Improved Tuberculosis Reinfection Dynamics Modeling with Delay Differential Equations

Tuberculosis Reactivation and Reinfection Dynamics Modeling with Delay Differential Equations | 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 Tuberculosis Reactivation and Reinfection Dynamics Modeling with Delay Differential Equations M. A. Elfouly, M. E. Fares, M. A. Sohaly This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5656738/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract Tuberculosis (TB) remains a major public health challenge due to its complex transmission dynamics, which are influenced by reactivation of latent infection, reinfection of recovered individuals, and time delays in disease progression. This study provides a differential delay equations model to investigate TB disease stability. This method offers a more reasonable representation of TB transmission by including reactivation and reinfection as well as time delays in incubation, recovery, and immunodeficiency. The findings underline the important part time delays play in determining TB disease dynamics. Longer incubation periods extend the latent phase, increasing undetected transmission; treatment delays extension infectious periods leading to more secondary infections and immunodeficiency delays increase the risk of reinfection and reactivation, affecting long-term disease persistence. Numerical simulations show that high reactivation rates extension infection cycles, amplify disease fluctuations, and delay stabilization, even when the basic reproduction number and the effective reproduction number indicate infection elimination. It increases the sensitivity of other parameters by increasing feedback loops. Conversely, low reactivation rates facilitate swift transitions to equilibrium and decrease endemicity. They decrease the sensitivity of additional parameters and constrain feedback effects. The findings indicate that reactivation, reinfection, and time delays are critical factors in the persistence and control of tuberculosis. Tuberculosis Reinfection rate Delay differential equations Sensitivity analysis Transmission dynamics Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 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. 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-5656738","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":405444608,"identity":"60488c46-4161-4d12-96d8-0bf05fee140e","order_by":0,"name":"M. A. Elfouly","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYFACxgcHPhjY1O8/3sDATKQWZsOHMyrSGBvOHCBei7Exz5nDjA03EojUott+mE1yZlsaM+PMN4afCypsGPjbuxPwajE7k8wm8bHNho1ZOsdYesaZNAaJM2c34NdyIP8YyBYeNukcA2netsMMBhK5BLScf8wGUinBI3nG+DdxWm4kM4O8byAhwWNGpC03HjOCAjnBgCetzJrnTBoPYb+cT2YARWWCAfvhzbd5Kmzk+Nt78WtBAhwGIJKHWOUgwP6AFNWjYBSMglEwggAAYgJI71NpwMEAAAAASUVORK5CYII=","orcid":"","institution":"Mansoura University","correspondingAuthor":true,"prefix":"","firstName":"M.","middleName":"A.","lastName":"Elfouly","suffix":""},{"id":405444609,"identity":"b6efae4c-f557-461d-9ba6-8499da335209","order_by":1,"name":"M. E. Fares","email":"","orcid":"","institution":"Mansoura University","correspondingAuthor":false,"prefix":"","firstName":"M.","middleName":"E.","lastName":"Fares","suffix":""},{"id":405444610,"identity":"a4167541-02cf-487d-8248-26697151c77c","order_by":2,"name":"M. A. Sohaly","email":"","orcid":"","institution":"Mansoura University","correspondingAuthor":false,"prefix":"","firstName":"M.","middleName":"A.","lastName":"Sohaly","suffix":""}],"badges":[],"createdAt":"2024-12-16 21:38:35","currentVersionCode":2,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-5656738/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-5656738/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eTuberculosis Reactivation and Reinfection Dynamics Modeling with Delay Differential Equations\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","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":"Tuberculosis, Reinfection rate, Delay differential equations, Sensitivity analysis, Transmission dynamics","lastPublishedDoi":"10.21203/rs.3.rs-5656738/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5656738/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTuberculosis (TB) remains a major public health challenge due to its complex transmission dynamics, which are influenced by reactivation of latent infection, reinfection of recovered individuals, and time delays in disease progression. This study provides a differential delay equations model to investigate TB disease stability. This method offers a more reasonable representation of TB transmission by including reactivation and reinfection as well as time delays in incubation, recovery, and immunodeficiency. The findings underline the important part time delays play in determining TB disease dynamics. Longer incubation periods extend the latent phase, increasing undetected transmission; treatment delays extension infectious periods leading to more secondary infections and immunodeficiency delays increase the risk of reinfection and reactivation, affecting long-term disease persistence. Numerical simulations show that high reactivation rates extension infection cycles, amplify disease fluctuations, and delay stabilization, even when the basic reproduction number and the effective reproduction number indicate infection elimination. It increases the sensitivity of other parameters by increasing feedback loops. Conversely, low reactivation rates facilitate swift transitions to equilibrium and decrease endemicity. They decrease the sensitivity of additional parameters and constrain feedback effects. The findings indicate that reactivation, reinfection, and time delays are critical factors in the persistence and control of tuberculosis.\u003c/p\u003e","manuscriptTitle":"Tuberculosis Reactivation and Reinfection Dynamics Modeling with Delay Differential Equations","msid":"","msnumber":"","nonDraftVersions":[{"code":2,"date":"2025-05-05 15:55:54","doi":"10.21203/rs.3.rs-5656738/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":"2025-01-22 07:18:04","doi":"10.21203/rs.3.rs-5656738/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":"66fc2425-c58c-4a68-bcbd-74ae17c81682","owner":[],"postedDate":"May 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-01-25T15:08:19+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-05 15:55:54","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v2","identity":"rs-5656738","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5656738","identity":"rs-5656738","version":["v2"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}