{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:03:56Z","timestamp":1772291036453,"version":"3.50.1"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"09","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11471044"],"award-info":[{"award-number":["11471044"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2018,8]]},"abstract":"<jats:p> We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in\u00a0vivo. In the model, we consider the proliferation of uninfected CD[Formula: see text] T\u00a0cells by a logistic function and the infected CD[Formula: see text] T cells are assumed to have an infection-age structure. Our main results concern the Hopf bifurcation of the model by using the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with nondense domain. Bifurcation analysis indicates that there exist some parameter values such that this HIV infection model has a nontrivial periodic solution which bifurcates from the positive equilibrium. The numerical simulations are also carried out. <\/jats:p>","DOI":"10.1142\/s0218127418501092","type":"journal-article","created":{"date-parts":[[2018,9,5]],"date-time":"2018-09-05T23:36:43Z","timestamp":1536190603000},"page":"1850109","source":"Crossref","is-referenced-by-count":22,"title":["Bifurcation Analysis of an Age Structured HIV Infection Model with Both Virus-to-Cell and Cell-to-Cell Transmissions"],"prefix":"10.1142","volume":"28","author":[{"given":"Xiangming","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6828-5573","authenticated-orcid":false,"given":"Zhihua","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,9,5]]},"reference":[{"key":"S0218127418501092BIB001","doi-asserted-by":"publisher","DOI":"10.1006\/jtbi.1997.0548"},{"key":"S0218127418501092BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2014.10.004"},{"key":"S0218127418501092BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-002-0191-5"},{"key":"S0218127418501092BIB004","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139902406905"},{"key":"S0218127418501092BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.09.074"},{"key":"S0218127418501092BIB006","doi-asserted-by":"publisher","DOI":"10.3934\/cpaa.2015.14.657"},{"key":"S0218127418501092BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2016.04.003"},{"key":"S0218127418501092BIB008","volume-title":"Mathematical Theory of Age-Structured Population Dynamics","author":"Iannelli M.","year":"1995"},{"key":"S0218127418501092BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2013.01.003"},{"key":"S0218127418501092BIB010","doi-asserted-by":"publisher","DOI":"10.1137\/130930145"},{"key":"S0218127418501092BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2014.10.086"},{"key":"S0218127418501092BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-010-0088-x"},{"key":"S0218127418501092BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-015-9245-x"},{"key":"S0218127418501092BIB014","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2015.20.1735"},{"key":"S0218127418501092BIB015","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2016.21.537"},{"key":"S0218127418501092BIB016","first-page":"1","volume":"2001","author":"Magal P.","year":"2001","journal-title":"Electron. J. Diff. Eqs."},{"key":"S0218127418501092BIB017","first-page":"1041","volume":"14","author":"Magal P.","year":"2009","journal-title":"Adv. Diff. Eqs."},{"key":"S0218127418501092BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(93)90043-A"},{"key":"S0218127418501092BIB019","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144598335107"},{"key":"S0218127418501092BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.coviro.2011.09.004"},{"key":"S0218127418501092BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2009.09.006"},{"key":"S0218127418501092BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2015.09.015"},{"key":"S0218127418501092BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2011.07.038"},{"key":"S0218127418501092BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2016.08.001"},{"key":"S0218127418501092BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2007.09.030"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127418501092","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T14:31:05Z","timestamp":1565101865000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127418501092"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8]]},"references-count":25,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2018,9,5]]},"published-print":{"date-parts":[[2018,8]]}},"alternative-id":["10.1142\/S0218127418501092"],"URL":"https:\/\/doi.org\/10.1142\/s0218127418501092","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8]]}}}