{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:07:55Z","timestamp":1740103675872,"version":"3.37.3"},"reference-count":32,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,3,19]],"date-time":"2020-03-19T00:00:00Z","timestamp":1584576000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004480","name":"Natural Science Foundation of Shanxi Province","doi-asserted-by":"publisher","award":["201801D121011"],"award-info":[{"award-number":["201801D121011"]}],"id":[{"id":"10.13039\/501100004480","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,3,19]]},"abstract":"<jats:p>In this paper, a stochastic delayed model is constructed to describe chronic hepatitis B infection with HBV DNA-containing capsids. At first, the existence and uniqueness of the global positive solution are obtained. Secondly, the sufficient conditions are derived that the solution of the stochastic system fluctuates around the disease-free equilibrium<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msub><mml:mrow><mml:mi>E<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>and the endemic equilibrium<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msup><mml:mrow><mml:mi>E<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>\u2217<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>. In the end, some numerical simulations are implemented to support our analytical results.<\/jats:p>","DOI":"10.1155\/2020\/1875475","type":"journal-article","created":{"date-parts":[[2020,3,19]],"date-time":"2020-03-19T23:30:48Z","timestamp":1584660648000},"page":"1-19","source":"Crossref","is-referenced-by-count":1,"title":["Asymptotic Behavior of a Stochastic Delayed Model for Chronic Hepatitis B Infection"],"prefix":"10.1155","volume":"2020","author":[{"given":"Bo","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, Shanxi, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0399-2979","authenticated-orcid":true,"given":"Jianwen","family":"Jia","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, Shanxi, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2007.02.017"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/s1286-4579(02)01603-9"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.7326\/0003-4819-101-5-613"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.tim.2018.01.009"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.antiviral.2018.07.019"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-009-0278-3"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2011.03.013"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2009.11.008"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2014.08.036"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-015-0242-3"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2017.04.022"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.05.083"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/3127404"},{"issue":"1","key":"14","doi-asserted-by":"crossref","first-page":"81","DOI":"10.11948\/jaac20190002","volume":"10","year":"2020","journal-title":"Journal of Applied Analysis and Computation"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2018.07.039"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2017.11.008"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2014.05.136"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2016.04.023"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2016.06.095"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2017.05.069"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2017.08.002"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2017.08.139"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2018.09.013"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2019303"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-018-4272-4"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-019-2352-5"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2019.01.033"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2017.08.125"},{"issue":"1","key":"29","first-page":"277","volume":"37","year":"2017","journal-title":"Journal of Systems Science and Mathematical Sciences"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2019.03.034"},{"year":"1994","key":"31"},{"year":"1997","key":"32"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/1875475.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/1875475.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/1875475.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,5]],"date-time":"2021-03-05T05:11:31Z","timestamp":1614921091000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/1875475\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,19]]},"references-count":32,"alternative-id":["1875475","1875475"],"URL":"https:\/\/doi.org\/10.1155\/2020\/1875475","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2020,3,19]]}}}