{
  "abstract": "We consider a reaction-diffusion system that arises in epidemiology to describe the spatial spread of a vector borne disease. Our model is a coupled version of the classical SIR model of Kermack and McKendrick. We study the long-time behavior of the solutions, giving optimal criteria on the propagation or extinction of the disease, and compute the asymptotic speed of spread of solutions, which is given by a Freidlin-Gärtner type formula. We also give some qualitative properties of the model, which yield information on the influence of the parameters on the system's long-time behavior. In particular, we identify the limit of the spreading speed when the diffusions are very large, and we show that the system behaves in this case similarly to a homogenized system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26195",
  "author_total": 1,
  "authors": [
    {
      "name": "Antoine Wolff"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bxhqx8dt8qg5d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26195",
  "fulltext_url": null,
  "id": "bxhqx8dt8qg5d",
  "issns": [],
  "landing_url": "https://hal.science/hal-05803300v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
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      "hal",
      "0.math"
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      "hal",
      "1.math.math-ap"
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    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
  ],
  "openalex": "W7223011382",
  "pdf_url": "https://hal.science/hal-05803300/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bxhqx8dt8qg5d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "hal-05803300",
      "source": "hal",
      "url": "https://hal.science/hal-05803300v1"
    },
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26195",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26195"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Geographic spread of vector borne diseases in periodic heterogeneous environments",
  "title_text": "Geographic spread of vector borne diseases in periodic heterogeneous environments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/bxhqx8dt8qg5d",
  "venue": "HAL",
  "versions": []
}