{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T03:07:02Z","timestamp":1761102422872,"version":"3.37.3"},"reference-count":29,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,9,19]],"date-time":"2020-09-19T00:00:00Z","timestamp":1600473600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Traditional Medicine Clinical Research Base Business Construction Special Topics","award":["JDZX2015299","FRF-BR-16-019A"],"award-info":[{"award-number":["JDZX2015299","FRF-BR-16-019A"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["JDZX2015299","FRF-BR-16-019A"],"award-info":[{"award-number":["JDZX2015299","FRF-BR-16-019A"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,9,19]]},"abstract":"<jats:p>In this paper, a fractional-order HBV model was set up based on standard mass action incidences and quasisteady assumption. The basic reproductive number <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:msub><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math> and the cytotoxic T lymphocytes\u2019 immune-response reproductive number <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:msub><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math> were derived. There were three equilibrium points of the model, and stable analysis of each equilibrium point was given with corresponding hypothesis about <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:msub><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math> or <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:msub><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math>. Some numerical simulations were also given based on HBeAg clinical data, and the simulation showed that there existed positive logarithmic correlation between the number of infected cells and HBeAg, which was consistent with the clinical facts. The simulation also showed that the clinical individual differences should be reflected by the fractional-order model.<\/jats:p>","DOI":"10.1155\/2020\/8864403","type":"journal-article","created":{"date-parts":[[2020,9,19]],"date-time":"2020-09-19T23:31:24Z","timestamp":1600558284000},"page":"1-11","source":"Crossref","is-referenced-by-count":5,"title":["Stability Analysis and Clinic Phenomenon Simulation of a Fractional-Order HBV Infection Model"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4488-5990","authenticated-orcid":true,"given":"Yongmei","family":"Su","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"}]},{"given":"Sinuo","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"}]},{"given":"Shurui","family":"Song","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"}]},{"given":"Xiaoke","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Liver Diseases, Beijing University of Chinese Medicine, Dongzhimen Hospital Affiliated to Beijing University of Chinese Medicine, Beijing 100700, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9765-4665","authenticated-orcid":true,"given":"Yongan","family":"Ye","sequence":"additional","affiliation":[{"name":"Institute of Liver Diseases, Beijing University of Chinese Medicine, Dongzhimen Hospital Affiliated to Beijing University of Chinese Medicine, Beijing 100700, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-012-9758-5"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-010-8467-0"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2009.06.004"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/s13160-011-0045-x"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-019-2438-0"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2019.102976"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-019-00621-0"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.virusres.2019.197841"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2020153"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1038\/nri700"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.93.9.4398"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1053\/jhep.2000.9143"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1155\/2015\/563127"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.joems.2013.11.001"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.01.080"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2012.01.004"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.joems.2017.06.003"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-018-0588-4"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1049\/iet-syb.2012.0054"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2006.12.001"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2011.8.689"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2015.10.027"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2016.05.007"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2006.04.087"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2015.05.014"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/939027"},{"issue":"4","key":"27","first-page":"316","volume":"18","year":"2012","journal-title":"Chinese Journal of Vaccines and Immunization"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1216\/RMJ-2008-38-5-1573"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1038\/4772"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8864403.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8864403.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8864403.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,19]],"date-time":"2020-09-19T23:31:27Z","timestamp":1600558287000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/8864403\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,19]]},"references-count":29,"alternative-id":["8864403","8864403"],"URL":"https:\/\/doi.org\/10.1155\/2020\/8864403","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2020,9,19]]}}}