Transmission dynamics of typhoid fever with non-linear incidence rate and saturated treatment

Transmission dynamics of typhoid fever with non-linear incidence rate and saturated treatment | 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 Transmission dynamics of typhoid fever with non-linear incidence rate and saturated treatment Lakshita Sharma, Indriputra Laxman Dhankrial, Rakesh Kumar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6508952/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Nov, 2025 Read the published version in International Journal of Dynamics and Control → Version 1 posted You are reading this latest preprint version Abstract Typhoid fever has always remained a highly endemic disease and posed a significant public health challenge, particularly in tropical developing nations. This paper presents a comprehensive model for typhoid fever which incorporates non-linear incidence and saturated treatment. We focus on the three control measures: prevention, vaccination, and treatment. We derive the basic reproduction number and analyze the local and global stability of the disease-free equilibrium using Lyapunov stability theory. Bifurcation analysis reveals that forward bifurcation can occur depending on the specific model parameters. Sensitivity analysis reveals that higher transmission rates can accelerate the spread of the epidemic; however, interventions influenced by non-linear rate such as increased awareness and behavioral changes along with saturated treatment strategies, are effective in lowering the basic reproduction number below one, thereby playing a key role in controlling the disease. Additionally, Pontryagin’s maximum principle is utilized to identify the most effective control strategies for minimizing the spread of typhoid fever. Numerical simulations support the analytical findings and illustrate the influence of various parameters on the dynamics of typhoid fever. Non-linear incidence Saturated treatment Sensitivity analysis Forward bifurcation Optimal control Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 21 Nov, 2025 Read the published version in International Journal of Dynamics and Control → 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. 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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-6508952","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":453124089,"identity":"63fa3acc-fe0c-4229-9db2-0119e39275dd","order_by":0,"name":"Lakshita Sharma","email":"","orcid":"","institution":"Central University of Himachal Pradesh","correspondingAuthor":false,"prefix":"","firstName":"Lakshita","middleName":"","lastName":"Sharma","suffix":""},{"id":453124090,"identity":"e2c03990-a282-4b72-ac02-792305f82dc5","order_by":1,"name":"Indriputra Laxman Dhankrial","email":"","orcid":"","institution":"Central University of Himachal Pradesh","correspondingAuthor":false,"prefix":"","firstName":"Indriputra","middleName":"Laxman","lastName":"Dhankrial","suffix":""},{"id":453124091,"identity":"0f6535f4-daff-454d-8990-80cd92ac4af9","order_by":2,"name":"Rakesh Kumar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7klEQVRIiWNgGAWjYFACNgYGxgYGGSCL8TFcMIEILTwMDMzMxiRrYZMmylnm7ccSH/7cwcDDz37+WHXhDrvEBvbDDxge7sCtReZM2mFj3jMMPJI9yWy3Z55JTmzgSTNgSDyDW4sEQ3qbNGMbA4/BDWa227xtBxIbGHIYGBLb8Gjhf97+8ydQiz1QSzFYC/8bAlok0o4x8IJskWBmYwZrkSBki8SzZGneNgkeiTPJxtK8QKJN4pnBAfwOSzP8+LPNRo6//eDDz7w77GT7+ZMfPvyJRws8FMAAGEGgeGI4QFADHIC0jIJRMApGwShABwCNMUb+/eYCzgAAAABJRU5ErkJggg==","orcid":"","institution":"Central University of Himachal Pradesh","correspondingAuthor":true,"prefix":"","firstName":"Rakesh","middleName":"","lastName":"Kumar","suffix":""}],"badges":[],"createdAt":"2025-04-23 05:08:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6508952/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6508952/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s40435-025-01953-7","type":"published","date":"2025-11-21T15:58:29+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":96650353,"identity":"a9093456-a8ba-42ae-9396-79e6fd064608","added_by":"auto","created_at":"2025-11-24 16:11:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1213533,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6508952/v1_covered_f21d34bf-29e3-46ae-9501-3e2842466d35.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Transmission dynamics of typhoid fever with non-linear incidence rate and saturated treatment","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"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":"Non-linear incidence, Saturated treatment, Sensitivity analysis, Forward bifurcation, Optimal control","lastPublishedDoi":"10.21203/rs.3.rs-6508952/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6508952/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Typhoid fever has always remained a highly endemic disease and posed a significant public health challenge, particularly in tropical developing nations. 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