{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T14:25:24Z","timestamp":1775485524550,"version":"3.50.1"},"reference-count":50,"publisher":"Public Library of Science (PLoS)","issue":"11","license":[{"start":{"date-parts":[[2024,11,13]],"date-time":"2024-11-13T00:00:00Z","timestamp":1731456000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DGE1255832"],"award-info":[{"award-number":["DGE1255832"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"<jats:p>In this paper, we reintroduce Dr. John Cross\u2019 neglected and unusually complete historical data set describing a smallpox epidemic occurring in Norwich, England in 1819. We analyze this epidemic data in the context of early models of epidemic spread including the Farr\u2013Evans\u2013Brownlee Normal law, the Kermack\u2013McKendrick square Hyperbolic Secant and SIR laws, along with the modern Volz\u2013Miller random-network law. We show that Cross\u2019 hypothesis of susceptible pool limitation is sufficient to explain the data under the SIR law, but requires parameter estimates differing from the modern understanding of smallpox epidemiology or large errors in Cross\u2019 data collection. We hypothesize that these discrepancies are due to the mass-action hypothesis in SIR theory, rather than significant errors by Cross, and use Volz\u2013Miller theory to support this. Our analysis demonstrates the difficulties arising in inference of attributes of the disease from death incidence data and how model hypotheses impact these inferences. Our study finds that, combined with Volz\u2013Miller modeling theory, Cross\u2019 death incidence data and population observations give smallpox attributes which largely cohere to those used in modern smallpox models.<\/jats:p>","DOI":"10.1371\/journal.pone.0312744","type":"journal-article","created":{"date-parts":[[2024,11,13]],"date-time":"2024-11-13T18:22:41Z","timestamp":1731522161000},"page":"e0312744","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":1,"title":["John Cross, epidemic theory, and mathematically modeling the Norwich smallpox epidemic of 1819"],"prefix":"10.1371","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5991-3865","authenticated-orcid":true,"given":"Connor D.","family":"Olson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Timothy C.","family":"Reluga","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2024,11,13]]},"reference":[{"key":"pone.0312744.ref001","volume-title":"Betrayers of the truth","author":"W Broad","year":"1983","edition":"1"},{"key":"pone.0312744.ref002","doi-asserted-by":"crossref","DOI":"10.2307\/j.ctv10tq47g","volume-title":"Ending the Mendel-Fisher controversy","author":"A Franklin","year":"2008"},{"issue":"4","key":"pone.0312744.ref003","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1177\/002182868801900401","article-title":"Kepler\u2019s Fabricated Figures: Covering up the Mess in the New Astronomy","volume":"19","author":"WH Donahue","year":"1988","journal-title":"Journal for the History of Astronomy"},{"key":"pone.0312744.ref004","first-page":"700","article-title":"Contributions to the mathematical-theory of epidemics","volume":"115","author":"WO Kermack","year":"1927","journal-title":"Proceedings of the Royal Society of London"},{"issue":"6","key":"pone.0312744.ref005","first-page":"724","article-title":"XXII. 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