M. Adimy, F. Crauste, and S. Et-ruan, A Mathematical Study of the Hematopoiesis Process with Applications to Chronic Myelogenous Leukemia, SIAM Journal on Applied Mathematics, vol.65, issue.4, pp.1-26, 2009.
DOI : 10.1137/040604698
URL : https://hal.archives-ouvertes.fr/hal-00375977

J. Bélair, M. Makey, and J. M. Et-mahaffy, Agestructured and two delay models for erythropoiesis, Math. Biosci, vol.346, pp.317-346, 1994.

L. Berezansky, A Mathematical Model of Imatinib and Interferon-alpha Combined Treatment of Chronic Myeloid Leukemia, Funct. Differ. Equations, vol.19, pp.257-266, 2012.

S. Bernard and F. Et-crauste, Optimal linear stability condition for scalar differential equations with distributed delay, Discrete and Continuous Dynamical Systems - Series B, vol.20, issue.7, pp.1-22, 2014.
DOI : 10.3934/dcdsb.2015.20.1855
URL : https://hal.archives-ouvertes.fr/hal-00997528

A. Besse, G. D. Clapp, S. Bernard, F. E. Nicolini, D. Levy et al., Stability Analysis of a Model of Interaction Between the Immune System and Cancer Cells in Chronic Myelogenous Leukemia, Bulletin of Mathematical Biology, vol.109, issue.1, 2017.
DOI : 10.1182/blood-2006-03-011239
URL : https://hal.archives-ouvertes.fr/hal-01539364

A. Besse, T. Lepoutre, and S. Bernard, Long-term treatment effects in chronic myeloid leukemia (accepted), J. Math. Biol, 2017.

D. Bortz, Eigenvalues for Two-Lag Linear Delay Differential Equations. IFAC-PapersOnLine, pp.1-16
DOI : 10.3934/dcdsb.2016053
URL : http://www.aimsciences.org/journals/doIpChk.jsp?paperID=12997&mode=full

S. Branford, N. C. Cross, A. Hochhaus, and J. P. Radich, Rationale for the recommendations for harmonizing current methodology for detecting BCR-ABL transcripts in patients with chronic myeloid leukaemia, Leukemia, vol.40, issue.11, pp.201925-1930, 2006.
DOI : 10.1182/blood-2006-02-005686

M. Breccia, L. Cannella, C. Stefanizzi, and R. Latagliata, Cytogenetic and molecular responses in chronic phase chronic myeloid leukaemia patients receiving low dose of imatinib for intolerance to standard dose, Hematological Oncology, vol.210, pp.89-92, 2010.
DOI : 10.1002/hon.920

A. Burchert, S. Inselmann, S. Saussele, and C. T. Dietz, Frequency of CTLA-4 Receptor Ligand (CD86, B7.2) -Positive Plasmacytoid Dendritic Cells Predicts Risk of Disease Recurrence after Tyrosine-Kinase Inhibitor Discontinuation in Chronic Myeloid Leukemia : Results from a Prospective Substudy of the Euroski Trial, Blood, issue.23, p.126599, 2015.

S. A. Campbell and I. Et-ncube, Stability in a scalar differential equation with multiple, distributed time delays, Journal of Mathematical Analysis and Applications, vol.450, issue.2, pp.1-16
DOI : 10.1016/j.jmaa.2017.01.060

A. Chavez-gonzalez, B. Bakhshinejad, K. Pakravan, M. L. Guzman, and S. Et-babashah, Novel strategies for targeting leukemia stem cells: sounding the death knell for blood cancer, Cellular Oncology, vol.6, issue.1, pp.1-20, 2016.
DOI : 10.4155/fmc.13.214

S. Chu, T. Mcdonald, A. Lin, and S. Chakraborty, Persistence of leukemia stem cells in chronic myelogenous leukemia patients in prolonged remission with imatinib treatment, Blood, vol.118, issue.20, pp.1185565-5572, 2011.
DOI : 10.1182/blood-2010-12-327437

J. Clairambault, S. Gaubert, and T. Et-lepoutre, Circadian rhythm and cell population growth, Mathematical and Computer Modelling, vol.53, issue.7-8, pp.1558-1567, 2011.
DOI : 10.1016/j.mcm.2010.05.034
URL : https://hal.archives-ouvertes.fr/hal-00492983

G. D. Clapp, Applying Mathematical Models to Study the Role of the Immune System in Chronic Myelogenous Leukemia, 2016.

G. D. Clapp, T. Lepoutre, R. Cheikh, and S. Bernard, Implication of the Autologous Immune System in BCR-ABL Transcript Variations in Chronic Myelogenous Leukemia Patients Treated with Imatinib, Cancer Research, vol.75, issue.19, pp.754053-4062, 2015.
DOI : 10.1158/0008-5472.CAN-15-0611
URL : https://hal.archives-ouvertes.fr/hal-01251396

R. Deconde, P. S. Kim, D. Levy, and P. P. Et-lee, Post-transplantation dynamics of the immune response to chronic myelogenous leukemia, Journal of Theoretical Biology, vol.236, issue.1, pp.39-59, 2005.
DOI : 10.1016/j.jtbi.2005.02.015

M. W. Deininger, J. M. Goldman, and J. V. Et-melo, Nilotinib product information, Blood, vol.18, issue.1, pp.31-43, 2015.

M. Doumic-jauffret, P. S. Kim, and B. Et-perthame, Stability Analysis of a Simplified Yet Complete Model for??Chronic Myelogenous Leukemia, Bulletin of Mathematical Biology, vol.287, issue.11, pp.1732-1759, 2010.
DOI : 10.1016/j.matpur.2005.04.001

B. J. Druker, Perspectives on the development of imatinib and the future of cancer research, Nature Medicine, vol.330, issue.10, pp.1149-1152, 2009.
DOI : 10.1182/blood-2008-05-158535

B. J. Druker, F. Guilhot, S. G. O-'brien, and I. Gathmann, Five-Year Follow-up of Patients Receiving Imatinib for Chronic Myeloid Leukemia, New England Journal of Medicine, vol.355, issue.23, pp.3552408-3552425, 2006.
DOI : 10.1056/NEJMoa062867

H. A. El-morshedy, G. Röst, and A. Et-ruiz-herrera, Global dynamics of delay recruitment models with maximized lifespan, Zeitschrift f??r angewandte Mathematik und Physik, vol.293, issue.3, p.56, 2016.
DOI : 10.1016/j.jtbi.2011.10.017

T. Erneux, Applied Delay Differential Equations, 2009.

J. H. Falkenburg, . R. Wafelman-a, P. Joosten, and W. M. Smit, Complete remission of accelerated phase chronic myeloid leukemia by treatment with leukemia-reactive cytotoxic T lymphocytes, Blood, vol.94, issue.4, pp.1201-1208, 1999.

C. Giallongo, N. Parrinello, M. V. Brundo, and S. A. Raccuia, Myeloid Derived Suppressor Cells in Chronic Myeloid Leukemia, Frontiers in Oncology, vol.92, issue.2, p.107, 2015.
DOI : 10.1111/j.1365-2141.2011.08939.x

I. Glauche, K. Horn, M. Horn, and L. Thielecke, Therapy of chronic myeloid leukaemia can benefit from the activation of stem cells: simulation studies of different treatment combinations, British Journal of Cancer, vol.114, issue.11, pp.1061742-52, 2012.
DOI : 10.1016/j.bbrc.2004.08.169

S. M. Graham, H. G. Jorgensen, E. K. Allan, and C. Pearson, Primitive, quiescent, Philadelphia-positive stem cells from patients with chronic myeloid leukemia are insensitive to STI571 in vitro, Blood, vol.99, issue.1, pp.99319-325, 2002.
DOI : 10.1182/blood.V99.1.319

J. Hale and W. Et-huang, Global Geometry of the Stable Regions for Two Delay Differential Equations, Journal of Mathematical Analysis and Applications, vol.178, issue.2, 1993.
DOI : 10.1006/jmaa.1993.1312

R. Hehlmann, M. C. Müller, M. Lauseker, and B. Hanfstein, Deep Molecular Response Is Reached by the Majority of Patients Treated With Imatinib, Predicts Survival, and Is Achieved More Quickly by Optimized High-Dose Imatinib: Results From the Randomized CML-Study IV, Journal of Clinical Oncology, vol.32, issue.5, pp.415-423, 2014.
DOI : 10.1200/JCO.2013.49.9020

M. Helal, M. Adimy, A. Lakmeche, and L. Et-pujo-menjouet, Analysis of mathematical model of leukemia, ITM Web of Conferences, vol.12, issue.10, p.1005, 2015.
DOI : 10.1038/nm1487

M. Ilander, A. Kreutzman, and S. Et-mustjoki, IFN?? induces prolonged remissions modeling curative immunologic responses in chronic myeloid leukemia, OncoImmunology, vol.62, issue.5, pp.3-28781, 2014.
DOI : 10.1182/blood-2011-02-336685
URL : http://www.tandfonline.com/doi/pdf/10.4161/onci.28781?needAccess=true

E. Kavalerchik, D. Goff, and C. H. Et-jamieson, Chronic Myeloid Leukemia Stem Cells, Journal of Clinical Oncology, vol.26, issue.17, pp.2911-2915, 2008.
DOI : 10.1200/JCO.2008.17.5745

P. S. Kim, P. P. Lee, and D. Levy, A PDE Model for Imatinib-Treated Chronic Myelogenous Leukemia, Bulletin of Mathematical Biology, vol.13, issue.11, pp.1994-2016, 2008.
DOI : 10.1007/s11538-008-9336-z

P. S. Kim, P. P. Lee, and D. Levy, Dynamics and Potential Impact of the Immune Response to Chronic Myelogenous Leukemia, PLoS Computational Biology, vol.17, issue.6, p.1000095, 2008.
DOI : 10.1371/journal.pcbi.1000095.t018

P. S. Kim, P. P. Lee, and D. Levy, Modeling Imatinib-Treated Chronic Myelogenous Leukemia: Reducing the Complexity of Agent-Based Models, Bulletin of Mathematical Biology, vol.33, issue.6, pp.728-744, 2008.
DOI : 10.1007/s11538-007-9276-z

N. L. Komarova and D. Et-wodarz, Effect of Cellular Quiescence on the Success of Targeted CML Therapy, PLoS ONE, vol.28, issue.10, p.990, 2007.
DOI : 10.1371/journal.pone.0000990.s001

Y. Kuang, Delay differential equations, Encycl. Theor. Ecol, pp.163-166, 2012.

V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor, and A. S. Et-perelson, Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis, Bulletin of Mathematical Biology, vol.2, issue.2, pp.295-321, 1994.
DOI : 10.1007/978-1-4757-4067-7

M. Lavielle, Mixed Effects Models for the Population Approach, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01122873

M. Loeffler, B. Bungart, H. Goris, S. Schmitz, and W. Et-nijhof, Hemopoiesis during thiamphenicol treatment. II. A theoretical analysis shows consistency of new data with a previously hypothesized model of stem cell regulation, Exp. Hematol, vol.17, issue.9, pp.962-967, 1989.

M. Mackey and J. Et-milton, Dynamical Diseases, Annals of the New York Academy of Sciences, vol.29, issue.1 Perspectives, pp.16-32, 1987.
DOI : 10.1017/CBO9780511897474

M. C. Mackey, Dynamic Haematological Disorders of Stem Cell Origin, Biophys. Biochem . Inf. Transf. Recognit, pp.373-409, 1979.
DOI : 10.1007/978-1-4899-5330-8_33

J. M. Mahaffy and T. C. Et-busken, Regions of stability for a linear differential equation with two rationally dependent delays, Discret. Contin. Dyn. Syst. Ser. A, issue.10, pp.354955-4986, 2015.

F. X. Mahon, D. Réa, J. Guilhot, and F. Guilhot, Discontinuation of imatinib in patients with chronic myeloid leukaemia who have maintained complete molecular remission for at least 2 years: the prospective, multicentre Stop Imatinib (STIM) trial, The Lancet Oncology, vol.11, issue.11, pp.111029-1035, 2010.
DOI : 10.1016/S1470-2045(10)70233-3

F. Michor, T. P. Hughes, Y. Iwasa, and S. Branford, Dynamics of chronic myeloid leukaemia, Nature, vol.81, issue.7046, pp.4351267-1270, 2005.
DOI : 10.1126/science.1099480

H. Moore and N. K. Et-li, A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction, Journal of Theoretical Biology, vol.227, issue.4, pp.513-523, 2004.
DOI : 10.1016/j.jtbi.2003.11.024

S. Nanda, H. Moore, and S. Et-lenhart, Optimal control of treatment in a mathematical model of chronic myelogenous leukemia, Mathematical Biosciences, vol.210, issue.1, pp.143-156, 2007.
DOI : 10.1016/j.mbs.2007.05.003

O. 'brien, S. G. Guilhot, F. Larson, R. A. Gathmann, and I. , Imatinib compared with interferon and low-dose cytarabine for newly diagnosed chronic-phase chronic myeloid leukemia, N. Engl. J. Med, issue.11, pp.348994-1004, 2003.

C. Preudhomme, J. Guilhot, F. E. Nicolini, and A. Guerci-bresler, Imatinib plus Peginterferon Alfa-2a in Chronic Myeloid Leukemia, New England Journal of Medicine, vol.363, issue.26, pp.3632511-3632532, 2010.
DOI : 10.1056/NEJMoa1004095

L. Pujo-menjouet, S. Bernard, and M. C. Et-mackey, Model of Hematopoietic Stem Cells, SIAM Journal on Applied Dynamical Systems, vol.4, issue.2, pp.312-332, 2005.
DOI : 10.1137/030600473

L. Pujo-menjouet and M. C. Et-mackey, Contribution to the study of periodic chronic myelogenous leukemia, Comptes Rendus Biologies, vol.327, issue.3, pp.235-244, 2004.
DOI : 10.1016/j.crvi.2003.05.004

C. Riether, C. M. Schürch, and A. F. Et-ochsenbein, Regulation of hematopoietic and leukemic stem cells by the immune system, Cell Death and Differentiation, vol.133, issue.2, pp.187-98, 2015.
DOI : 10.1002/ijc.28198

I. Roeder, M. Herberg, and M. Et-horn, An ???Age??? Structured Model of Hematopoietic Stem Cell Organization with Application to Chronic Myeloid Leukemia, Bulletin of Mathematical Biology, vol.7, issue.2, pp.602-626, 2009.
DOI : 10.1007/978-3-662-13159-6

I. Roeder, M. Horn, I. Glauche, A. Hochhaus, M. C. Mueller et al., Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications, Nature Medicine, vol.13, issue.10, pp.121181-1184, 2006.
DOI : 10.1038/nm1487

D. M. Ross, S. Branford, J. F. Seymour, and . P. Schwarer-a, Patients with chronic myeloid leukemia who maintain a complete molecular response after stopping imatinib treatment have evidence of persistent leukemia by DNA PCR, Leukemia, vol.5, issue.10, 2010.
DOI : 10.1111/j.1365-2141.1995.tb03392.x

P. Rousselot, F. Huguet, D. Rea, and L. Legros, Imatinib mesylate discontinuation in patients with chronic myelogenous leukemia in complete molecular remission for more than 2 years, Blood, vol.109, issue.1, pp.58-60, 2007.
DOI : 10.1182/blood-2006-03-011239

S. Ruan and J. Wei, On the zeros of transcendental functions with applications to stability of delay differential equations with two delays, Dyn. Contin. Discret. Impuls. Syst, 2003.

A. Samson, M. Lavielle, and F. Et-mentré, Extension of the SAEM algorithm to left-censored data in nonlinear mixed-effects model: Application to HIV dynamics model, Computational Statistics & Data Analysis, vol.51, issue.3, pp.1562-1574, 2006.
DOI : 10.1016/j.csda.2006.05.007
URL : https://hal.archives-ouvertes.fr/hal-00263506