{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T13:08:37Z","timestamp":1771938517940,"version":"3.50.1"},"reference-count":26,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,1,22]],"date-time":"2020-01-22T00:00:00Z","timestamp":1579651200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2020,1,22]]},"abstract":"<jats:p>Hepatitis B epidemic was and is still a rich subject that sparks the interest of epidemiological researchers. The dynamics of this epidemic is often modeled by a system with constant parameters. In reality, the parameters associated with the Hepatitis B model are not certain, but the interval in which it belongs to can readily be determined. Our paper focuses on an imprecise Hepatitis B model perturbed by L\u00e9vy noise due to unexpected environmental disturbances. This model has a global positive solution. Under an appropriate assumption, we prove the existence of a unique ergodic stationary distribution by using the mutually exclusive possibilities lemma demonstrated by Stettner in 1986. Our main effort is to establish an almost perfect condition for the existence of the stationary distribution. Numerical simulations are introduced to illustrate the analytical results.<\/jats:p>","DOI":"10.1155\/2020\/9676501","type":"journal-article","created":{"date-parts":[[2020,1,22]],"date-time":"2020-01-22T18:33:08Z","timestamp":1579717988000},"page":"1-12","source":"Crossref","is-referenced-by-count":23,"title":["Ergodic Stationary Distribution of a Stochastic Hepatitis B Epidemic Model with Interval-Valued Parameters and Compensated Poisson Process"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1497-3028","authenticated-orcid":true,"given":"Driss","family":"Kiouach","sequence":"first","affiliation":[{"name":"Modelling, Systems and Technologies of Information Team, High School of Technology, Ibn Zohr University, Agadir, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1127-4395","authenticated-orcid":true,"given":"Yassine","family":"Sabbar","sequence":"additional","affiliation":[{"name":"Modelling, Systems and Technologies of Information Team, High School of Technology, Ibn Zohr University, Agadir, Morocco"},{"name":"National School of Applied Sciences, Ibn Zohr University, Agadir, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2008.06.022"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2009.09.035"},{"key":"4","year":"2018"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.93.9.4398"},{"key":"6","year":"1991"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2010.05.038"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/150681"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2018.01.036"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/7570296"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/7360685"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/7873902"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/7294761"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/4820183"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1063\/1.5090643"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1063\/1.5090643"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.06.043"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2015.11.023"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2012.11.007"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.fiae.2017.10.001"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2019.01.027"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1007\/s12190-017-1083-6"},{"key":"23","volume":"7","year":"1980","journal-title":"A Monographs and Textbooks on Mechanics of Solids and Fluids"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2012.11.003"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2018.07.020"},{"key":"26","year":"1997"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2018.12.008"}],"container-title":["Computational and Mathematical Methods in Medicine"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2020\/9676501.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2020\/9676501.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2020\/9676501.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,22]],"date-time":"2020-01-22T18:33:10Z","timestamp":1579717990000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/cmmm\/2020\/9676501\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,22]]},"references-count":26,"alternative-id":["9676501","9676501"],"URL":"https:\/\/doi.org\/10.1155\/2020\/9676501","relation":{},"ISSN":["1748-670X","1748-6718"],"issn-type":[{"value":"1748-670X","type":"print"},{"value":"1748-6718","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,22]]}}}