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R. Soc. Interface."],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:p>\n                    A key challenge for many infectious diseases is to predict the time to extinction under specific interventions. In general, this question requires the use of stochastic models which recognize the inherent individual-based, chance-driven nature of the dynamics; yet stochastic models are inherently computationally expensive, especially when parameter uncertainty also needs to be incorporated. Deterministic models are often used for prediction as they are more tractable; however, their inability to precisely reach zero infections makes forecasting extinction times problematic. Here, we study the extinction problem in deterministic models with the help of an effective \u2018birth\u2013death\u2019 description of infection and recovery processes. We present a practical method to estimate the distribution, and therefore robust means and prediction intervals, of extinction times by calculating their different moments within the birth\u2013death framework. We show that these predictions agree very well with the results of stochastic models by analysing the simplified susceptible\u2013infected\u2013susceptible (SIS) dynamics as well as studying an example of more complex and realistic dynamics accounting for the infection and control of African sleeping sickness (\n                    <jats:italic>Trypanosoma brucei gambiense<\/jats:italic>\n                    ).\n                  <\/jats:p>","DOI":"10.1098\/rsif.2020.0540","type":"journal-article","created":{"date-parts":[[2020,12,9]],"date-time":"2020-12-09T03:15:58Z","timestamp":1607483758000},"page":"20200540","update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":24,"title":["Estimating the distribution of time to extinction of infectious diseases in mean-field approaches"],"prefix":"10.1098","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2268-2295","authenticated-orcid":true,"given":"Maryam","family":"Aliee","sequence":"first","affiliation":[{"name":"Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK"},{"name":"Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, Coventry CV4 7AL, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8414-7648","authenticated-orcid":true,"given":"Kat S.","family":"Rock","sequence":"additional","affiliation":[{"name":"Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK"},{"name":"Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, Coventry CV4 7AL, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4639-4765","authenticated-orcid":true,"given":"Matt J.","family":"Keeling","sequence":"additional","affiliation":[{"name":"Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK"},{"name":"Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, Coventry CV4 7AL, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"175","published-online":{"date-parts":[[2020,12,9]]},"reference":[{"key":"e_1_3_6_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0264-410X(98)80107-2"},{"key":"e_1_3_6_3_2","doi-asserted-by":"publisher","DOI":"10.1056\/NEJMra1200391"},{"key":"e_1_3_6_4_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2016.0847"},{"key":"e_1_3_6_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/j.ctvcm4gk0"},{"key":"e_1_3_6_6_2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198545996.001.0001","volume-title":"Infectious diseases of humans","author":"Anderson RM","year":"1991"},{"key":"e_1_3_6_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5564(02)00098-6"},{"key":"e_1_3_6_8_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2007.1106"},{"key":"e_1_3_6_9_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.290.5497.1758"},{"key":"e_1_3_6_10_2","doi-asserted-by":"publisher","DOI":"10.1006\/tpbi.2000.1475"},{"key":"e_1_3_6_11_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13071-015-1235-1"},{"key":"e_1_3_6_12_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13071-017-2256-8"},{"key":"e_1_3_6_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(85)90021-3"},{"key":"e_1_3_6_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20530-9"},{"key":"e_1_3_6_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-009-0320-5"},{"key":"e_1_3_6_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11009-018-9621-8"},{"key":"e_1_3_6_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/s002850000060"},{"key":"e_1_3_6_18_2","doi-asserted-by":"publisher","DOI":"10.1137\/030602800"},{"key":"e_1_3_6_19_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.101.078101"},{"key":"e_1_3_6_20_2","doi-asserted-by":"publisher","DOI":"10.1137\/17M1142028"},{"key":"e_1_3_6_21_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.81.021116"},{"key":"e_1_3_6_22_2","unstructured":"Gilbert JA Ancel Meyers L Galvaniad AP Townsend JP. 2014 Probabilistic uncertainty analysis of epidemiological modeling to guide public health intervention policy. 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