{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T20:01:40Z","timestamp":1791144100007,"version":"4.1.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2011,8,13]],"date-time":"2011-08-13T00:00:00Z","timestamp":1313193600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Biol."],"published-print":{"date-parts":[[2012,8]]},"DOI":"10.1007\/s00285-011-0459-8","type":"journal-article","created":{"date-parts":[[2011,8,12]],"date-time":"2011-08-12T05:08:07Z","timestamp":1313125687000},"page":"263-291","source":"Crossref","is-referenced-by-count":18,"title":["Mathematical model of the primary CD8 T cell immune response: stability analysis of a nonlinear age-structured system"],"prefix":"10.1007","volume":"65","author":[{"given":"Emmanuelle","family":"Terry","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jacqueline","family":"Marvel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christophe","family":"Arpin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Olivier","family":"Gandrillon","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fabien","family":"Crauste","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2011,8,13]]},"reference":[{"key":"459_CR1","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.cam.2005.02.004","volume":"184","author":"B Adams","year":"2005","unstructured":"Adams B, Banks H, Davidian M, Kwon HD, Tran H, Wynne S, Rosenberg E (2005) HIV dynamics: modeling, data analysis, and optimal treatment protocols. J Comput Appl Math 184: 10\u201349","journal-title":"J Comput Appl Math"},{"key":"459_CR2","doi-asserted-by":"crossref","first-page":"2944","DOI":"10.4049\/jimmunol.179.5.2944","volume":"179","author":"C Althaus","year":"2007","unstructured":"Althaus C, Ganusov V, De Boer R (2007) Dynamics of CD8 T cell responses during acute and chronic lymphocytic choriomeningitis virus infection. J Immunol 179: 2944\u20132951","journal-title":"J Immunol"},{"key":"459_CR3","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1006\/jtbi.2003.3208","volume":"221","author":"R Antia","year":"2003","unstructured":"Antia R, Bergstrom C, Pilyugin S, Kaech S, Ahmed R (2003) Models of {CD8+ Responses: 1. What is the antigen-independent proliferation program. J Theor Biol 221: 585\u2013598","journal-title":"J Theor Biol"},{"key":"459_CR4","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1038\/nri1550","volume":"5","author":"R Antia","year":"2005","unstructured":"Antia R, Ganusov V, Ahmed R (2005) The role of models in understanding CD8+ T-cell memory. Nat Rev 5: 101\u2013111","journal-title":"Nat Rev"},{"key":"459_CR5","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.smim.2004.02.007","volume":"16","author":"V Appay","year":"2004","unstructured":"Appay V, Rowland-Jones S (2004) Lessons from the study of T-cell differentiation in persistent human virus infection. Seminars Immunol 16: 205\u2013212","journal-title":"Seminars Immunol"},{"key":"459_CR6","doi-asserted-by":"crossref","first-page":"2147","DOI":"10.4049\/jimmunol.168.5.2147","volume":"168","author":"C Arpin","year":"2002","unstructured":"Arpin C, Angelov G, Walzer T, Tomkowiak M, Beloeil L, Marvel J (2002) Hyperproliferative response of a monoclonal memory CD8 T cell population is characterized by an increased frequency of clonogenic precursors. J Immunol 168: 2147\u20132153","journal-title":"J Immunol"},{"key":"459_CR7","doi-asserted-by":"crossref","first-page":"7590","DOI":"10.1128\/JVI.01623-05","volume":"80","author":"P Baccam","year":"2006","unstructured":"Baccam P, Beauchemin C, Macken C, Hayden F, Perelson A (2006) Kinetics of influenza A virus infection in humans. J Virol 80: 7590\u20137599","journal-title":"J Virol"},{"key":"459_CR8","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1126\/science.1166831","volume":"323","author":"O Bannard","year":"2009","unstructured":"Bannard O, Kraman M, Fearon D (2009) Secondary replicative function of CD8+ T cells that had developed an effector function. Science 323: 505\u2013509","journal-title":"Science"},{"key":"459_CR9","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.jtbi.2008.05.031","volume":"254","author":"C Beauchemin","year":"2008","unstructured":"Beauchemin C, McSharry J, Drusano G, Nguyen J, Went G, Ribeiro R, Perelson A (2008) Modeling amantadine treatment of influenza A virus in vitro. J Theor Biol 254: 439\u2013451","journal-title":"J Theor Biol"},{"key":"459_CR10","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1089\/cmb.2007.0125","volume":"15","author":"C Bidot","year":"2008","unstructured":"Bidot C, Gruy F, Haudin CS, Hentati FE, Guy B, Lambert C (2008) Mathematical modeling of T-cell activation kinetic. J Comput Biol 15: 105\u2013128","journal-title":"J Comput Biol"},{"issue":"22","key":"459_CR11","doi-asserted-by":"crossref","first-page":"10663","DOI":"10.1128\/JVI.75.22.10663-10669.2001","volume":"75","author":"R De Boer","year":"2001","unstructured":"De Boer R, Oprea M, Antia R, Murali-Krishna K, Ahmed R, Perelson A (2001) Recruitment times, proliferation, and apoptosis rates during the CD8 T-cell response to lymphocytic choriomeningitis virus. J Virol 75(22): 10663\u201310669","journal-title":"J Virol"},{"key":"459_CR12","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1016\/S0140-6736(81)91389-1","volume":"ii","author":"F Ennis","year":"1981","unstructured":"Ennis F, Yi-Hua Q, Riley D, Rook A, Schild G, Pratt R, Potter C (1981) HLA-restricted virus-specific cytotoxic T-lymphocyte responses to live and inactivated influenza vaccines. The Lancet ii: 887\u2013891","journal-title":"The Lancet"},{"key":"459_CR13","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1038\/ni1469","volume":"8","author":"G Guarda","year":"2007","unstructured":"Guarda G, Hons M, Soriano S, Huang A, Polley R, Martin-Fontecha A, Stein J, Germain R, Lanzavecchia A, Sallusto F (2007) L-selectin-negative CCR7\u2212 effector and memory CD8+ T cells enter reactive lymph nodes and kill dendritic cells. Nat Immunol 8: 743\u2013752","journal-title":"Nat Immunol"},{"key":"459_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4342-7","volume-title":"Introduction to functional differential equations, Applied Mathematical Sciences, vol 99","author":"J Hale","year":"1993","unstructured":"Hale J, Verduyn Lunel S (1993) Introduction to functional differential equations, Applied Mathematical Sciences, vol 99. Springer, New York"},{"key":"459_CR15","doi-asserted-by":"crossref","first-page":"3095","DOI":"10.4049\/jimmunol.164.6.3095","volume":"164","author":"I Hermans","year":"2000","unstructured":"Hermans I, Ritchie D, Yang J, Roberts J, Ronchese F (2000) CD8+ T cell-dependent elimination of DC in vivo limits the induction of antitumor immunity. J Immunol 164: 3095\u20133101","journal-title":"J Immunol"},{"key":"459_CR16","doi-asserted-by":"crossref","first-page":"3818","DOI":"10.4049\/jimmunol.181.6.3818","volume":"181","author":"M Jenkins","year":"2008","unstructured":"Jenkins M, Mintern J, LaGruta N, Kedzierska K, Doherty P, Turner S (2008) Cell cycle-related acquisition of cytotoxic mediators defines the progressive differentiation to effector status for virus-specific CD8 T cells. J Immunol 181: 3818\u20133822","journal-title":"J Immunol"},{"key":"459_CR17","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1038\/87720","volume":"2","author":"S Kaech","year":"2001","unstructured":"Kaech S, Ahmed R (2001) Memory CD8+ T cell differentiation : initial antigen encounter triggers a developmental program in nave cells. Nat Immunol 2: 415\u2013422","journal-title":"Nat Immunol"},{"key":"459_CR18","doi-asserted-by":"crossref","first-page":"2923","DOI":"10.4049\/jimmunol.173.5.2923","volume":"179","author":"R Kemp","year":"2004","unstructured":"Kemp R, Powell T, Dwyer D, Dutton R (2004) Cutting edge: regulation of CD8+ T cell effector population size. J Immunol 179: 2923\u20132927","journal-title":"J Immunol"},{"key":"459_CR19","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.jtbi.2006.12.012","volume":"246","author":"P Kim","year":"2007","unstructured":"Kim P, Lee P, Levy D (2007) Modeling regulation mechanisms in the immune system. J Theor Biol 246: 33\u201369","journal-title":"J Theor Biol"},{"key":"459_CR20","doi-asserted-by":"crossref","first-page":"7151","DOI":"10.1128\/JVI.00098-09","volume":"83","author":"H Lee","year":"2009","unstructured":"Lee H, Topham D, Park S, Hollenbaugh J, Treanor J, Mosmann T, Jin X, Ward B, Miao H, Holden-Wiltse J, Perelson A, Zand M, Wu H (2009) Simulation and prediction of the adaptative immune response to influenza A virus infection. J Virol 83: 7151\u20137165","journal-title":"J Virol"},{"key":"459_CR21","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/S1074-7613(00)80470-7","volume":"8","author":"K Murali-Krishna","year":"1998","unstructured":"Murali-Krishna K, Altman J, MSuresh , Sourdive D, Zajax A, Miller J, Slansky J, Ahmed R (1998) Counting antigen-specific CD8 T cells: a reevaluation of bystander activation during viral infection. Immunity 8: 177\u2013187","journal-title":"Immunity"},{"key":"459_CR22","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1038\/nri700","volume":"2","author":"A Perelson","year":"2001","unstructured":"Perelson A (2001) Modelling viral and immune system dynamics. Nat Rev Immunol 2: 28\u201336","journal-title":"Nat Rev Immunol"},{"key":"459_CR23","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/j.cam.2004.08.018","volume":"184","author":"I Rouzine","year":"2005","unstructured":"Rouzine I, Murali-Krishna K, Ahmed R (2005) Generals die in friendly fire, or modeling immune response to HIV. J Comput Appl Math 184: 258\u2013274","journal-title":"J Comput Appl Math"},{"key":"459_CR24","doi-asserted-by":"crossref","first-page":"3974","DOI":"10.1128\/JVI.02078-09","volume":"84","author":"R Saenz","year":"2010","unstructured":"Saenz R, Quinlivan M, Elton D, MacRae S, Blunden A, Mumford J, Daly J, Digard P, Cullinane A, Grenfell B, McCauley J, Wood J, Gog J (2010) Dynamics of influenza virus infection and pathology. J Virol 84: 3974\u20133983","journal-title":"J Virol"},{"key":"459_CR25","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/S0952-7915(00)00211-9","volume":"13","author":"J Sprent","year":"2001","unstructured":"Sprent J, Surh C (2001) Generation and maintenance of memory T cells. Curr Opin Immunol 13: 248\u2013254","journal-title":"Curr Opin Immunol"},{"key":"459_CR26","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1038\/87730","volume":"2","author":"MV Stipdonk","year":"2001","unstructured":"Stipdonk MV, Lemmens E, Schoenberger S (2001) Naive CTLs require a single brief period of antigenic stimulation for clonal expansion and differentiation. Nat Immunol 2: 423\u2013429","journal-title":"Nat Immunol"},{"key":"459_CR27","doi-asserted-by":"crossref","first-page":"658","DOI":"10.4049\/jimmunol.151.2.658","volume":"151","author":"M Su","year":"1993","unstructured":"Su M, Wladen P, Golan D, Eisen H (1993) Cognate peptide-induced destruction of CD8+ cytotoxic T lymphocytes is due to fratricide. J Immunol 151: 658\u2013667","journal-title":"J Immunol"},{"key":"459_CR28","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1038\/76907","volume":"1","author":"H Veiga-Fernandes","year":"2000","unstructured":"Veiga-Fernandes H, Walter U, Bourgeois C, McLean A, Rocha B (2000) Response of naive and memory CD8+ T Cells to antigen stimulation in vivo. Nat Immunol 1: 47\u201353","journal-title":"Nat Immunol"},{"key":"459_CR29","unstructured":"Webb G (1985) Theory of nonlinear age-dependent population dynamics, Monographs and textbooks. In: Pure and Applied Mathematics, vol 89. Marcel Dekker, New York"},{"key":"459_CR30","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1093\/intimm\/12.4.467","volume":"12","author":"D Wodarz","year":"2000","unstructured":"Wodarz D, May R, Nowak M (2000) The role of antigen-independent persistence of memory cytotoxic T lymphocytes. Int Immunol 12: 467\u2013477","journal-title":"Int Immunol"}],"container-title":["Journal of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00285-011-0459-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00285-011-0459-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00285-011-0459-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,8]],"date-time":"2023-06-08T17:56:38Z","timestamp":1686246998000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00285-011-0459-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,8,13]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["459"],"URL":"https:\/\/doi.org\/10.1007\/s00285-011-0459-8","relation":{},"ISSN":["0303-6812","1432-1416"],"issn-type":[{"value":"0303-6812","type":"print"},{"value":"1432-1416","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,8,13]]}}}