Vaccination Games of Boundedly Rational Parents toward New Childhood Immunization

Vaccination Games of Boundedly Rational Parents toward New Childhood Immunization | 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 Vaccination Games of Boundedly Rational Parents toward New Childhood Immunization Wei Yin, Martial L Ndeffo-Mbah, Tamer Oraby This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4572949/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 Infectious diseases harm societies through disease-induced morbidity, mortality, loss of productivity, and inequality. Thus, controlling and preventing them is critical for public health and societal well-being. However, societies can hamper efforts to control the spread of diseases by non-adherence to public health recommendations; like, through vaccine hesitancy. Various disease-transmission models have been utilized to help policymakers respond to (re)emerging outbreaks. The usefulness of such models in assessing the effectiveness of public health policies is significantly dependent on human behavior. This paper introduces a new model of parental behavior toward a new childhood immunization. The model incorporates societal features, social norms, and bounded rationality. We integrate that model with the dynamics of childhood disease depicted by a standard susceptible-infected-recovered model to offer a detailed perspective on vaccine acceptance dynamics. We found that the behavioral model provides a new population game theory's replicator dynamical equation with an entropy-like term. Interestingly, societal norms and bounded rationality play an important role in shaping vaccine uptake through a new function, which we call the critical societal vaccine cost. The results suggest that reduced vaccine costs below that critical societal vaccine cost and higher initial acceptance rates increase the probability of disease elimination. A gradual increase in the cost of vaccination as an adaptive dynamical policy of disease eradication is also possible. In particular, strong social norms and low levels of bounded rationality positively contribute to disease eradication even when the basic reproduction number of the disease in that society is large. Mathematical and Theoretical Biology Replicator dynamics Bounded rationality Game theory Disease models. 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-4572949","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":313804902,"identity":"542b0b4b-4415-4cdb-b610-e86c251294b1","order_by":0,"name":"Wei Yin","email":"","orcid":"","institution":"The University of Texas Rio Grande Valley","correspondingAuthor":false,"prefix":"","firstName":"Wei","middleName":"","lastName":"Yin","suffix":""},{"id":313804957,"identity":"a168d8fb-51af-4545-82a8-72581576a8f7","order_by":1,"name":"Martial L Ndeffo-Mbah","email":"","orcid":"","institution":"Texas A\\\u0026M University","correspondingAuthor":false,"prefix":"","firstName":"Martial","middleName":"L","lastName":"Ndeffo-Mbah","suffix":""},{"id":313804980,"identity":"7bb12317-efc8-4b9f-8ccd-464c1a070546","order_by":2,"name":"Tamer Oraby","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6ElEQVRIiWNgGAWjYFADCQbGBwg2HsCDpIXZgCGBRC1sEkRpsWc/nfi4gsEmn392j1k17497dhsOMB+8zYNHCw9P7mbDMwxpljPunDG7zZNQnLzhAFuyNV4tDLnbJBsYDhsw3MgBaUlIlmzgMZPGq4X/7fafIC3yQC3FEC383/BrkcjdxgjSYgDUwgzUYsfPwMOGX8uNt5slGwzSDAzvHCuWnJOWkMDPzGZsOQePFvb+3I0fGypsDORuN2/88MYmwZ6NvfnhjTd4tECAAYjgAJOJDcwElSMsfAAi7YnXMApGwSgYBSMFAABFYESbHIFNxgAAAABJRU5ErkJggg==","orcid":"","institution":"The University of Texas Rio Grande Valley","correspondingAuthor":true,"prefix":"","firstName":"Tamer","middleName":"","lastName":"Oraby","suffix":""}],"badges":[],"createdAt":"2024-06-13 01:58:34","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4572949/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4572949/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":58327916,"identity":"7c5e2c67-a8d9-43f6-9e6d-33c7195a561a","added_by":"auto","created_at":"2024-06-14 02:54:55","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":951041,"visible":true,"origin":"","legend":"","description":"","filename":"SIRBoundedRationalCopy2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4572949/v1_covered_ba241f5e-fe22-48d6-8285-7b0ca1f171e7.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eVaccination Games of Boundedly Rational Parents toward New Childhood Immunization\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"The University of Texas Rio Grande Valley","isAcceptedByJournal":false,"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":"Replicator dynamics, Bounded rationality, Game theory, Disease models.","lastPublishedDoi":"10.21203/rs.3.rs-4572949/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4572949/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eInfectious diseases harm societies through disease-induced morbidity, mortality, loss of productivity, and inequality. 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