Variation of positiveness to enhance testing of specimens during an epidemic

Variation of positiveness to enhance testing of specimens during an epidemic | 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 Variation of positiveness to enhance testing of specimens during an epidemic Usama Kadri This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-28144/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 Rapid testing of appropriate specimens from patients suspected for a disease during an epidemic, such as the current Coronavirus outbreak, is of a great importance for the disease management and control. We propose a method to enhance processing large amounts of collected samples. The method is based on mixing samples in testing tubes in a specific configuration, as opposed to testing single samples in each tube, and accounting for natural virus amounts in infected patients from variation of positiveness in test tubes. To illustrate the efficiency of the suggested method we carry out numerical tests for actual scenarios under various tests. Applying the proposed method enhances the number of tests by order of magnitudes, where all positives are identified with no false negatives, and the effective testing time can be reduced drastically even when the uncertainty in the test is relatively high. Applied Mathematics Infectious Diseases epidemic mathematical model rapid testing combined sample testing Figures Figure 1 Figure 2 Full Text Supplementary Files Supplementaryinformation.pdf 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-28144","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":563643,"identity":"4c525538-e967-4f23-91ca-c2a410bcb59c","order_by":1,"name":"Usama Kadri","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIie3RPQrCMByH4V8RnAJdUwrtFVK6+nGVlEInB6EgjoKgo2vASygF50DW0B7AycXJoW6OmuomxI4OeZdkeZL8CeBy/WEUYOAYmT2Ty27FoA8p3kQXfQmgOoJeJNiqU3vZNLG/V0cpOWJ/RVJmIyEpSpFtzomoi7khiZAk5TYSYZbiRTg0Yer+gHcASaWV+DdDah6/iLll+pOEtLtFcvYhmSHWhwXiWoLXeXLUQzMLzYUaltbxaZNX3mMxiSM9qFrJR+Pddl1RG/k64tevuFwul6tPTwVfSUDr1SfaAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-5441-1812","institution":"Cardiff University, School of Mathema","correspondingAuthor":true,"prefix":"","firstName":"Usama","middleName":"","lastName":"Kadri","suffix":""}],"badges":[],"createdAt":"2020-05-08 19:37:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-28144/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-28144/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":1069109,"identity":"4eac73af-1738-4e84-a9a8-71b8f0d3a235","added_by":"auto","created_at":"2020-05-11 14:16:16","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":283234,"visible":true,"origin":"","legend":"Fixed number of positives. Uncertainty analysis in tests using 8 tubes (m = 8), for fixed number of randomly\nselected positives, ranging from 2.86% to 21.43% of total patients. Each calculation point is an average of 100 repetitions. Left column: percentage of negative patients successfully identified. Right column: solutions found for positive patients (note that once a solution is found 100% of positives are identified). Rows top to bottom: l = 3, 4, and 5, with n = 28, 56, and 70, respectively.","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-28144/v1/1.png"},{"id":1069112,"identity":"3dd5ea1c-8ca0-4d39-8962-719ec11c9b23","added_by":"auto","created_at":"2020-05-11 14:16:16","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":167712,"visible":true,"origin":"","legend":"Random number of positives. Uncertainty analysis in tests for random number of positives (randomly\nselected), ranging from 0.8% to 5% of total patients. Using 10 tubes (m = 10), and l = 3, 4, and 5, corresponding to a total number of patients n = 120, 210, and 252, respectively. Left plot: percentage of negative patients successfully identified. Right column: solutions found for positive patients (note that once a solution is found 100% of positives are identified).","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-28144/v1/2.png"},{"id":1069127,"identity":"00b878b4-8273-49a4-b2f6-f9b4bd5b0527","added_by":"auto","created_at":"2020-05-11 14:16:31","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":255386,"visible":true,"origin":"","legend":"","description":"","filename":"7438e7ef820c4c0eb1ba74f64a7a85a6covlettandsuppremoved.pdf","url":"https://assets-eu.researchsquare.com/files/rs-28144/v1_stamped.pdf"},{"id":1069111,"identity":"2d39147b-cf50-4eb6-9719-c39372fa972d","added_by":"auto","created_at":"2020-05-11 14:16:16","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":216589,"visible":true,"origin":"","legend":"","description":"","filename":"7438e7ef820c4c0eb1ba74f64a7a85a6covlettandsuppremoved.pdf","url":"https://assets-eu.researchsquare.com/files/rs-28144/v1/7438e7ef820c4c0eb1ba74f64a7a85a6covlettandsuppremoved.pdf"},{"id":13502418,"identity":"b55a4c67-cf46-4eab-9e16-e42b640c73d5","added_by":"auto","created_at":"2021-09-16 23:14:32","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":420553,"visible":true,"origin":"","legend":"","description":"","filename":"7438e7ef820c4c0eb1ba74f64a7a85a6covlettandsuppremoved.pdf","url":"https://assets-eu.researchsquare.com/files/rs-28144/v1_covered.pdf"},{"id":1069110,"identity":"cb5b8b69-13a7-4e16-84f9-cdd19ab845c5","added_by":"auto","created_at":"2020-05-11 14:16:16","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":258386,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementaryinformation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-28144/v1/Supplementaryinformation.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eVariation of positiveness to enhance testing of specimens during an epidemic\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"\u003cp\u003eThis preprint is available for \u003ca href='/article/rs-28144/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e.\u003c/p\u003e"}],"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":false,"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":"epidemic, mathematical model, rapid testing, combined sample testing","lastPublishedDoi":"10.21203/rs.3.rs-28144/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-28144/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRapid testing of appropriate specimens from patients suspected for a disease during an epidemic, such as the current Coronavirus outbreak, is of a great importance for the disease management and control. We propose a method to enhance processing large amounts of collected samples. The method is based on mixing samples in testing tubes in a specific configuration, as opposed to testing single samples in each tube, and accounting for natural virus amounts in infected patients from variation of positiveness in test tubes. To illustrate the efficiency of the suggested method we carry out numerical tests for actual scenarios under various tests. Applying the proposed method enhances the number of tests by order of magnitudes, where all positives are identified with no false negatives, and the effective testing time can be reduced drastically even when the uncertainty in the test is relatively high.\u003c/p\u003e","manuscriptTitle":"Variation of positiveness to enhance testing of specimens during an epidemic","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2020-05-11 14:15:40","doi":"10.21203/rs.3.rs-28144/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":"d4f551a4-4107-41cb-9d76-848787369619","owner":[],"postedDate":"May 11th, 2020","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":97494,"name":"Applied Mathematics"},{"id":97495,"name":"Infectious Diseases"}],"tags":[],"updatedAt":"2020-07-20T23:52:57+00:00","versionOfRecord":[],"versionCreatedAt":"2020-05-11 14:15:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-28144","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-28144","identity":"rs-28144","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}