Stochastic Modeling of Viral Reproductive Cycle: Study of Viral and Cell Extinction

Stochastic Modeling of Viral Reproductive Cycle: Study of Viral and Cell Extinction | 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 Stochastic Modeling of Viral Reproductive Cycle: Study of Viral and Cell Extinction Rahnuma Islam, David Swigon This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6623135/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 Although viral dynamics is typically modeled using ordinary differential equations, a natural way to address the phenomena of viral persistence and host cell survival is to use stochastic models of viral reproduction. Here we present a study of viral and substrate cell extinction and their dependence on viral production rate for two simple stochastic models of viral reproduction that differ in the method of viral release: one accounts for viral bursting, in which the release of viruses is instantaneous after cell lesion, the other for viral budding, in which new viral particles are released from infected cells gradually. We show that for both viral release mechanisms, simulation of continuous-time Markov chain versions of the stochastic models is the most accurate but also time-consuming way to obtain the results and that traditional diffusion approximation methods lead to serious discrepancies in extinction probabilities and mean times. We then propose a modified stochastic differential equation approach that achieves a significant improvement in simulation speed while maintaining accuracy. Computational Biology Mathematical and Theoretical Biology Stochastic modeling Viral reproduction Continuous-time Markov chain Stochastic differential equation Jump-diffusion process Full Text Additional Declarations The authors declare no competing interests. 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-6623135","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":453957401,"identity":"dad9e9c3-6d45-4d10-bafc-67024cfe3fb2","order_by":0,"name":"Rahnuma Islam","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAr0lEQVRIiWNgGAWjYFACxuYHCRUMPGA2D5Fa2gwenGHg4WEjXgsDg+TDNqBqorWYtx9uMEicd0fGXr6B8cHbNiK0yJxJbHiQuO0ZyGHMhnOJ0SLBkAi0ZdthkBY2aV6itPA/bJBInAPWwv6bOC0SiUAtDRBbmInU8rDNIOEY0C/HEpsl55wjymHpjx/+qLljz958+OCHN2VEaIGCA0DM2EC8eqiWUTAKRsEoGAU4AAAFkDK+QNPOWwAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-9420-5896","institution":"University of Pittsburgh","correspondingAuthor":true,"prefix":"","firstName":"Rahnuma","middleName":"","lastName":"Islam","suffix":""},{"id":453957727,"identity":"1f4ade59-11e3-4ff9-969a-17846291b686","order_by":1,"name":"David Swigon","email":"","orcid":"","institution":"University of Pittsburgh","correspondingAuthor":false,"prefix":"","firstName":"David","middleName":"","lastName":"Swigon","suffix":""}],"badges":[],"createdAt":"2025-05-08 19:08:40","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-6623135/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6623135/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":82483503,"identity":"2728689f-dc59-443f-85ba-05222eb4deb8","added_by":"auto","created_at":"2025-05-12 04:19:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2931975,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6623135/v1_covered_f6d0079d-713d-4945-8d91-337986fa8fed.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eStochastic Modeling of Viral Reproductive Cycle: Study of Viral and Cell Extinction\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Pittsburgh","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"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":"Stochastic modeling, Viral reproduction, Continuous-time Markov chain, Stochastic differential equation, Jump-diffusion process","lastPublishedDoi":"10.21203/rs.3.rs-6623135/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6623135/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAlthough viral dynamics is typically modeled using ordinary differential equations, a natural way to address the phenomena of viral persistence and host cell survival is to use stochastic models of viral reproduction. 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