{
  "abstract": "This paper develops a one-dimensional model for a mobile viral component propagating through a spatially distributed susceptible population. Random viral motion produces diffusion, whereas a response to the relative gradient of susceptible density generates directed transport. The existence of a positive entire traveling wave is proved when directed transport dominates diffusion, and the limiting case of equal transport and diffusion coefficients is constructed separately. A dimensionless transformation then converts the remaining equation into a logistic equation and supplies closed-form profiles. These formulas identify the unique viral maximum and the far-field behavior. A conservative implicit-explicit finite-difference method provides an independent numerical check. Diffusion is evaluated at the new time level, the gradient-driven flux explicitly at cell interfaces, and susceptible depletion pointwise. Exact traveling-wave values specify the initial data and time-dependent Dirichlet conditions at both endpoints. Thus, the computation tests preservation and translation of the analytical profiles. A calculation with eight hundred spatial subintervals reproduces the localized viral band and the monotone susceptible front. The largest uniform errors are approximately $1.70\\cdot10^{-2}$ for viral density and $2.22\\cdot10^{-3}$ for susceptible density. The numerical results corroborate the analytical construction and show that the conservative discretization captures the proposed propagation mechanism.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04732",
  "author_total": 2,
  "authors": [
    {
      "name": "Yizhou Wang"
    },
    {
      "name": "Akif Ibragimov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/316w871y213vc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04732",
  "fulltext_url": null,
  "id": "316w871y213vc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04732",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "q-bio.QM"
    ],
    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
  ],
  "openalex": "W7220720816",
  "pdf_url": "https://arxiv.org/pdf/2610.04732",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/316w871y213vc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04732",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04732"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.QM",
      "subfield": "bioinformatics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "On the Spread of a Virus and Traveling Waves, Part I",
  "title_text": "On the Spread of a Virus and Traveling Waves, Part I",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:11Z",
  "url": "https://research.draconitic.com/paper/316w871y213vc",
  "venue": "arXiv",
  "versions": []
}