A Multi-Scale Model Coupling Population-Level Dynamics with Within-Host Physiology for Diabetes and Hypertension

A Multi-Scale Model Coupling Population-Level Dynamics with Within-Host Physiology for Diabetes and Hypertension | 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 A Multi-Scale Model Coupling Population-Level Dynamics with Within-Host Physiology for Diabetes and Hypertension A. S Eegunjobi, O. D Makinde, A. S Kubeka This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9166886/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 The synergistic epidemic of type 2 diabetes mellitus (T2DM) and essential hyper-tension requires a departure from traditional, phenomenological compartmental modeling. This paper establishes a rigorous multi-scale mathematical framework that mechanistically couples the fast within-host physiological continuous dynamics (glucose-insulin homeostasis and vascular hemodynamics) with the slow macroscopic epidemiological transitions. Utilizing Geometric Singular Perturbation Theory (GSPT), we prove the existence of a normally hyperbolic invariant slow manifold, allowing for the rigorous separation of physiological and demographic time scales. We conduct a rigorous bifurcation analysis using center manifold reduction to demonstrate the existence of subcritical (backward) bifur-cations driven by micro-scale hysteresis in insulin sensitivity, proving that pushing the basic reproduction number below unity is insufficient for disease eradication in highly endemic regimes. Furthermore, we formulate an optimal control problem using Pontryagin’s Maximum Principle to identify optimal intervention trajec-tories. The theoretical results are corroborated by high-order implicit numerical schemes handling the system’s inherent stiffness. This work provides a deep, mathematically unified paradigm for understanding how localized physiological dysregulation cascades into population-level comorbidity regime shifts. Multi-scale modeling Geometric Singular Perturbation Theory backward bifurcation optimal control Pontryagin’s Maximum Principle metabolic-cardiovascular coupling mathematical epidemiology Full Text Additional Declarations No competing interests reported. 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-9166886","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":612315038,"identity":"f7d1e75b-aaa4-4178-b959-0d802313c8b6","order_by":0,"name":"A. 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