{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T05:28:02Z","timestamp":1782710882884,"version":"3.54.5"},"reference-count":47,"publisher":"The Royal Society","issue":"2293","license":[{"start":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T00:00:00Z","timestamp":1743552000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T00:00:00Z","timestamp":1743552000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000265","name":"Medical Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000265","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100018336","name":"National Institute for Health Research Health Protection Research Unit","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100018336","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":["Phil. Trans. R. Soc. A."],"published-print":{"date-parts":[[2025,4,2]]},"abstract":"\n During infectious disease outbreaks, the time-dependent reproduction number (\n \n \n \n \n R<\/mml:mi>\n <\/mml:mrow>\n \n t<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:inline-formula>\n ) can be estimated to monitor pathogen transmission. In previous work, we developed a simulation-based method for estimating\n \n \n \n \n R<\/mml:mi>\n <\/mml:mrow>\n \n t<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:inline-formula>\n from temporally aggregated disease incidence data (e.g. weekly case reports). While that approach is straightforward to use, it assumes implicitly that all cases are reported and the computation can be slow when applied to large datasets. In this article, we extend our previous approach and develop a computationally efficient simulation-based method for estimating\n \n \n \n \n R<\/mml:mi>\n <\/mml:mrow>\n \n t<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:inline-formula>\n in real-time accounting for both temporal aggregation of incidence data and under-reporting (with a fixed reporting probability per case). Using simulated data, we show that failing to consider stochastic under-reporting can lead to inappropriately precise estimates, including scenarios in which the true\n \n \n \n \n R<\/mml:mi>\n <\/mml:mrow>\n \n t<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:inline-formula>\n value lies outside inferred credible intervals more often than expected. We then apply our approach to data from the 2018 to 2020 Ebola outbreak in the Democratic Republic of the Congo (DRC), again exploring the effects of case under-reporting. Finally, we show how our method can be extended to account for temporal variations in reporting. Given information about the level of case reporting, our framework can be used to estimate\n \n \n \n \n R<\/mml:mi>\n <\/mml:mrow>\n \n t<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:inline-formula>\n during future outbreaks with under-reported and temporally aggregated case data.\n <\/jats:p>\n This article is part of the theme issue \u2018Uncertainty quantification for healthcare and biological systems (Part 2)\u2019.<\/jats:p>","DOI":"10.1098\/rsta.2024.0412","type":"journal-article","created":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T17:01:34Z","timestamp":1743613294000},"update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Simulation-based inference of the time-dependent reproduction number from temporally aggregated and under-reported disease incidence time series data"],"prefix":"10.1098","volume":"383","author":[{"given":"Isaac","family":"Ogi-Gittins","sequence":"first","affiliation":[{"name":"Mathematics Institute, University of Warwick","place":["Coventry, UK"]},{"name":"Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research (SBIDER), University of Warwick","place":["Coventry, UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicholas","family":"Steyn","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Oxford","place":["Oxford, UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jonathan","family":"Polonsky","sequence":"additional","affiliation":[{"name":"Geneva Centre of Humanitarian Studies, University of Geneva","place":["Geneva, Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William S.","family":"Hart","sequence":"additional","affiliation":[{"name":"Mathematical Institute, University of Oxford","place":["Oxford, UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mory","family":"Keita","sequence":"additional","affiliation":[{"name":"World Health Organization, Regional Office for Africa","place":["Brazzaville, Republic of the Congo"]},{"name":"Faculty of Medicine, Institute of Global Health, University of Geneva","place":["Geneva, Switzerland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Steve","family":"Ahuka-Mundeke","sequence":"additional","affiliation":[{"name":"National Institute of Biomedical Research","place":["Kinshasa, Democratic Republic of the Congo"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2992-2004","authenticated-orcid":true,"given":"Edward M.","family":"Hill","sequence":"additional","affiliation":[{"name":"Civic Health Innovation Labs and Institute of Population Health, University of Liverpool","place":["Liverpool, UK"]},{"name":"NIHR Health Protection Research Unit in Gastrointestinal Infections, University of Liverpool","place":["Liverpool, UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8545-5212","authenticated-orcid":true,"given":"Robin N.","family":"Thompson","sequence":"additional","affiliation":[{"name":"Mathematical Institute, University of Oxford","place":["Oxford, UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"175","published-online":{"date-parts":[[2025,4,2]]},"reference":[{"key":"e_1_3_8_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1473-3099(20)30785-4"},{"key":"e_1_3_8_3_2","doi-asserted-by":"publisher","DOI":"10.12688\/wellcomeopenres.16006.2"},{"key":"e_1_3_8_4_2","first-page":"1","article-title":"Temporal Changes in Ebola Transmission in Sierra Leone and Implications for Control Requirements: a Real-time Modelling Study","volume":"7","author":"Camacho A","year":"2015","unstructured":"Camacho A et al . 2015 Temporal Changes in Ebola Transmission in Sierra Leone and Implications for Control Requirements: a Real-time Modelling Study. 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