{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T00:23:45Z","timestamp":1778545425778,"version":"3.51.4"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1009652","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T00:00:00Z","timestamp":1639353600000}}],"reference-count":58,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T00:00:00Z","timestamp":1638316800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100011310","name":"Rural and Environment Science and Analytical Services Division","doi-asserted-by":"publisher","award":["BIO\/01\/16"],"award-info":[{"award-number":["BIO\/01\/16"]}],"id":[{"id":"10.13039\/100011310","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Biomathematics and Statistics Scotland, SRUC and University of Stirling"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Variants of the susceptible-infected-removed (SIR) model of Kermack &amp; McKendrick (1927) enjoy wide application in epidemiology, offering simple yet powerful inferential and predictive tools in the study of diverse infectious diseases across human, animal and plant populations. Direct transmission models (DTM) are a subset of these that treat the processes of disease transmission as comprising a series of discrete instantaneous events. Infections transmitted indirectly by persistent environmental pathogens, however, are examples where a DTM description might fail and are perhaps better described by models that comprise explicit environmental transmission routes, so-called environmental transmission models (ETM). In this paper we discuss the stochastic susceptible-exposed-infected-removed (SEIR) DTM and susceptible-exposed-infected-removed-pathogen (SEIR-P) ETM and we show that the former is the timescale separation limit of the latter, with ETM host-disease dynamics increasingly resembling those of a DTM when the pathogen\u2019s characteristic timescale is shortened, relative to that of the host population. Using graphical posterior predictive checks (GPPC), we investigate the validity of the SEIR model when fitted to simulated SEIR-P host infection and removal times. Such analyses demonstrate how, in many cases, the SEIR model is robust to departure from direct transmission. Finally, we present a case study of white spot disease (WSD) in penaeid shrimp with rates of environmental transmission and pathogen decay (SEIR-P model parameters) estimated using published results of experiments. Using SEIR and SEIR-P simulations of a hypothetical WSD outbreak management scenario, we demonstrate how relative shortening of the pathogen timescale comes about in practice. With atttempts to remove diseased shrimp from the population every 24h, we see SEIR and SEIR-P model outputs closely conincide. However, when removals are 6-hourly, the two models\u2019 mean outputs diverge, with distinct predictions of outbreak size and duration.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1009652","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T18:38:07Z","timestamp":1638383887000},"page":"e1009652","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":10,"title":["When and why direct transmission models can be used for environmentally persistent pathogens"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2874-037X","authenticated-orcid":true,"given":"Lee","family":"Benson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1468-5867","authenticated-orcid":true,"given":"Ross S.","family":"Davidson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Darren M.","family":"Green","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9117-7041","authenticated-orcid":true,"given":"Andrew","family":"Hoyle","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mike R.","family":"Hutchings","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0454-9338","authenticated-orcid":true,"given":"Glenn","family":"Marion","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2021,12,1]]},"reference":[{"issue":"772","key":"pcbi.1009652.ref001","first-page":"700","article-title":"A contribution to the mathematical theory of epidemics","volume":"115","author":"WO Kermack","year":"1927","journal-title":"Proceedings of the Royal Society of London Series A, Containing Papers of a Mathematical and Physical Character"},{"issue":"1775","key":"pcbi.1009652.ref002","doi-asserted-by":"crossref","first-page":"20180255","DOI":"10.1098\/rstb.2018.0255","article-title":"One model to rule them all? 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