{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T03:32:43Z","timestamp":1787801563498,"version":"build-2784847793"},"reference-count":49,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T00:00:00Z","timestamp":1694563200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"name":"PRAIRIE","award":["ANR-19-P3IA-0001"],"award-info":[{"award-number":["ANR-19-P3IA-0001"]}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["810367"],"award-info":[{"award-number":["810367"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,12,30]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Multi-type birth\u2013death (MTBD) models are phylodynamic analogies of compartmental models in classical epidemiology. They serve to infer such epidemiological parameters as the average number of secondary infections Re and the infectious time from a phylogenetic tree (a genealogy of pathogen sequences). The representatives of this model family focus on various aspects of pathogen epidemics. For instance, the birth\u2013death exposed-infectious (BDEI) model describes the transmission of pathogens featuring an incubation period (when there is a delay between the moment of infection and becoming infectious, as for Ebola and SARS-CoV-2), and permits its estimation along with other parameters. With constantly growing sequencing data, MTBD models should be extremely useful for unravelling information on pathogen epidemics. However, existing implementations of these models in a phylodynamic framework have not yet caught up with the sequencing speed. Computing time and numerical instability issues limit their applicability to medium data sets (\u2264 500 samples), while the accuracy of estimations should increase with more data.<\/jats:p>\n                  <jats:p>We propose a new highly parallelizable formulation of ordinary differential equations for MTBD models. We also extend them to forests to represent situations when a (sub-)epidemic started from several cases (e.g., multiple introductions to a country). We implemented it for the BDEI model in a maximum likelihood framework using a combination of numerical analysis methods for efficient equation resolution. Our implementation estimates epidemiological parameter values and their confidence intervals in two minutes on a phylogenetic tree of 10,000 samples. Comparison to the existing implementations on simulated data shows that it is not only much faster but also more accurate. An application of our tool to the 2014 Ebola epidemic in Sierra-Leone is also convincing, with very fast calculation and precise estimates. As MTBD models are closely related to Cladogenetic State Speciation and Extinction (ClaSSE)-like models, our findings could also be easily transferred to the macroevolution domain.<\/jats:p>","DOI":"10.1093\/sysbio\/syad059","type":"journal-article","created":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T14:01:33Z","timestamp":1694613693000},"page":"1387-1402","source":"Crossref","is-referenced-by-count":14,"title":["Fast and Accurate Maximum-Likelihood Estimation of Multi-Type Birth\u2013Death Epidemiological Models from Phylogenetic Trees"],"prefix":"10.1093","volume":"72","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2200-7935","authenticated-orcid":false,"given":"Anna","family":"Zhukova","sequence":"first","affiliation":[{"name":"Unit\u00e9 Bioinformatique Evolutive, Institut Pasteur, Universit\u00e9 de Paris , 28 rue du docteur Roux, 75015 Paris , France"},{"name":"Bioinformatics and Biostatistics Hub, Institut Pasteur , Universit\u00e9 de Paris, 28 rue du docteur Roux, 75015 Paris , France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fr\u00e9d\u00e9ric","family":"Hecht","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, CNRS, Universit\u00e9 Paris Cit\u00e9, Laboratoire Jacques-Louis Lions (LJLL) , 4 place Jussieu, F-75005 Paris , France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yvon","family":"Maday","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, CNRS, Universit\u00e9 Paris Cit\u00e9, Laboratoire Jacques-Louis Lions (LJLL) , 4 place Jussieu, F-75005 Paris , France"},{"name":"Institut Universitaire de France, 1 rue Descartes , 75231 Paris CEDEX 05 , France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9412-9723","authenticated-orcid":false,"given":"Olivier","family":"Gascuel","sequence":"additional","affiliation":[{"name":"Unit\u00e9 Bioinformatique Evolutive, Institut Pasteur, Universit\u00e9 de Paris , 28 rue du docteur Roux, 75015 Paris , France"},{"name":"Institut de Syst\u00e9matique, Evolution , Biodiversit\u00e9 (ISYEB) - URM 7205 CNRS, Museum National d\u2019Histoire Naturelle, SU, EPHE & UA, 57 rue Cuvier, CP 50 75005 Paris , France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,9,13]]},"reference":[{"key":"2024031007493854100_CIT0001","first-page":"270","article-title":"Accuracy and Performance of single versus double precision arithmetics for maximum likelihood phylogeny reconstruction Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)","author":"Berger","year":"2009"},{"key":"2024031007493854100_CIT0002","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1006650","article-title":"BEAST 25: An advanced software platform for Bayesian evolutionary analysis","volume":"15","author":"Bouckaert","year":"2019","journal-title":"PLoS Comput. 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