Network Behavioral-Feedback SIR Epidemic Model

[2507.03852] Network Behavioral-Feedback SIR Epidemic Model Skip to main content Search Submit Donate Log in Mathematics > Dynamical Systems arXiv:2507.03852 (math) [Submitted on 5 Jul 2025 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Network Behavioral-Feedback SIR Epidemic Model Authors: Martina Alutto , Leonardo Cianfanelli , Giacomo Como , Fabio Fagnani View PDF HTML (experimental) Abstract: We propose a network behavioral-feedback Susceptible-Infected-Recovered (SIR) epidemic model in which the interaction matrix describing the infection rates across subpopulations depends in feedback on the current epidemic state. This model captures both heterogeneities in individuals mixing, contact frequency, aptitude to contract and spread the infection, and endogenous behavioral responses such as voluntary social distancing and the adoption of self-protective measures. We study the stability of the equilibria and illustrate through several examples how the shape of the stability region depends on the structure of the interaction matrix, providing insights for the design of effective control strategies. We then analyze the transient behavior of the dynamics, showing that, for a special class of rank-1 interaction matrices, there always exists an aggregate infection curve that exhibits a unimodal behavior, expanding the results on the unimodality of infection curve known in the literature of epidemic models and paving the way for future control applications. Comments: 10 pages, 2 figures Subjects: Dynamical Systems (math.DS) ; Optimization and Control (math.OC); Populations and Evolution (q-bio.PE) Cite as: arXiv:2507.03852 [math.DS] (or arXiv:2507.03852v2 [math.DS] for this version) https://doi.org/10.48550/arXiv.2507.03852 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Martina Alutto [ view email ] [v1] Sat, 5 Jul 2025 01:19:57 UTC (145 KB) [v2] Thu, 27 Aug 2026 02:31:19 UTC (142 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.DS < prev | next > new | recent | 2025-07 Change to browse by: math math.OC q-bio q-bio.PE References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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