution":"Federal University Wukari","correspondingAuthor":false,"prefix":"","firstName":"Abdul","middleName":"Kareem","lastName":"Adamu","suffix":""},{"id":501802904,"identity":"713bbd8d-8a66-4bdd-832e-b39b69d59f95","order_by":3,"name":"Philip Oladapo Olanrewaju","email":"","orcid":"","institution":"Federal University Wukari","correspondingAuthor":false,"prefix":"","firstName":"Philip","middleName":"Oladapo","lastName":"Olanrewaju","suffix":""},{"id":501802905,"identity":"99edf80d-c1c9-43d5-ad4d-051637c2a286","order_by":4,"name":"Nkpe-Enamhe Grace Uwaunyin","email":"","orcid":"","institution":"Federal University Wukari","correspondingAuthor":false,"prefix":"","firstName":"Nkpe-Enamhe","middleName":"Grace","lastName":"Uwaunyin","suffix":""}],"badges":[],"createdAt":"2025-08-14 10:31:57","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7372710/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7372710/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":89693062,"identity":"a588a076-0a23-4a16-9dac-5a50d77fdd57","added_by":"auto","created_at":"2025-08-22 17:16:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":949367,"visible":true,"origin":"","legend":"","description":"","filename":"YellowFeverSpringer.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7372710/v1_covered_effce2dc-a95d-44f8-a9e5-7290a4a67b07.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Mathematical Model for the Transmission Dynamics of Yellow Fever with Vaccination and Vector Control","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"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":"Yellow fever, Vaccination, Vector control, Mathematical modeling, Effective reproduction number, Stability analysis, Sensitivity analysis, Numerical simulation","lastPublishedDoi":"10.21203/rs.3.rs-7372710/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7372710/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eYellow fever, a mosquito borne viral hemorrhagic disease endemic in sub Saharan Africa, remains a significant public health challenge due to insufficient vaccination coverage and inadequate vector control. This study proposes a deterministic model for the transmission dynamics of yellow fever, explicitly incorporating the effect of vaccination alongside vector control as intervention strategies. The model categorized the human population into susceptible, exposed, infectious, and recovered classes, while the vector population is partitioned into susceptible, exposed and infectious compartments, capturing the human-mosquito-human transmission pathway. The model's mathematical wellposedness is established by proving the positivity, boundedness, and uniqueness of solutions. Equilibrium analysis reveals the existence of both disease free and endemic steady states. The effective reproduction number \u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e, is derived using the next generation matrix method. Local stability of the disease free equilibrium is examined by linearizing the Jacobian matrix at the disease free state, while the endemic equilibrium is analyzed using the Routh Hurwitz criterion. Global stability results are established via the Castillo Chavez theorem for the disease free equilibrium and an appropriate Lyapunov function for the endemic equilibrium. Sensitivity analysis identifies key parameters influencing \u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e, with vaccination coverage and vector control exhibiting strong negative impacts on transmission. Numerical simulations demonstrate that increasing vaccination rates and intensifying mosquito control efforts can reduce \u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e below unity, thereby preventing outbreaks. This study emphasizes the importance of combined vaccination and vector control strategies in reducing the burden of yellow fever.\u003c/p\u003e","manuscriptTitle":"A Mathematical Model for the Transmission Dynamics of Yellow Fever with Vaccination and Vector Control","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-22 03:51:07","doi":"10.21203/rs.3.rs-7372710/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":"35a3e25e-a3d4-4f64-a788-0994ae746512","owner":[],"postedDate":"August 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-22T17:08:39+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-22 03:51:07","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7372710","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7372710","identity":"rs-7372710","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}