D. Verkoeijen, G. A. Pouw, G. M. Meesters, and E. B. Scarlett, Population balances for particulate processes???a volume approach, Chemical Engineering Science, vol.57, issue.12, pp.12-2287, 2002.
DOI : 10.1016/S0009-2509(02)00118-5

D. Ramkrishna, Population Balances: Theory and Applications to Particulate Systems in Engineering, 2000.

C. Bidot, Mathematical Modeling of T-Cell Activation Kinetic, Journal of Computational Biology, vol.15, issue.1, pp.105-128, 2008.
DOI : 10.1089/cmb.2007.0125

URL : https://hal.archives-ouvertes.fr/emse-00449722

M. Hjortso, Population Balances in Biomedical Engineering, 2005.

Y. Sidorenko, J. Schulze-horsel, A. Voigt, U. Reichl, and E. A. Kienle, Stochastic population balance modeling of influenza virus replication in vaccine production processes, Chemical Engineering Science, vol.63, issue.1, pp.157-169, 2008.
DOI : 10.1016/j.ces.2007.09.014

Y. Sidorenko, A. Voigt, J. Schulze-horsel, and U. Reichl, Kienle, « Stochastic population balance modeling of influenza virus replication in vaccine production processes. II. Detailed description of the replication mechanism, Chem. Eng. Sci, vol.63, issue.8, 2008.

C. Bidot, « Modélisation mathématique de la réponse lymphocytaire T spécifique à une infection virale, Ecole Nationale Supérieure des Mines de Saint-Etienne, 2006.

M. J. Feito, S. Ballester, R. Díez-orejas, G. Ojeda, G. Criado et al., CD4 Dependence of Activation Threshold and TCR Signalling in Mouse T Lymphocytes, Scandinavian Journal of Immunology, vol.45, issue.2, pp.166-174, 1997.
DOI : 10.1046/j.1365-3083.1997.d01-388.x

G. Denkberg, C. J. Cohen, and E. Y. Reiter, Critical Role for CD8 in Binding of MHC Tetramers to TCR: CD8 Antibodies Block Specific Binding of Human Tumor- Specific MHC-Peptide Tetramers to TCR, The Journal of Immunology, vol.167, issue.1, pp.270-276, 2001.
DOI : 10.4049/jimmunol.167.1.270

C. S. Guy and D. A. Vignali, Organization of proximal signal initiation at the TCR:CD3 complex, Immunological Reviews, vol.3, issue.1, pp.7-21, 2009.
DOI : 10.1111/j.1600-065X.2009.00843.x

S. Valitutti, S. Muller, M. Salio, and E. A. Lanzavecchia, Degradation of ???T Cell Receptor (TCR)???CD3-?? Complexes after Antigenic Stimulation, The Journal of Experimental Medicine, vol.262, issue.10, pp.1859-1864, 1997.
DOI : 10.1084/jem.184.2.777

G. M. Lord, R. I. Lechler, and A. J. George, A kinetic differentiation model for the action of altered TCR ligands, Immunology Today, vol.20, issue.1, pp.33-39, 1999.
DOI : 10.1016/S0167-5699(98)01379-6

F. Hentati, F. Gruy, C. Iobagiu, and E. C. Lambert, Variability of CD3 membrane expression and T cell activation capacity, Cytometry Part B: Clinical Cytometry, vol.24, issue.2, pp.105-114, 2010.
DOI : 10.1002/cyto.b.20496

URL : https://hal.archives-ouvertes.fr/hal-00471266

J. Rachmilewitz, Serial Triggering Model, Serial triggering model, pp.95-102, 2008.
DOI : 10.1007/978-0-387-09789-3_9

S. Shahabuddin, Expression and release of IL-2 receptor and production of IL-2 by activated T lymphocyte subsets, J. Clin. Lab. Immunol, vol.36, issue.1, pp.27-32, 1991.

S. Hodge, G. Hodge, R. Flower, and P. Han, Surface and Intracellular Interleukin-2 Receptor Expression on Various Resting and Activated Populations Involved in Cell-Mediated Immunity in Human Peripheral Blood, Scandinavian Journal of Immunology, vol.51, issue.1, pp.67-72, 2000.
DOI : 10.1046/j.1365-3083.2000.00644.x

L. J. Carreno, S. M. Bueno, P. Bull, S. G. Nathenson, and A. M. Kalergis, The half-life of the T-cell receptor/peptide?major histocompatibility complex interaction can modulate T-cell activation in response to bacterial challenge, Immunology, vol.173, issue.2, pp.227-237, 2007.
DOI : 10.1074/jbc.M201613200

J. Madrenas, Differential signalling by variant ligands of the T cell receptor and the kinetic model of T cell activation, Life Sciences, vol.64, issue.9, pp.717-731, 1999.
DOI : 10.1016/S0024-3205(98)00381-6

L. Rong, J. Guedj, H. Dahari, D. J. Coffield-jr, M. Levi et al., Analysis of Hepatitis C Virus Decline during Treatment with the Protease Inhibitor Danoprevir Using a Multiscale Model, PLoS Computational Biology, vol.56, issue.3, p.1002959, 2013.
DOI : 10.1371/journal.pcbi.1002959.s001

A. Saxena, J. Jacobson, W. Yamanashi, B. Scherlag, J. Lamberth et al., A hypothetical mathematical construct explaining the mechanism of biological amplification in an experimental model utilizing picoTesla (PT) electromagnetic fields, Medical Hypotheses, vol.60, issue.6, pp.821-839, 2003.
DOI : 10.1016/S0306-9877(03)00011-2

B. Kohler, Mathematically modeling dynamics of T cell responses: Predictions concerning the generation of memory cells, Journal of Theoretical Biology, vol.245, issue.4, pp.669-676, 2007.
DOI : 10.1016/j.jtbi.2006.10.017

D. Ramkrishna and A. W. Mahoney, Population balance modeling. Promise for the future, Chemical Engineering Science, vol.57, issue.4, pp.595-606, 2002.
DOI : 10.1016/S0009-2509(01)00386-4

A. D. Randolph and M. A. Larson, Theory of particulate processes: analysis and techniques of continuous crystallization, 1988.

M. E. Kavousanakis, N. V. Mantzaris, and A. G. , Boudouvis, « A novel free boundary algorithm for the solution of cell population balance models, Chem. Eng. Sci, vol.64, pp.20-4247, 2009.

M. Stamatakis, Cell population balance, ensemble and continuum modeling frameworks: Conditional equivalence and hybrid approaches, Chemical Engineering Science, vol.65, issue.2, pp.1008-1015, 2010.
DOI : 10.1016/j.ces.2009.09.054

URL : http://discovery.ucl.ac.uk/1356192/1/Stamatakis_-_Chem_Eng_Sci_2010_-_Cell_population_balance,_ensemble_and_continuum_modeling_frameworks.pdf

V. Sivadon-tardy, D. Orlikowski, R. Porcher, T. Sharshar, M. Durand et al., Guillain???Barr?? Syndrome and Influenza Virus Infection, Clinical Infectious Diseases, vol.48, issue.1, pp.48-56, 2009.
DOI : 10.1086/594124

H. Kropshofer, A. B. Vogt, and É. , Antigen Presenting Cells: From Mechanisms to Drug Development, 2006.
DOI : 10.1002/3527607021

M. Lefranc and G. Lefranc, The T Cell Receptor FactsBook, 2001.

R. N. Germain, T-cell development and the CD4???CD8 lineage decision, Nature Reviews Immunology, vol.1, issue.5, pp.309-322, 2002.
DOI : 10.1126/science.286.5443.1374

B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts et al., « Helper T Cells and Lymphocyte Activation, Disponible sur, pp.15-2013, 2002.

M. Freeman, « Feedback control of intercellular signalling in development, Nature, vol.408, issue.6810, pp.313-319, 2000.
DOI : 10.1038/35042500

R. N. Germain, MHC-dependent antigen processing and peptide presentation: Providing ligands for T lymphocyte activation, Cell, vol.76, issue.2, pp.287-299, 1994.
DOI : 10.1016/0092-8674(94)90336-0

M. P. Rout, J. D. Aitchison, A. Suprapto, K. Hjertaas, Y. Zhao et al., The Yeast Nuclear Pore Complex, The Journal of Cell Biology, vol.17, issue.4, pp.635-651, 2000.
DOI : 10.1016/S1097-2765(00)80023-4

S. J. Singer and G. L. Nicolson, The Fluid Mosaic Model of the Structure of Cell Membranes, Science, vol.175, issue.4023, pp.720-731, 1972.
DOI : 10.1126/science.175.4023.720

B. Favier, N. J. Burroughs, L. Wedderburn, and E. S. Valitutti, TCR dynamics on the surface of living T cells, TCR dynamics on the surface of living T cells, pp.1525-1532, 2001.
DOI : 10.1093/intimm/13.12.1525

M. P. Keith, Interleukin-2 Signal Transduction: A Diffusion-Kinetics Model, 1993.

T. K. Dasaklis, C. P. Pappis, and N. P. , Epidemics control and logistics operations: A review, International Journal of Production Economics, vol.139, issue.2, pp.393-410
DOI : 10.1016/j.ijpe.2012.05.023

H. Trottier, Deterministic Modeling Of Infectious Diseases: Theory And Methods », Internet J. Infect. Dis, vol.1, issue.2, 2001.

F. Ball, Analysis of a stochastic SIR epidemic on a random network incorporating household structure, Mathematical Biosciences, vol.224, issue.2, pp.53-73, 2010.
DOI : 10.1016/j.mbs.2009.12.003

H. W. Hethcote, The Mathematics of Infectious Diseases, The Mathematics of Infectious Diseases, pp.599-653, 2000.
DOI : 10.1137/S0036144500371907

L. Star and S. M. Moghadas, « The Role of Mathematical Modeling in Public Health Planning and Decision Making, p.2010

E. Terry, J. Marvel, C. Arpin, O. Gandrillon, and E. F. Crauste, Mathematical model of the primary CD8 T cell immune response: stability analysis of a nonlinear age-structured system, Journal of Mathematical Biology, vol.12, issue.22, pp.263-291, 2012.
DOI : 10.1007/s00285-011-0459-8

URL : https://hal.archives-ouvertes.fr/hal-00649219

S. M. Kaech, E. J. Wherry, and E. R. Ahmed, VACCINES: EFFECTOR AND MEMORY T-CELL DIFFERENTIATION: IMPLICATIONS FOR VACCINE DEVELOPMENT, Nature Reviews Immunology, vol.166, issue.4, pp.251-262, 2002.
DOI : 10.1046/j.1365-2249.2001.01600.x

E. L. Haseltine, D. B. Patience, and J. B. Rawlings, On the stochastic simulation of particulate systems, Chemical Engineering Science, vol.60, issue.10, pp.2627-2641, 2005.
DOI : 10.1016/j.ces.2004.05.038

S. Qamar, M. P. Elsner, I. A. Angelov, and G. Warnecke, Seidel-Morgenstern, « A comparative study of high resolution schemes for solving population balances in crystallization, Comput. Chem. Eng, vol.30, pp.6-7, 2006.

S. Qamar and S. M. Ur-rehman, High Resolution Finite Volume Schemes for Solving Multivariable Biological Cell Population Balance Models, Industrial & Engineering Chemistry Research, vol.52, issue.11, pp.4323-4341, 2013.
DOI : 10.1021/ie302253m

B. Koren, « A robust upwind discretization method for advection, diffusion and source terms ». [En ligne] Disponible sur: http://www.tue.nl, Consulté le, pp.1-2013, 272984.

R. J. Leveque, Finite Volume Methods for Hyperbolic Problems, 2002.
DOI : 10.1017/CBO9780511791253

O. Dushek, Analysis of Serial Engagement and Peptide-MHC Transport in T Cell Receptor Microclusters, Biophysical Journal, vol.94, issue.9, pp.3447-3460, 2008.
DOI : 10.1529/biophysj.107.116897

S. Tian, R. Maile, E. J. Collins, J. A. Frelinger, and «. Cd8+, CD8+ T Cell Activation Is Governed by TCR-Peptide/MHC Affinity, Not Dissociation Rate, The Journal of Immunology, vol.179, issue.5, pp.2952-2960, 2007.
DOI : 10.4049/jimmunol.179.5.2952

T. W. Mckeithan, Kinetic proofreading in T-cell receptor signal transduction., Proceedings of the National Academy of Sciences, vol.92, issue.11, pp.5042-5046, 1995.
DOI : 10.1073/pnas.92.11.5042

H. Liu, M. Rhodes, D. L. Wiest, and D. A. , On the Dynamics of TCR:CD3 Complex Cell Surface Expression and Downmodulation, Immunity, vol.13, issue.5, pp.665-675, 2000.
DOI : 10.1016/S1074-7613(00)00066-2

Q. Ali, T. Eric, G. Frederic, and L. Claude, Mathematical Modeling for the Activation of T- Lymphocytes: Population Balance Modeling with Non Conventional Growth Law, pp.2012-662
URL : https://hal.archives-ouvertes.fr/hal-00721905

K. A. Smith, The quantal theory of immunity, Cell Research, vol.172, issue.1, pp.11-19, 2006.
DOI : 10.1038/ni1263

M. B. Abbott, An Introduction to the Method of Characteristics, 1966.

A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, 1 re éd, 2001.

P. Wong and E. G. Pamer, Cutting Edge: Antigen-Independent CD8 T Cell Proliferation, The Journal of Immunology, vol.166, issue.10, pp.5864-5868, 2001.
DOI : 10.4049/jimmunol.166.10.5864

S. M. Kaech and R. Ahmed, « Memory CD8+ T-cell differentiation: initial antigen encounter triggers a developmental program in naive cells, Nat. Immunol, vol.2, pp.415-422, 2001.

R. Mercado, Early Programming of T Cell Populations Responding to Bacterial Infection, The Journal of Immunology, vol.165, issue.12, pp.6833-6839, 2000.
DOI : 10.4049/jimmunol.165.12.6833

K. E. Foulds, L. A. Zenewicz, D. J. Shedlock, J. Jiang, A. E. Troy et al., Cutting Edge: CD4 and CD8 T Cells Are Intrinsically Different in Their Proliferative Responses, Cutting Edge: CD4 and CD8 T Cells Are Intrinsically Different in Their Proliferative Responses, pp.1528-1532, 2002.
DOI : 10.4049/jimmunol.168.4.1528

J. T. Chang, Asymmetric T Lymphocyte Division in the Initiation of Adaptive Immune Responses, Science, vol.315, issue.5819, pp.1687-1691, 2007.
DOI : 10.1126/science.1139393