A Graph-Theoretic Framework for Zika Virus through Vertical Transmission and Stability Analysis.

A Graph-Theoretic Framework for Zika Virus through Vertical Transmission and Stability Analysis. | 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 Graph-Theoretic Framework for Zika Virus through Vertical Transmission and Stability Analysis. Renisa P, Sujitha S, Angel Jebitha M K This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9221185/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 The Zika virus, a mosquito-borne pathogen, poses a serious global health threat due to its ability to transmit vertically from infected mothers to newborns, leading to congenital abnormalities and adverse neurological outcomes. A rigorous understanding of vertical transmission dynamics is therefore essential for effective disease prevention and control. In this study, a graph-theoretic framework is proposed to model the human vertical transmission of Zika virus, the birth of babies with microcephaly and asymptomatic infected individuals. The model explicitly incorporates maternal infection states and vertically infected newborn compartments, capturing the mother-to-child transmission pathway. The resulting system is represented as a weighted directed graph, where vertices correspond to epidemiological compartments and directed edges denote transition mechanisms between states. The basic reproduction number $R_0$ is derived using an energy-based approach applied to the characteristic polynomial associated with the digraph structure, providing an analytical threshold for disease invasion. Furthermore, the Jacobian matrix obtained directly from the digraph at the disease-free equilibrium (DFE) is analyzed to investigate local stability using the Routh--Hurwitz and Gershgorin criteria. The analytical results highlight the critical role of vertical transmission pathways in shaping the overall dynamics of Zika virus spread and underscore the importance of maternal-focused intervention strategies in mitigating congenital Zika outcomes. Zika virus vertical transmission newborn babies microcephaly basic reproduction number adjacency matrix energy disease-free equilibrium stability 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-9221185","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":613688318,"identity":"afa0909f-deb3-4e62-8378-de7c47b8abc5","order_by":0,"name":"Renisa P","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABD0lEQVRIiWNgGAWjYJCCAwwMNnIghkQCAwOYceABYS1pxjAtYMaBBMIWHU5sAGkBYjCDAZ8W8/begwd/1Bw2Nmc/e/DGg5o76fPDDj8E2mInp9uAXYvMmXMJh3mOpctZ9uQlWyQce5a78XaaAVBLsrHZAexaJCRyDA4zsFkbGxzIMZNIYDucu3F2AkjLgcRtuLTIvzE4+OMfc+KG82+AWv4dTjecnf4BvxYJHoMDvG3OiRtuAG1JbDucIC+dQ8AWHqDDePvSjC1nvDG2SOw7bLhBOqfgQIIBHr+wnzH++OObjZw5f47hzR/fDsvLz07f/OFDhZ0cLi1wYABnHEDhEqNFvoEI1aNgFIyCUTCiAABxEmdTezZoxQAAAABJRU5ErkJggg==","orcid":"","institution":"Manonmaniam Sundaranar University","correspondingAuthor":true,"prefix":"","firstName":"Renisa","middleName":"","lastName":"P","suffix":""},{"id":613688319,"identity":"85cc32c7-b6bd-46a2-b6f6-768f6615b451","order_by":1,"name":"Sujitha S","email":"","orcid":"","institution":"Manonmaniam Sundaranar University","correspondingAuthor":false,"prefix":"","firstName":"Sujitha","middleName":"","lastName":"S","suffix":""},{"id":613688320,"identity":"318ac9ea-003a-4c20-bac1-ca2bbe4c765e","order_by":2,"name":"Angel Jebitha M K","email":"","orcid":"","institution":"Manonmaniam Sundaranar University","correspondingAuthor":false,"prefix":"","firstName":"Angel","middleName":"Jebitha M","lastName":"K","suffix":""}],"badges":[],"createdAt":"2026-03-25 09:40:36","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9221185/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9221185/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105775825,"identity":"78bde3ba-c42e-434d-b86e-dfedd934a9ab","added_by":"auto","created_at":"2026-03-31 03:16:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":369655,"visible":true,"origin":"","legend":"","description":"","filename":"IJDACpaper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9221185/v1_covered_ad9ec89c-257c-41dc-91e9-dcfb60571a03.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Graph-Theoretic Framework for Zika Virus through Vertical Transmission and Stability Analysis.","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":"Zika virus, vertical transmission, newborn babies, microcephaly, basic reproduction number, adjacency matrix, energy, disease-free equilibrium, stability","lastPublishedDoi":"10.21203/rs.3.rs-9221185/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9221185/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The Zika virus, a mosquito-borne pathogen, poses a serious global health threat due to its ability to transmit vertically from infected mothers to newborns, leading to congenital abnormalities and adverse neurological outcomes. A rigorous understanding of vertical transmission dynamics is therefore essential for effective disease prevention and control. In this study, a graph-theoretic framework is proposed to model the human vertical transmission of Zika virus, the birth of babies with microcephaly and asymptomatic infected individuals. The model explicitly incorporates maternal infection states and vertically infected newborn compartments, capturing the mother-to-child transmission pathway. The resulting system is represented as a weighted directed graph, where vertices correspond to epidemiological compartments and directed edges denote transition mechanisms between states. The basic reproduction number $R_0$ is derived using an energy-based approach applied to the characteristic polynomial associated with the digraph structure, providing an analytical threshold for disease invasion. Furthermore, the Jacobian matrix obtained directly from the digraph at the disease-free equilibrium (DFE) is analyzed to investigate local stability using the Routh--Hurwitz and Gershgorin criteria. The analytical results highlight the critical role of vertical transmission pathways in shaping the overall dynamics of Zika virus spread and underscore the importance of maternal-focused intervention strategies in mitigating congenital Zika outcomes.","manuscriptTitle":"A Graph-Theoretic Framework for Zika Virus through Vertical Transmission and Stability Analysis.","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-31 03:15:56","doi":"10.21203/rs.3.rs-9221185/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":"569473f1-0ef4-466a-ad08-0f51346b1fd0","owner":[],"postedDate":"March 31st, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-31T03:15:57+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-31 03:15:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9221185","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9221185","identity":"rs-9221185","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}