{
  "abstract": "The basic reproduction number $R_0$ is the central dimensionless quantity in mathematical epidemiology, characterizing the threshold for disease outbreak and the early growth rate of an epidemic. The algebraic form of $R_0$ varies widely across models of distinct transmission mechanisms, and its interpretation can yield further biological insight into transmission dynamics and disease intervention. We present a structural taxonomy of $R_0$ for compartmental ordinary differential equation models spanning a range of disease transmission features, including staged progression, differential infectivity, competing strains, vector-borne transmission, sexually transmitted infection, recurrent infection, maternal transmission, and gene drive inheritance. For each structural class, we provide a worked example, deriving $R_0$ via the next-generation matrix approach and interpreting the resulting algebraic expression in terms of the underlying transmission pathway. By unifying disparate derivations under a single structural framework, we clarify when and why particular algebraic forms of $R_0$ arise. This review serves both as a research synthesis and as a self-contained pedagogical reference for students and researchers entering the field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13668",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhuolin Qu"
    },
    {
      "name": "Abhi Ashwath"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/crpsh6hj2cbdn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13668",
  "fulltext_url": null,
  "id": "crpsh6hj2cbdn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13668",
  "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.DS"
    ],
    [
      "arxiv",
      "q-bio.PE"
    ],
    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
  ],
  "openalex": "W7213314136",
  "pdf_url": "https://arxiv.org/pdf/2609.13668",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/crpsh6hj2cbdn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13668",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13668"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Structures of the Basic Reproduction Number $R_0$ Across Compartmental Disease Models",
  "title_text": "Structures of the Basic Reproduction Number R_0 Across Compartmental Disease Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:30Z",
  "url": "https://research.draconitic.com/paper/crpsh6hj2cbdn",
  "venue": "arXiv",
  "versions": []
}