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We formulate the model and then fractionalize it using the concept of fractional calculus. For the purpose of fractionalizing, we use the Caputo\u2013Fabrizio operator. Once we develop the model under consideration, existence and uniqueness analysis will be discussed. We use fixed point theory for the existence and uniqueness analysis. We also prove that the model under consideration possesses a bounded and positive solution. We then find the basic reproductive number to perform the steady\u2010state analysis and to show that the fractional\u2010order epidemiological model is locally and globally asymptotically stable under certain conditions. For the local and global analysis, we use linearization, mean value theorem, and fractional Barbalat\u2019s lemma, respectively. Finally, we perform some numerical findings to support the analytical work with the help of graphical representations.<\/jats:p>","DOI":"10.1155\/2021\/8752161","type":"journal-article","created":{"date-parts":[[2021,12,28]],"date-time":"2021-12-28T00:35:16Z","timestamp":1640651716000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["The Transmission Dynamics of Hepatitis B Virus via the Fractional\u2010Order Epidemiological Model"],"prefix":"10.1155","volume":"2021","author":[{"given":"Tahir","family":"Khan","sequence":"first","affiliation":[]},{"given":"Zi-Shan","family":"Qian","sequence":"additional","affiliation":[]},{"given":"Roman","family":"Ullah","sequence":"additional","affiliation":[]},{"given":"Basem","family":"Al Alwan","sequence":"additional","affiliation":[]},{"given":"Gul","family":"Zaman","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2853-9337","authenticated-orcid":false,"given":"Qasem M.","family":"Al-Mdallal","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7663-2675","authenticated-orcid":false,"given":"Youssef","family":"El Khatib","sequence":"additional","affiliation":[]},{"given":"Khaled","family":"Kheder","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,12,27]]},"reference":[{"key":"e_1_2_11_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2010.10.028"},{"key":"e_1_2_11_2_2","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-2893.2003.00487.x"},{"key":"e_1_2_11_3_2","doi-asserted-by":"publisher","DOI":"10.1053\/gast.2001.24839"},{"key":"e_1_2_11_4_2","doi-asserted-by":"publisher","DOI":"10.1055\/s-2005-915644"},{"key":"e_1_2_11_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.siny.2007.01.013"},{"key":"e_1_2_11_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2008.06.022"},{"key":"e_1_2_11_7_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1525-1446.2009.00790.x"},{"key":"e_1_2_11_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/hep.21347"},{"key":"e_1_2_11_9_2","doi-asserted-by":"publisher","DOI":"10.1093\/clinids\/11.supplement_3.s574"},{"key":"e_1_2_11_10_2","doi-asserted-by":"publisher","DOI":"10.1093\/epirev\/mxj009"},{"key":"e_1_2_11_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2009.11.008"},{"key":"e_1_2_11_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2010.06.009"},{"key":"e_1_2_11_13_2","doi-asserted-by":"publisher","DOI":"10.1155\/2015\/842792"},{"key":"e_1_2_11_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2013.10.006"},{"key":"e_1_2_11_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-014-0028-6"},{"key":"e_1_2_11_16_2","volume-title":"Infectious Diseases Of Humans: Dynamics And Control","author":"Anderson R.","year":"1992"},{"key":"e_1_2_11_17_2","doi-asserted-by":"publisher","DOI":"10.1017\/s0950268800058970"},{"key":"e_1_2_11_18_2","doi-asserted-by":"publisher","DOI":"10.1038\/87953"},{"key":"e_1_2_11_19_2","doi-asserted-by":"publisher","DOI":"10.1093\/ije\/29.4.744"},{"key":"e_1_2_11_20_2","doi-asserted-by":"publisher","DOI":"10.14419\/ijamr.v3i3.2872"},{"key":"e_1_2_11_21_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/475451"},{"key":"e_1_2_11_22_2","doi-asserted-by":"publisher","DOI":"10.4236\/am.2014.516242"},{"key":"e_1_2_11_23_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0138765"},{"key":"e_1_2_11_24_2","doi-asserted-by":"publisher","DOI":"10.1186\/s40064-016-2706-3"},{"key":"e_1_2_11_25_2","doi-asserted-by":"publisher","DOI":"10.1080\/17513758.2016.1256441"},{"key":"e_1_2_11_26_2","doi-asserted-by":"publisher","DOI":"10.5923\/j.am.20170701.02"},{"key":"e_1_2_11_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2020.109860"},{"key":"e_1_2_11_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2020.103593"},{"key":"e_1_2_11_29_2","volume-title":"Fractional Integrals and Derivatives, Theory and Applications","author":"Samko S. 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