{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,29]],"date-time":"2026-08-29T06:10:13Z","timestamp":1787983813252,"version":"build-2784847793"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,5,19]],"date-time":"2024-05-19T00:00:00Z","timestamp":1716076800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,19]],"date-time":"2024-05-19T00:00:00Z","timestamp":1716076800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["202006840122"],"award-info":[{"award-number":["202006840122"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Changzhou Scientific and Technological Program grant","award":["CJ20220134"],"award-info":[{"award-number":["CJ20220134"]}]},{"name":"Natural Science Foundation of Jiangsu Higher Education","award":["22KJB110007"],"award-info":[{"award-number":["22KJB110007"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071217"],"award-info":[{"award-number":["12071217"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12201077"],"award-info":[{"award-number":["12201077"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NSERC of Canada","award":["RGPIN-2019-05892"],"award-info":[{"award-number":["RGPIN-2019-05892"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Math. Biol."],"published-print":{"date-parts":[[2024,7]]},"DOI":"10.1007\/s00285-024-02104-w","type":"journal-article","created":{"date-parts":[[2024,5,19]],"date-time":"2024-05-19T09:01:15Z","timestamp":1716109275000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A mathematical model for HIV dynamics with multiple infections: implications for immune escape"],"prefix":"10.1007","volume":"89","author":[{"given":"Qi","family":"Deng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ting","family":"Guo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhipeng","family":"Qiu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuming","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,5,19]]},"reference":[{"issue":"5","key":"2104_CR1","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.tim.2015.02.003","volume":"23","author":"LM Agosto","year":"2015","unstructured":"Agosto LM, Uchil PD, Mothes W (2015) HIV cell-to-cell transmission: effects on pathogenesis and antiretroviral therapy. Trends Microbiol 23(5):289\u2013295","journal-title":"Trends Microbiol"},{"issue":"1740","key":"2104_CR2","doi-asserted-by":"crossref","first-page":"3003","DOI":"10.1098\/rspb.2012.0328","volume":"279","author":"CL Althaus","year":"2012","unstructured":"Althaus CL, De Boer RJ (2012) Impaired immune evasion in HIV through intracellular delays and multiple infection of cells. Proceed Roy Soc B: Biol Sci 279(1740):3003\u20133010","journal-title":"Proceed Roy Soc B: Biol Sci"},{"issue":"3","key":"2104_CR3","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1038\/nm0304-229","volume":"10","author":"JD Altman","year":"2004","unstructured":"Altman JD, Feinberg MB (2004) HIV escape: there and back again. Nature Med 10(3):229\u2013230","journal-title":"Nature Med"},{"issue":"1","key":"2104_CR4","doi-asserted-by":"crossref","first-page":"14531","DOI":"10.1371\/journal.pone.0014531","volume":"6","author":"R Balagam","year":"2011","unstructured":"Balagam R, Singh V, Sagi AR (2011) Taking multiple infections of cells and recombination into account leads to small within-host effective-population-size estimates of HIV-1. PLoS One 6(1):14531","journal-title":"PLoS One"},{"issue":"5","key":"2104_CR5","doi-asserted-by":"crossref","first-page":"2472","DOI":"10.1128\/JVI.80.5.2472-2482.2006","volume":"80","author":"C Charpentier","year":"2006","unstructured":"Charpentier C, Nora T, Tenaillon O (2006) Extensive recombination among human immunodeficiency virus type 1 quasispecies makes an important contribution to viral diversity in individual patients. J Virol 80(5):2472\u20132482","journal-title":"J Virol"},{"key":"2104_CR6","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.trsl.2020.04.008","volume":"223","author":"Z Chen","year":"2020","unstructured":"Chen Z, Julg B (2020) Therapeutic vaccines for the treatment of HIV. Transl Res 223:61\u201375","journal-title":"Transl Res"},{"issue":"1","key":"2104_CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1745-6150-7-16","volume":"7","author":"KW Cummings","year":"2012","unstructured":"Cummings KW, Levy DN, Wodarz D (2012) Increased burst size in multiply infected cells can alter basic virus dynamics. Biol Direct 7(1):1\u201315","journal-title":"Biol Direct"},{"issue":"3","key":"2104_CR8","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1007\/s12539-022-00512-4","volume":"14","author":"C Dai","year":"2022","unstructured":"Dai C, Wang K (2022) Adaptive weighted neighbors method for sensitivity analysis. Interdiscip Sci: Comput Life Sci 14(3):652\u2013668","journal-title":"Interdiscip Sci: Comput Life Sci"},{"issue":"14","key":"2104_CR9","doi-asserted-by":"crossref","first-page":"7169","DOI":"10.1128\/JVI.00231-11","volume":"85","author":"A Del Portillo","year":"2011","unstructured":"Del Portillo A, Tripodi J, Najfeld V (2011) Multiploid inheritance of HIV-1 during cell-to-cell infection. J Virol 85(14):7169\u20137176","journal-title":"J Virol"},{"issue":"7","key":"2104_CR10","first-page":"3543","volume":"26","author":"Q Deng","year":"2021","unstructured":"Deng Q, Qiu Z, Guo T (2021) Modeling within-host viral dynamics: The role of CTL immune responses in the evolution of drug resistance. Discrete Cont Dyn Sys-B 26(7):3543\u20133562","journal-title":"Discrete Cont Dyn Sys-B"},{"key":"2104_CR11","doi-asserted-by":"crossref","DOI":"10.1016\/j.mbs.2022.108954","volume":"355","author":"Q Deng","year":"2023","unstructured":"Deng Q, Guo T, Qiu Z (2023) Towards a new combination therapy with vectored immunoprophylaxis for HIV: Modeling \u201cshock and kill\u2019\u2019 strategy. Math Biosci 355:108954","journal-title":"Math Biosci"},{"issue":"16","key":"2104_CR12","doi-asserted-by":"crossref","first-page":"8942","DOI":"10.1128\/JVI.78.16.8942-8945.2004","volume":"78","author":"NM Dixit","year":"2004","unstructured":"Dixit NM, Perelson AS (2004) Multiplicity of human immunodeficiency virus infections in lymphoid tissue. J Virol 78(16):8942\u20138945","journal-title":"J Virol"},{"issue":"23","key":"2104_CR13","doi-asserted-by":"crossref","first-page":"8198","DOI":"10.1073\/pnas.0407498102","volume":"102","author":"NM Dixit","year":"2005","unstructured":"Dixit NM, Perelson AS (2005) HIV dynamics with multiple infections of target cells. Proc Natl Acad Sci USA 102(23):8198\u20138203","journal-title":"Proc Natl Acad Sci USA"},{"issue":"1\u20132","key":"2104_CR14","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","volume":"180","author":"P Driessche","year":"2002","unstructured":"Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180(1\u20132):29\u201348","journal-title":"Math Biosci"},{"key":"2104_CR15","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.matcom.2017.07.006","volume":"144","author":"P Dubey","year":"2018","unstructured":"Dubey P, Dubey US, Dubey B (2018) Modeling the role of acquired immune response and antiretroviral therapy in the dynamics of HIV infection. Math Comput Simul 144:120\u2013137","journal-title":"Math Comput Simul"},{"issue":"10227","key":"2104_CR16","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1016\/S0140-6736(19)32990-3","volume":"395","author":"S Fidler","year":"2020","unstructured":"Fidler S, St\u00f6hr W, Pace M (2020) Antiretroviral therapy alone versus antiretroviral therapy with a kick and kill approach, on measures of the HIV reservoir in participants with recent HIV infection (the RIVER trial): a phase 2, randomised trial. The Lancet 395(10227):888\u2013898","journal-title":"The Lancet"},{"issue":"01","key":"2104_CR17","doi-asserted-by":"crossref","first-page":"01010","DOI":"10.1088\/1742-5468\/2013\/01\/P01010","volume":"2013","author":"VV Ganusov","year":"2013","unstructured":"Ganusov VV, Neher RA, Perelson AS (2013) Mathematical modeling of escape of HIV from cytotoxic T lymphocyte responses. J Stat Mech: Theory Exp 2013(01):01010","journal-title":"J Stat Mech: Theory Exp"},{"key":"2104_CR18","volume":"536","author":"S Gao","year":"2022","unstructured":"Gao S, Martcheva M, Miao H (2022) A two-sex model of human papillomavirus infection: Vaccination strategies and a case study. J Theor Biol 536:111006","journal-title":"J Theor Biol"},{"key":"2104_CR19","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s00285-020-01513-x","volume":"81","author":"T Guo","year":"2020","unstructured":"Guo T, Qiu Z, Rong L (2020) Modeling the role of macrophages in HIV persistence during antiretroviral therapy. J Math Biol 81:369\u2013402","journal-title":"J Math Biol"},{"key":"2104_CR20","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1007\/s40840-018-0699-5","volume":"43","author":"T Guo","year":"2020","unstructured":"Guo T, Qiu Z, Rong L (2020) Analysis of an HIV model with immune responses and cell-to-cell transmission. Bull Malays Math Sci Soc 43:581\u2013607","journal-title":"Bull Malays Math Sci Soc"},{"key":"2104_CR21","volume":"509","author":"T Guo","year":"2021","unstructured":"Guo T, Qiu Z, Kitagawa K (2021) Modeling HIV multiple infection. J Theor Biol 509:110502","journal-title":"J Theor Biol"},{"issue":"6","key":"2104_CR22","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1002\/cpa.3160380607","volume":"38","author":"WM Hirsch","year":"1985","unstructured":"Hirsch WM, Hanisch H, Gabriel J-P (1985) Differential equation models of some parasitic infections: methods for the study of asymptotic behavior. Commun Pur Appl Math 38(6):733\u2013753","journal-title":"Commun Pur Appl Math"},{"issue":"1","key":"2104_CR23","doi-asserted-by":"crossref","first-page":"6559","DOI":"10.1038\/s41598-017-03954-9","volume":"7","author":"Y Ito","year":"2017","unstructured":"Ito Y, Remion A, Tauzin A (2017) Number of infection events per cell during HIV-1 cell-free infection. Sci Rep 7(1):6559","journal-title":"Sci Rep"},{"key":"2104_CR24","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.jtbi.2018.06.025","volume":"455","author":"Y Ito","year":"2018","unstructured":"Ito Y, Tauzin A, Remion A (2018) Dynamics of HIV-1 coinfection in different susceptible target cell populations during cell-free infection. J Theor Biol 455:39\u201346","journal-title":"J Theor Biol"},{"issue":"6894","key":"2104_CR25","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1038\/418144a","volume":"418","author":"A Jung","year":"2002","unstructured":"Jung A, Maier R, Vartanian J-P (2002) Multiply infected spleen cells in HIV patients. Nature 418(6894):144\u2013144","journal-title":"Nature"},{"key":"2104_CR26","doi-asserted-by":"crossref","unstructured":"Kaseke C, Tano-Menka R, Senjobe F (2021) The emerging role for CTL epitope specificity in HIV cure efforts. J Infect Diseases 223(Supplement_1), 32\u201337","DOI":"10.1093\/infdis\/jiaa333"},{"issue":"5","key":"2104_CR27","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1016\/j.immuni.2020.10.015","volume":"53","author":"SW Kazer","year":"2020","unstructured":"Kazer SW, Walker BD, Shalek AK (2020) Evolution and diversity of immune responses during acute HIV infection. Immunity 53(5):908\u2013924","journal-title":"Immunity"},{"key":"2104_CR28","doi-asserted-by":"crossref","unstructured":"Kedzierska K, Koutsakos M (2020) The ABC of major histocompatibility complexes and T cell receptors in health and disease. Viral Immunol","DOI":"10.1089\/vim.2019.0184"},{"issue":"2","key":"2104_CR29","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.mbs.2013.01.003","volume":"242","author":"NL Komarova","year":"2013","unstructured":"Komarova NL, Wodarz D (2013) Virus dynamics in the presence of synaptic transmission. Math Biosci 242(2):161\u2013171","journal-title":"Math Biosci"},{"issue":"1","key":"2104_CR30","doi-asserted-by":"crossref","first-page":"2103","DOI":"10.1038\/srep02103","volume":"3","author":"NL Komarova","year":"2013","unstructured":"Komarova NL, Levy DN, Wodarz D (2013) Synaptic transmission and the susceptibility of HIV infection to anti-viral drugs. Sci Rep 3(1):2103","journal-title":"Sci Rep"},{"issue":"1","key":"2104_CR31","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0025-5564(93)90043-A","volume":"114","author":"AS Perelson","year":"1993","unstructured":"Perelson AS, Kirschner DE, De Boer R (1993) Dynamics of HIV infection of CD4+ T cells. Math Biosci 114(1):81\u2013125","journal-title":"Math Biosci"},{"key":"2104_CR32","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.mbs.2015.03.001","volume":"264","author":"D Phan","year":"2015","unstructured":"Phan D, Wodarz D (2015) Modeling multiple infection of cells by viruses: Challenges and insights. Math Biosci 264:21\u201328","journal-title":"Math Biosci"},{"issue":"12","key":"2104_CR33","doi-asserted-by":"crossref","first-page":"3118","DOI":"10.1016\/j.camwa.2008.09.002","volume":"56","author":"Z Qiu","year":"2008","unstructured":"Qiu Z (2008) Dynamical behavior of a vector-host epidemic model with demographic structure. Comput Math Appl 56(12):3118\u20133129","journal-title":"Comput Math Appl"},{"key":"2104_CR34","doi-asserted-by":"crossref","unstructured":"Rong L, Feng Z, Perelson AS (2007) Emergence of HIV-1 drug resistance during antiretroviral treatment. Bull Math Biol 69:2027\u20132060","DOI":"10.1007\/s11538-007-9203-3"},{"key":"2104_CR35","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.mbs.2019.01.007","volume":"309","author":"M Shen","year":"2019","unstructured":"Shen M, Xiao Y, Rong L (2019) Conflict and accord of optimal treatment strategies for HIV infection within and between hosts. Math Biosci 309:107\u2013117","journal-title":"Math Biosci"},{"issue":"7362","key":"2104_CR36","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1038\/nature10347","volume":"477","author":"A Sigal","year":"2011","unstructured":"Sigal A, Kim JT, Balazs AB (2011) Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy. Nature 477(7362):95\u201398","journal-title":"Nature"},{"issue":"9","key":"2104_CR37","doi-asserted-by":"crossref","first-page":"1008011","DOI":"10.1371\/journal.ppat.1008011","volume":"15","author":"M Surenaud","year":"2019","unstructured":"Surenaud M, Montes M, Lindestam Arlehamn CS (2019) Anti-HIV potency of T-cell responses elicited by dendritic cell therapeutic vaccination. PLoS Pathog 15(9):1008011","journal-title":"PLoS Pathog"},{"issue":"7","key":"2104_CR38","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1007\/BF00173267","volume":"30","author":"HR Thieme","year":"1992","unstructured":"Thieme HR (1992) Convergence results and a poincar\u00e9-bendixson trichotomy for asymptotically autonomous differential equations. J Math Biol 30(7):755\u2013763","journal-title":"J Math Biol"},{"issue":"2","key":"2104_CR39","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1137\/0524026","volume":"24","author":"HR Thieme","year":"1993","unstructured":"Thieme HR (1993) Persistence under relaxed point-dissipativity (with application to an endemic model). SIAM J Math Anal 24(2):407\u2013435","journal-title":"SIAM J Math Anal"},{"key":"2104_CR40","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.aml.2019.02.019","volume":"94","author":"X Wang","year":"2019","unstructured":"Wang X, Rong L (2019) HIV low viral load persistence under treatment: Insights from a model of cell-to-cell viral transmission. Appl Math Lett 94:44\u201351","journal-title":"Appl Math Lett"},{"issue":"1","key":"2104_CR41","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.mbs.2002.11.001","volume":"190","author":"W Wang","year":"2004","unstructured":"Wang W, Zhao X-Q (2004) An epidemic model in a patchy environment. Math Biosci 190(1):97\u2013112","journal-title":"Math Biosci"},{"key":"2104_CR42","doi-asserted-by":"crossref","unstructured":"Wang J, Guo M, Liu X (2016) Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay. Appl Math Comput 291:149\u2013161","DOI":"10.1016\/j.amc.2016.06.032"},{"issue":"04","key":"2104_CR43","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1142\/S021833901740006X","volume":"25","author":"S Wang","year":"2017","unstructured":"Wang S, Xu F, Rong L (2017) Bistability analysis of an HIV model with immune response. J Biol Sys 25(04):677\u2013695","journal-title":"J Biol Sys"},{"key":"2104_CR44","unstructured":"WHO: HIV\/AIDS: key facts. http:\/\/www.who.int\/news-room\/fact-sheets\/detail\/hiv-aids (2023)"},{"issue":"9","key":"2104_CR45","doi-asserted-by":"crossref","first-page":"2326","DOI":"10.1111\/j.1558-5646.2009.00727.x","volume":"63","author":"D Wodarz","year":"2009","unstructured":"Wodarz D, Levy DN (2009) Multiple HIV-1 infection of cells and the evolutionary dynamics of cytotoxic T lymphocyte escape mutants. Evolu 63(9):2326\u20132339","journal-title":"Evolu"},{"issue":"55","key":"2104_CR46","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1098\/rsif.2010.0266","volume":"8","author":"D Wodarz","year":"2011","unstructured":"Wodarz D, Levy DN (2011) Effect of different modes of viral spread on the dynamics of multiply infected cells in human immunodeficiency virus infection. J Roy Soc Interface 8(55):289\u2013300","journal-title":"J Roy Soc Interface"},{"issue":"7","key":"2104_CR47","doi-asserted-by":"crossref","first-page":"2625","DOI":"10.1007\/s11538-019-00621-0","volume":"81","author":"C Yan","year":"2019","unstructured":"Yan C, Wang W (2019) Modeling HIV dynamics under combination therapy with inducers and antibodies. Bull Math Biol 81(7):2625\u20132648","journal-title":"Bull Math Biol"}],"container-title":["Journal of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00285-024-02104-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00285-024-02104-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00285-024-02104-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T06:10:03Z","timestamp":1719468603000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00285-024-02104-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,19]]},"references-count":47,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,7]]}},"alternative-id":["2104"],"URL":"https:\/\/doi.org\/10.1007\/s00285-024-02104-w","relation":{},"ISSN":["0303-6812","1432-1416"],"issn-type":[{"value":"0303-6812","type":"print"},{"value":"1432-1416","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,19]]},"assertion":[{"value":"26 August 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 December 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 April 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 May 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"6"}}