Dynamic optimization of disease co-infection: Evaluating the effects of changes in human behavior caused by self-precautions and vaccinations

Dynamic optimization of disease co-infection: Evaluating the effects of changes in human behavior caused by self-precautions and vaccinations | 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 Dynamic optimization of disease co-infection: Evaluating the effects of changes in human behavior caused by self-precautions and vaccinations Muhammad Imran, Salihu S. Musa, Ismail Abdulrashid, Brett A. McKinney This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9519020/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 Disease co-infections pose substantial epidemiological and public health challenges by amplifying disease severity, prolonging recovery, and increasing mortality. Notable examples include COVID-19–tuberculosis, dengue–malaria, and COVID-19–influenza, where pathogen interactions reshape transmission dynamics and clinical outcomes. Understanding the interplay between co-infections and behavior is therefore critical for effective mitigation. We develop a dynamical SEIR-type model that captures single and dual infections while explicitly incorporating behaviorally driven self-precaution and vaccination uptake. We derive the basic reproduction number ($R_0$), characterize disease-free and endemic equilibria, and establish conditions for global stability. Sensitivity analysis identifies the parameters most influential for transmission and control. To optimize interventions, we formulate an optimal control problem with both constant and time-varying controls representing self-precaution (masking, distancing, hygiene) and vaccination. Using Pontryagin’s Maximum Principle, we obtain structure of the optimal policies and quantify trade-offs between epidemiological impact and implementation cost. Numerical experiments show that combining self-precaution with vaccination yields synergistic reductions in co-infection prevalence and overall disease burden, outperforming either measure alone across wide parameter ranges. By integrating adaptive human behavior with pathogen dynamics under a rigorous control framework, this study provides a quantitative basis for evidence-based policies that can be tuned in real time to evolving epidemic conditions. Mathematical and Theoretical Biology Co-infection dynamics Epidemiological modeling Human behavioral adaptation Optimal control Sensitivity analysis Vaccination impact intervention measures 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-9519020","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":629117896,"identity":"08f6aed0-89c2-4c49-b45f-f94d2bcee2ec","order_by":0,"name":"Muhammad Imran","email":"","orcid":"","institution":"University of Tulsa, 800 S. 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Notable examples include COVID-19–tuberculosis, dengue–malaria, and COVID-19–influenza, where pathogen interactions reshape transmission dynamics and clinical outcomes. Understanding the interplay between co-infections and behavior is therefore critical for effective mitigation. We develop a dynamical SEIR-type model that captures single and dual infections while explicitly incorporating behaviorally driven self-precaution and vaccination uptake. We derive the basic reproduction number ($R_0$), characterize disease-free and endemic equilibria, and establish conditions for global stability. Sensitivity analysis identifies the parameters most influential for transmission and control. To optimize interventions, we formulate an optimal control problem with both constant and time-varying controls representing self-precaution (masking, distancing, hygiene) and vaccination. Using Pontryagin’s Maximum Principle, we obtain structure of the optimal policies and quantify trade-offs between epidemiological impact and implementation cost. Numerical experiments show that combining self-precaution with vaccination yields synergistic reductions in co-infection prevalence and overall disease burden, outperforming either measure alone across wide parameter ranges. By integrating adaptive human behavior with pathogen dynamics under a rigorous control framework, this study provides a quantitative basis for evidence-based policies that can be tuned in real time to evolving epidemic conditions.\u003c/p\u003e","manuscriptTitle":"Dynamic optimization of disease co-infection: Evaluating the effects of changes in human behavior caused by self-precautions and vaccinations","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-27 09:37:12","doi":"10.21203/rs.3.rs-9519020/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":"a47b812b-9cf3-4a16-ae1b-85ed463dd5dc","owner":[],"postedDate":"April 27th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":66966427,"name":"Mathematical and Theoretical Biology"}],"tags":[],"updatedAt":"2026-04-27T09:37:12+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-27 09:37:12","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9519020","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9519020","identity":"rs-9519020","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}