{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T03:45:24Z","timestamp":1777866324630,"version":"3.51.4"},"reference-count":35,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"funder":[{"DOI":"10.13039\/501100002701","name":"Ministry of Education","doi-asserted-by":"publisher","award":["230806194185656"],"award-info":[{"award-number":["230806194185656"]}],"id":[{"id":"10.13039\/501100002701","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004761","name":"Natural Science Foundation of Hainan Province","doi-asserted-by":"publisher","award":["825MS085"],"award-info":[{"award-number":["825MS085"]}],"id":[{"id":"10.13039\/501100004761","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12261029"],"award-info":[{"award-number":["12261029"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Mathematics and Computers in Simulation"],"published-print":{"date-parts":[[2026,9]]},"DOI":"10.1016\/j.matcom.2026.02.035","type":"journal-article","created":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:25:59Z","timestamp":1773249959000},"page":"266-285","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Long-term behavior of a stochastic HBV model with logistic hepatocyte growth and log-normal Ornstein\u2013Uhlenbeck process"],"prefix":"10.1016","volume":"247","author":[{"given":"Hong","family":"Tao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2439-6292","authenticated-orcid":false,"given":"Li","family":"Zu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daqing","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.matcom.2026.02.035_b1","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.jtbi.2007.02.017","article-title":"Modeling the mechanisms of acute hepatitis B virus infection","volume":"247","author":"Ciupe","year":"2007","journal-title":"J. Theoret. Biol."},{"key":"10.1016\/j.matcom.2026.02.035_b2","first-page":"3","article-title":"Management of hepatitis B in China","volume":"122","author":"Lu","year":"2009","journal-title":"Chin. Med. J."},{"key":"10.1016\/j.matcom.2026.02.035_b3","doi-asserted-by":"crossref","first-page":"50","DOI":"10.7150\/ijms.2.50","article-title":"Epidemiology and prevention of hepatitis B virus infection","volume":"2","author":"Hou","year":"2005","journal-title":"Int. J. Med. Sci."},{"key":"10.1016\/j.matcom.2026.02.035_b4","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1046\/j.1365-2893.2003.00487.x","article-title":"Hepatitis B virus epidemiology, disease burden, treatment, and current and emerging prevention and control measures","volume":"11","author":"D.","year":"2004","journal-title":"J. Viral. Hepatitis"},{"key":"10.1016\/j.matcom.2026.02.035_b5","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1216\/RMJ-2008-38-5-1573","article-title":"Mathematical analysis of a basic virus infection model with application to HBV infection","volume":"38","author":"Min","year":"2008","journal-title":"Rocky Mt. J. Math."},{"key":"10.1016\/j.matcom.2026.02.035_b6","doi-asserted-by":"crossref","first-page":"S47","DOI":"10.1016\/0264-410X(95)93547-M","article-title":"Global programme for control of hepatitis B infection","volume":"13","author":"Kane","year":"1995","journal-title":"Vaccine"},{"key":"10.1016\/j.matcom.2026.02.035_b7","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2024.115840","article-title":"Stochastic analysis of a HBV epidemic model with two-dimensional noises","volume":"191","author":"Liu","year":"2025","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.matcom.2026.02.035_b8","doi-asserted-by":"crossref","DOI":"10.1016\/j.aml.2024.109234","article-title":"Stochastic dynamics on HBV infection in vivo with interval delay","volume":"158","author":"Zhong","year":"2024","journal-title":"Appl. Math. Lett."},{"key":"10.1016\/j.matcom.2026.02.035_b9","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2024.115208","article-title":"Dynamics of a stochastic HBV infection model with general incidence rate, cell-to-cell transmission, immune response and ornstein\u2013uhlenbeck process","volume":"186","author":"Su","year":"2024","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.matcom.2026.02.035_b10","doi-asserted-by":"crossref","first-page":"9657","DOI":"10.1007\/s11071-024-09537-4","article-title":"Ergodic stationary distribution of age-structured HBV epidemic model with standard incidence rate","volume":"112","author":"Din","year":"2024","journal-title":"Nonlinear Dyn."},{"key":"10.1016\/j.matcom.2026.02.035_b11","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s00332-022-09883-w","article-title":"Analysis of a stochastic HBV infection model with DNA-containing capsids and virions","volume":"33","author":"Liu","year":"2023","journal-title":"J. Nonlinear Sci."},{"key":"10.1016\/j.matcom.2026.02.035_b12","doi-asserted-by":"crossref","first-page":"11930","DOI":"10.1002\/mma.8547","article-title":"A delayed diffusive HBV model with nonlinear incidence and CTL immune response","volume":"45","author":"Li","year":"2022","journal-title":"Math. Methods Appl. Sci."},{"key":"10.1016\/j.matcom.2026.02.035_b13","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2022.112195","article-title":"Ergodic stationary distribution of stochastic epidemic model for HBV with double saturated incidence rates and vaccination","volume":"160","author":"Hussain","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.matcom.2026.02.035_b14","first-page":"6","article-title":"Dynamics of a fractional order HBV infection model with capsids and CTL immune response","volume":"2019","author":"Bachraoui","year":"2019","journal-title":"Commun. Math. Biol. Neurosci."},{"key":"10.1016\/j.matcom.2026.02.035_b15","first-page":"4223","article-title":"Global stability of a diffusive and delayed HBV infection model with HBV dna-containing capsids and general incidence rate","volume":"23","author":"Guo","year":"2018","journal-title":"Discret. Contin. Dyn. Syst.-B"},{"key":"10.1016\/j.matcom.2026.02.035_b16","doi-asserted-by":"crossref","first-page":"4398","DOI":"10.1073\/pnas.93.9.4398","article-title":"Viral dynamics in hepatitis B virus infection","volume":"93","author":"Nowak","year":"1996","journal-title":"Proc. Natl. Acad. Sci."},{"key":"10.1016\/j.matcom.2026.02.035_b17","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1126\/science.272.5258.74","article-title":"Population dynamics of immune responses to persistent viruses","volume":"272","author":"Nowak","year":"1996","journal-title":"Science"},{"key":"10.1016\/j.matcom.2026.02.035_b18","doi-asserted-by":"crossref","first-page":"704","DOI":"10.1016\/j.mcm.2011.03.013","article-title":"Dynamical behaviors of an HBV infection model with logistic hepatocyte growth","volume":"54","author":"Li","year":"2011","journal-title":"Math. Comput. Model."},{"key":"10.1016\/j.matcom.2026.02.035_b19","doi-asserted-by":"crossref","first-page":"5194","DOI":"10.3934\/mbe.2021264","article-title":"Analysis of a stochastic HBV infection model with delayed immune response","volume":"18","author":"Rihan","year":"2021","journal-title":"Math. Biosci. Eng."},{"key":"10.1016\/j.matcom.2026.02.035_b20","first-page":"630","article-title":"Periodic solution of a stochastic HBV infection model with logistic hepatocyte growth","volume":"293","author":"Xie","year":"2017","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.matcom.2026.02.035_b21","doi-asserted-by":"crossref","first-page":"816","DOI":"10.1016\/j.physa.2016.06.052","article-title":"Periodic solution for a stochastic nonautonomous SIR epidemic model with logistic growth","volume":"462","author":"Liu","year":"2016","journal-title":"Phys. A: Stat. Mech. Appl."},{"key":"10.1016\/j.matcom.2026.02.035_b22","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1142\/S0218339019500177","article-title":"Analysis of a stochastic HBV infection model with nonlinear incidence rate","volume":"27","author":"Hui","year":"2019","journal-title":"J. Biological Syst."},{"key":"10.1016\/j.matcom.2026.02.035_b23","doi-asserted-by":"crossref","DOI":"10.1016\/j.mbs.2024.109154","article-title":"Dynamic behaviors of a stochastic virus infection model with beddington\u2013deangelis incidence function, eclipse-stage and ornstein\u2013uhlenbeck process","volume":"369","author":"Liu","year":"2024","journal-title":"Math. Biosci."},{"key":"10.1016\/j.matcom.2026.02.035_b24","article-title":"Dynamical behaviors of a stochastic SIVS epidemic model with the ornstein\u2013uhlenbeck process and vaccination of newborns","volume":"19","author":"Li","year":"2024","journal-title":"PLoS One"},{"key":"10.1016\/j.matcom.2026.02.035_b25","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2022.106878","article-title":"Dynamical behavior of a stochastic SIQR epidemic model with ornstein\u2013uhlenbeck process and standard incidence rate after dimensionality reduction","volume":"116","author":"Zhou","year":"2023","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"10.1016\/j.matcom.2026.02.035_b26","first-page":"b11","article-title":"Dynamical behaviors of a Lotka\u2013Volterra competition system with the ornstein\u2013uhlenbeck process","volume":"1","author":"Wei","year":"2023","journal-title":"Math. Biosci. Equilib."},{"key":"10.1016\/j.matcom.2026.02.035_b27","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2022.106450","article-title":"Analysis of a stochastic population model with mean-reverting ornstein\u2013uhlenbeck process and allee effects","volume":"111","author":"Zhou","year":"2022","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"10.1016\/j.matcom.2026.02.035_b28","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2023.114235","article-title":"Dynamical analysis of a stochastic epidemic HBV model with log-normal ornstein\u2013uhlenbeck process and vertical transmission term","volume":"177","author":"Wang","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.matcom.2026.02.035_b29","doi-asserted-by":"crossref","DOI":"10.1016\/j.jmaa.2025.129253","article-title":"The threshold of a stochastic SIVS model with saturated incidence based on logarithmic ornstein\u2013uhlenbeck process","volume":"547","author":"Zhou","year":"2025","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/j.matcom.2026.02.035_b30","series-title":"Stochastic Differential Equations and Applications","author":"Mao","year":"1997"},{"key":"10.1016\/j.matcom.2026.02.035_b31","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1016\/j.aml.2013.03.013","article-title":"Stochastic SIR model with jumps","volume":"26","author":"Zhang","year":"2013","journal-title":"Appl. Math. Lett."},{"key":"10.1016\/j.matcom.2026.02.035_b32","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2023.113256","article-title":"Stationary distribution and probability density for a stochastic SEIR-type model of coronavirus (COVID-19) with asymptomatic carriers","volume":"169","author":"Liu","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.matcom.2026.02.035_b33","series-title":"Handbook of Stochastic Methods for Physics","first-page":"1","author":"Gardiner","year":"1983"},{"key":"10.1016\/j.matcom.2026.02.035_b34","doi-asserted-by":"crossref","first-page":"1793","DOI":"10.1137\/0149110","article-title":"An asymptotic solution to a two-dimensional exit problem arising in population dynamics","volume":"49","author":"Roozen","year":"1989","journal-title":"SIAM J. Appl. Math."},{"key":"10.1016\/j.matcom.2026.02.035_b35","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1137\/S0036144500378302","article-title":"An algorithmic introduction to numerical simulation of stochastic differential equations","volume":"43","author":"Higham","year":"2001","journal-title":"SIAM Rev."}],"container-title":["Mathematics and Computers in Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426000972?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426000972?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T08:27:40Z","timestamp":1777537660000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0378475426000972"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9]]},"references-count":35,"alternative-id":["S0378475426000972"],"URL":"https:\/\/doi.org\/10.1016\/j.matcom.2026.02.035","relation":{},"ISSN":["0378-4754"],"issn-type":[{"value":"0378-4754","type":"print"}],"subject":[],"published":{"date-parts":[[2026,9]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Long-term behavior of a stochastic HBV model with logistic hepatocyte growth and log-normal Ornstein\u2013Uhlenbeck process","name":"articletitle","label":"Article Title"},{"value":"Mathematics and Computers in Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.matcom.2026.02.035","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}]}}