Spatial spreading of a logistic SI epidemic model with partially degenerate diffusion and double free boundaries

Spatial spreading of a logistic SI epidemic model with partially degenerate diffusion and double free boundaries | 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 Spatial spreading of a logistic SI epidemic model with partially degenerate diffusion and double free boundaries Siyu Liu, Haomin Huang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7495012/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Feb, 2026 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted 9 You are reading this latest preprint version Abstract In this paper, we investigate a logistic SI epidemic model with partially degenerate diffusion and double free boundaries to describe the spatial spreading of disease. The existence, uniqueness, and estimates of the global solution are discussed firstly. Then we prove a spreading-vanishing dichotomy. Namely the infective class either successfully spreads to infinity as t → ∞, or vanishes in a finite area. Besides, the long time behavior of the solution and criteria for spreading and vanishing are also obtained. Especially, we find the Basic Reproduction Number R₀ is not the unique factor which determine whether or not an infectious disease can spread through a population: when R₀ ≤ 1, vanishing always happens and the disease will die out; when R₀ > 1, whether or not to vanish depends on the size of the initial habitat and the rate of expansion. This phenomenon reveals the role of free boundaries in the epidemic. In the end, we give some numerical results as supplements to the theoretical results. SI epidemic model Partially degenerate diffusion Free boundary Reproduction number Spreading and vanishing Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 04 Feb, 2026 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted Editorial decision: Revision requested 07 Dec, 2025 Reviews received at journal 07 Dec, 2025 Reviews received at journal 09 Sep, 2025 Reviewers agreed at journal 07 Sep, 2025 Reviewers agreed at journal 07 Sep, 2025 Reviewers invited by journal 07 Sep, 2025 Editor assigned by journal 02 Sep, 2025 Submission checks completed at journal 02 Sep, 2025 First submitted to journal 30 Aug, 2025 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. 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