{
  "abstract": "Infectious disease time series are often used to estimate a pathogen's basic reproduction number, $R_0$. However, fits of epidemic models to time series conflate pathogen transmissibility with pre-existing population immunity, so only the *effective* reproduction number, $R_{eff}$, can be inferred. This composite parameter is the product of the underlying $R_0$ and the pre-epidemic susceptible fraction, $x^-$. We show that a conservation law associated with epidemic momentum---prevalence weighted by potential to infect---makes it possible to disentangle transmissibility from prior immunity and to infer $R_0$ and $x^-$ separately from a single epidemic time series. We test the methodology using stochastic epidemic simulations, and illustrate the approach with a reappraisal of influenza transmissibility during the 1918 pandemic, estimating rather than assuming the degree of prior population immunity. For the autumn wave in Philadelphia, USA, we find $R_0\\approx2.7$ and $x^-\\approx0.8$, implying that about 20% of the population was already immune before that wave, plausibly as a result of infection during the spring 1918 herald wave.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.21657",
  "author_total": 2,
  "authors": [
    {
      "name": "David J. D. Earn"
    },
    {
      "name": "Todd L. Parsons"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/egmp0ttp9p0nt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.21657",
  "fulltext_url": null,
  "id": "egmp0ttp9p0nt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.21657",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "q-bio.PE"
    ],
    [
      "arxiv",
      "q-bio.QM"
    ],
    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
  ],
  "openalex": "W7171452345",
  "pdf_url": "https://arxiv.org/pdf/2607.21657",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/egmp0ttp9p0nt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:02Z",
      "native_id": "2607.21657",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.21657"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.QM",
      "subfield": "bioinformatics"
    },
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    }
  ],
  "title": "Jointly estimating transmissibility and prior immunity from epidemic time series",
  "title_text": "Jointly estimating transmissibility and prior immunity from epidemic time series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:02Z",
  "url": "https://research.draconitic.com/paper/egmp0ttp9p0nt",
  "venue": "arXiv",
  "versions": []
}