{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:29Z","timestamp":1753894409257,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T00:00:00Z","timestamp":1750723200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T00:00:00Z","timestamp":1750723200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T00:00:00Z","timestamp":1750723200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,9]]},"abstract":"<jats:p>We study algorithms to analyze a particular class of Markov population processes that is often used in epidemiology. More specifically, Markov binomial chains are the model that arises from stochastic time-discretizations of classical compartmental models. In this work we formalize this class of Markov population processes and focus on the problem of computing the expected time to termination in a given such model. Our theoretical contributions include proving that Markov binomial chains whose flow of individuals through compartments is acyclic almost surely terminate. We give a PSPACE algorithm for the problem of approximating the time to termination and a direct algorithm for the exact problem in the Blum-Shub-Smale model of computation. Finally, we provide a natural encoding of Markov binomial chains into a common input language for probabilistic model checkers. We implemented the latter encoding and present some initial empirical results showcasing what formal methods can do for practicing epidemiologists.<\/jats:p>","DOI":"10.46298\/lmcs-21(2:28)2025","type":"journal-article","created":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T12:10:08Z","timestamp":1750767008000},"source":"Crossref","is-referenced-by-count":0,"title":["Algorithms for Markov Binomial Chains"],"prefix":"10.46298","volume":"Volume 21, Issue 2","author":[{"given":"Alejandro Alarc\u00f3n","family":"Gonzalez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1881-0637","authenticated-orcid":false,"given":"Niel","family":"Hens","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tim","family":"Leys","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1200-4952","authenticated-orcid":false,"given":"Guillermo A.","family":"P\u00e9rez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2025,6,24]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2408.04902v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2408.04902v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T21:50:10Z","timestamp":1750974610000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/14046"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,24]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(2:28)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2408.04902v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2408.04902v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2408.04902","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2408.04902","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2025,6,24]]},"article-number":"14046"}}