{"paper":{"title":"SIR Epidemics on Evolving Erd\\H{o}s-R\\'enyi Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dong Yao, Wenze Chen, Yuewen Hou","submitted_at":"2022-08-25T08:08:05Z","abstract_excerpt":"In the standard SIR model, infected vertices infect their neighbors at rate $\\lambda$ independently across each edge. They also recover at rate $\\gamma$. In this work we consider the SIR-$\\omega$ model where the graph structure itself co-evolves with the SIR dynamics. Specifically, $S-I$ connections are broken at rate $\\omega$. Then, with probability $\\alpha$, $S$ rewires this edge to another uniformly chosen vertex; and with probability $1-\\alpha$, this edge is simply dropped. When $\\alpha=1$ the SIR-$\\omega$ model becomes the evoSIR model. Jiang et al. proved in \\cite{DOMath} that the probab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.11923","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.11923/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}