M. Adimy, A. Chekroun, and T. M. Touaoula, A delay differential-difference system of hematopoietic stem cell dynamics, Comptes Rendus Mathematique, vol.353, issue.4, pp.303-307, 2015.
DOI : 10.1016/j.crma.2015.01.018
URL : https://hal.archives-ouvertes.fr/hal-01249894

M. Adimy, A. Chekroun, and T. M. Touaoula, Age-structured and delay differential-difference model of hematopoietic stem cell dynamics, Discrete and Continuous Dynamical Systems -Series B, pp.2765-2791, 2015.

M. Adimy, A. Chekroun, and T. M. Touaoula, Global asymptotic stability for an agestructured model of hematopoietic stem cell dynamics, Applicable Analysis, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01396691

M. Adimy, A. Chekroun, and B. Kazmierczak, Traveling waves in a coupled reactiondiffusion and difference model of hematopoiesis, 2016.

]. M. Bibliographie1, O. Adimy, C. Angulo, L. Marquet, and . Sebaa, A mathematical model of multistage hematopoietic cell lineages. Discrete and Continuous Dynamical Systems, Series B, vol.19, issue.1, pp.1-26, 2014.

M. Adimy, A. Chekroun, and T. Touaoula, Age-structured and delay differentialdifference model of hematopoietic stem cell dynamics. Discrete and Continuous Dynamical Systems -Series B, pp.2765-2791, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01249892

M. Adimy, A. Chekroun, and T. Touaoula, A delay differential-difference system of hematopoietic stem cell dynamics, Comptes Rendus Mathematique, vol.353, issue.4, pp.303-307, 2015.
DOI : 10.1016/j.crma.2015.01.018
URL : https://hal.archives-ouvertes.fr/hal-01249894

M. Adimy and F. Crauste, Global stability of a partial differential equation with distributed delay due to cellular replication. Nonlinear Analysis : Theory, Methods & Applications, pp.1469-1491, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00375926

M. Adimy and F. Crauste, Modeling and asymptotic stability of a growth factordependent stem cell dynamics model with distributed delay, Discrete and Continuous Dynamical Systems -Series B, pp.19-38, 2007.

M. Adimy and F. Crauste, Mathematical model of hematopoiesis dynamics with growth factor-dependent apoptosis and proliferation regulations, Mathematical and Computer Modelling, vol.49, issue.11-12, pp.11-122128, 2009.
DOI : 10.1016/j.mcm.2008.07.014

M. Adimy, F. Crauste, and A. Abdllaoui, Asymptotic Behavior of a Discrete Maturity Structured System of Hematopoietic Stem Cell Dynamics with Several Delays, Mathematical Modelling of Natural Phenomena, vol.1, issue.2, pp.1-22, 2006.
DOI : 10.1051/mmnp:2008001

M. Adimy, F. Crauste, and A. Abdllaoui, DISCRETE-MATURITY STRUCTURED MODEL OF CELL DIFFERENTIATION WITH APPLICATIONS TO ACUTE MYELOGENOUS LEUKEMIA, Journal of Biological Systems, vol.16, issue.03, pp.395-424, 2008.
DOI : 10.1142/S0218339008002599
URL : https://hal.archives-ouvertes.fr/hal-00750276

M. Adimy, F. Crauste, M. Hbid, and R. Qesmi, Stability and Hopf Bifurcation for a Cell Population Model with State-Dependent Delay, SIAM Journal on Applied Mathematics, vol.70, issue.5, pp.1611-1633, 2010.
DOI : 10.1137/080742713
URL : https://hal.archives-ouvertes.fr/hal-00542655

M. Adimy, F. Crauste, and C. Marquet, Asymptotic behavior and stability switch for a mature???immature model of cell differentiation, Nonlinear Analysis: Real World Applications, vol.11, issue.4, pp.2913-2929, 2010.
DOI : 10.1016/j.nonrwa.2009.11.001
URL : https://hal.archives-ouvertes.fr/hal-00542644

M. Adimy, F. Crauste, and S. Ruan, A Mathematical Study of the Hematopoiesis Process with Applications to Chronic Myelogenous Leukemia, SIAM Journal on Applied Mathematics, vol.65, issue.4, pp.1328-1352, 2005.
DOI : 10.1137/040604698
URL : https://hal.archives-ouvertes.fr/hal-00375977

M. Adimy, F. Crauste, and S. Ruan, Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics, Nonlinear Analysis: Real World Applications, vol.6, issue.4, pp.651-670, 2005.
DOI : 10.1016/j.nonrwa.2004.12.010
URL : https://hal.archives-ouvertes.fr/hal-00375966

M. Adimy, F. Crauste, and S. Ruan, Modelling Hematopoiesis Mediated by Growth Factors With Applications to Periodic Hematological Diseases, Bulletin of Mathematical Biology, vol.76, issue.4, pp.2321-2351, 2006.
DOI : 10.1007/s11538-006-9121-9
URL : https://hal.archives-ouvertes.fr/hal-00376087

M. Adimy, F. Crauste, and S. Ruan, Periodic oscillations in leukopoiesis models with two delays, Journal of Theoretical Biology, vol.242, issue.2, pp.288-299, 2006.
DOI : 10.1016/j.jtbi.2006.02.020
URL : https://hal.archives-ouvertes.fr/hal-00258393

W. Aiello, H. Freedman, and J. Wu, Analysis of a Model Representing Stage-Structured Population Growth with State-Dependent Time Delay, SIAM Journal on Applied Mathematics, vol.52, issue.3, pp.855-869, 1992.
DOI : 10.1137/0152048

J. Omari and S. A. Gourley, Monotone travelling fronts in an age-structured reaction-diffusion model of a single species, Journal of Mathematical Biology, vol.45, issue.4, pp.294-312, 2002.
DOI : 10.1007/s002850200159

O. Arino, M. Hbid, and E. A. Dads, Delay Differential Equations and Applications. NATO Science Series, 2006.

D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, Partial Differential Equations and Related Topics, number 446 in Lecture Notes in Mathematics, pp.5-49, 1975.
DOI : 10.1109/TCT.1965.1082476

B. Balachandran, T. Kalmar-nagy, and D. E. Gilsinn, Delay Differential Equations : Recent Advances and New Directions, 2009.

V. Barroca, Renouvellement des cellules souches : plasticité des progéniteurs germinaux et rôle du gène Fancg dans la fonction des cellules souches hématopoïétiques, 2009.

D. Beaudry, Introduction à l'apopstos. Site Web

E. Beretta and Y. Kuang, Geometric Stability Switch Criteria in Delay Differential Systems with Delay Dependent Parameters, SIAM Journal on Mathematical Analysis, vol.33, issue.5, pp.1144-1165, 2002.
DOI : 10.1137/S0036141000376086

S. Bernard, J. Bélair, and M. C. Mackey, Oscillations in cyclical neutropenia: new evidence based on mathematical modeling, Journal of Theoretical Biology, vol.223, issue.3, pp.283-298, 2003.
DOI : 10.1016/S0022-5193(03)00090-0

S. Bernard, J. Bélair, and M. C. Mackey, Bifurcations in a white-blood-cell production model, Comptes Rendus Biologies, vol.327, issue.3, pp.201-210, 2004.
DOI : 10.1016/j.crvi.2003.05.005
URL : https://hal.archives-ouvertes.fr/hal-00542530

S. Bernard, J. Bélair, and M. C. Mackey, Sufficient conditions for stability of linear differential equations with distributed delay. Discrete and Continuous Dynamical Systems -Series B, pp.233-256, 2001.

J. Bélair, M. C. Mackey, and J. M. Mahaffy, Age-structured and two-delay models for erythropoiesis, Mathematical Biosciences, vol.128, issue.1-2, pp.317-346, 1995.
DOI : 10.1016/0025-5564(94)00078-E

S. P. Blythe, R. M. Nisbet, and W. S. Gurney, Instability and complex dynamic behaviour in population models with long time delays, Theoretical Population Biology, vol.22, issue.2, pp.147-176, 1982.
DOI : 10.1016/0040-5809(82)90040-5

O. Bonnefon, J. Garnier, F. Hamel, and L. Roques, Inside Dynamics of Delayed Traveling Waves, Mathematical Modelling of Natural Phenomena, vol.8, issue.3, pp.42-59, 2013.
DOI : 10.1051/mmnp/20138305

E. Bouin, V. Calvez, and G. Nadin, Propagation in a Kinetic Reaction-Transport Equation: Travelling Waves And Accelerating Fronts, Archive for Rational Mechanics and Analysis, vol.179, issue.2, pp.571-617, 2015.
DOI : 10.1007/s00205-014-0837-7
URL : https://hal.archives-ouvertes.fr/hal-00849405

G. B. Bradford, B. Williams, R. Rossi, and I. Bertoncello, Quiescence, cycling, and turnover in the primitive hematopoietic stem cell compartment, Exp. Hematol, vol.25, issue.5, pp.445-453, 1997.

K. J. Brown and J. Carr, Deterministic epidemic waves of critical velocity, Mathematical Proceedings of the Cambridge Philosophical Society, vol.80, issue.03, pp.431-433, 1977.
DOI : 10.1017/S0305004100053494

F. J. Burns and I. F. Tannock, -PHASE IN THE CELL CYCLE, Cell Proliferation, vol.8, issue.4, pp.321-334, 1970.
DOI : 10.1016/0014-4827(59)90063-1
URL : https://hal.archives-ouvertes.fr/hal-01057010

S. Chen and J. Shi, Stability and Hopf bifurcation in a diffusive logistic population model with nonlocal delay effect, Journal of Differential Equations, vol.253, issue.12, pp.3440-3470, 2012.
DOI : 10.1016/j.jde.2012.08.031

G. Chikkappa, G. Borner, H. Burlington, A. D. Chanana, E. P. Cronkite et al., Periodic oscillation of blood leukocytes, platelets, and reticulocytes in a patient with chronic myelocytic leukemia, Blood, issue.6, pp.471023-1030, 1976.

C. Colijn and M. C. Mackey, A mathematical model of hematopoiesis???I. Periodic chronic myelogenous leukemia, Journal of Theoretical Biology, vol.237, issue.2, pp.117-132, 2005.
DOI : 10.1016/j.jtbi.2005.03.033

K. L. Cooke, Stability analysis for a vector disease model, Rocky Mountain Journal of Mathematics, vol.9, issue.1, pp.31-42, 1979.
DOI : 10.1216/RMJ-1979-9-1-31

F. Crauste, Etude mathématique d'équations aux dérivées partielles hyperboliques modélisant les processus de régulation des cellules sanguines -Application aux maladies hématologiques cycliques, 2005.

M. A. Cruz and J. K. Hale, Stability of functional differential equations of neutral type, Journal of Differential Equations, vol.7, issue.2, pp.334-355, 1970.
DOI : 10.1016/0022-0396(70)90114-2

J. Cushing, An Introduction to Structured Population Dynamics, CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics, 1998.
DOI : 10.1137/1.9781611970005

D. C. Dale and W. P. Hammond, Cyclic neutropenia: A clinical review, Blood Reviews, vol.2, issue.3, pp.178-185, 1988.
DOI : 10.1016/0268-960X(88)90023-9

J. C. De-oliveira, Hopf bifurcation for functional differential equations. Nonlinear Analysis : Theory, Methods & Applications, vol.4, issue.2, pp.217-229, 1980.

T. Faria, Stability and Bifurcation for a Delayed Predator???Prey Model and the Effect of Diffusion, Journal of Mathematical Analysis and Applications, vol.254, issue.2, pp.433-463, 2001.
DOI : 10.1006/jmaa.2000.7182

F. Ferré, Isolation et caractérisation des cellules souches gingivales : étude de leur potentiel multipotent, 2013.

F. Ficara, M. J. Murphy, M. Lin, and M. L. Cleary, Pbx1 Regulates Self-Renewal of Long-Term Hematopoietic Stem Cells by Maintaining Their Quiescence, Cell Stem Cell, vol.2, issue.5, pp.484-496, 2008.
DOI : 10.1016/j.stem.2008.03.004

P. C. Fife, Mathematical Aspects of Reacting and Diffusing Systems, Lecture Notes in Biomathematics, vol.28, 1979.
DOI : 10.1007/978-3-642-93111-6

R. A. Fisher, THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES, Annals of Eugenics, vol.7, issue.4, pp.353-369, 1937.
DOI : 10.1111/j.1469-1809.1937.tb02153.x

E. Fridman, Stability of linear descriptor systems with delay: a Lyapunov-based approach, Journal of Mathematical Analysis and Applications, vol.273, issue.1, pp.24-44, 2002.
DOI : 10.1016/S0022-247X(02)00202-0

J. Garnier, L. Roques, and F. Hamel, Success rate of a biological invasion in terms of the spatial distribution of the founding population, Bulletin of Mathematical Biology, vol.19, issue.12, pp.453-473, 2011.
DOI : 10.1007/s11538-011-9694-9
URL : https://hal.archives-ouvertes.fr/hal-01257398

S. Giroux, Analyse fonctionnelle de facteurs impliqués dans l'émergence des précurseurs hématopoïétiques de l'embryon de souris, 2006.

C. Gonneau, Cellules souches sanguines : les pionnières de la recherche sur les cellules souches, pp.10-2015

S. A. Gourley, Travelling front solutions of a nonlocal Fisher equation, Journal of Mathematical Biology, vol.41, issue.3, pp.272-284, 2000.
DOI : 10.1007/s002850000047

S. Gourley and J. Wu, Delayed non-local diffusive systems in biological invasion and disease spread, Nonlinear Dynamics and Evolution Equations, pp.137-200, 2006.
DOI : 10.1090/fic/048/06

B. Greiner and D. Pralet, L'apoptose : détection qualitative et évaluation quantitative, Rev. Fr. Histotechnol, vol.17, pp.95-105, 2004.

K. Gu and Y. Liu, Lyapunov???Krasovskii functional for uniform stability of coupled differential-functional equations, Automatica, vol.45, issue.3, pp.798-804, 2009.
DOI : 10.1016/j.automatica.2008.10.024

D. Guerry, D. C. Dale, M. Omine, S. Perry, and S. M. Wolff, Periodic Hematopoiesis in Human Cyclic Neutropenia, Journal of Clinical Investigation, vol.52, issue.12, pp.3220-3230, 1973.
DOI : 10.1172/JCI107522

M. E. Gurtin and R. C. Maccamy, Non-linear age-dependent population dynamics, Archive for Rational Mechanics and Analysis, vol.54, issue.3, pp.281-300, 1974.
DOI : 10.1007/BF00250793

K. P. Hadeler and F. Rothe, Travelling fronts in nonlinear diffusion equations, Journal Of Mathematical Biology, vol.A, issue.1, pp.251-263, 1975.
DOI : 10.1007/BF00277154

J. K. Hale and M. A. Cruz, Existence, uniqueness and continuous dependence for hereditary systems, Annali di Matematica Pura ed Applicata, Series 4, vol.I, issue.3, pp.63-81, 1970.
DOI : 10.1007/BF02413530

J. K. Hale and W. Huang, Variation of constants for hybrid systems of functional differential equations, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.8, issue.01, pp.1-12, 1995.
DOI : 10.1016/0030-4018(79)90090-7

J. K. Hale and P. Martinez-amores, Stability in neutral equations. Nonlinear Analysis : Theory, Methods & Applications, vol.1, issue.2, pp.161-173, 1977.

J. K. Hale and S. M. , Introduction to Functional Differential Equations, 1993.
DOI : 10.1007/978-1-4612-4342-7

C. Haurie, D. C. Dale, and M. C. Mackey, Cyclical neutropenia and other periodic hematological disorders : A review of mechanisms and mathematical models, Blood, issue.8, pp.922629-2640, 1998.

C. Haurie, D. C. Dale, and M. C. Mackey, Occurrence of periodic oscillations in the differential blood counts of congenital, idiopathic, and cyclical neutropenic patients before and during treatment with G-CSF, Experimental Hematology, vol.27, issue.3, pp.401-409, 1999.
DOI : 10.1016/S0301-472X(98)00061-7

G. Hu and W. Li, Hopf bifurcation analysis for a delayed predator???prey system with diffusion effects, Nonlinear Analysis: Real World Applications, vol.11, issue.2, pp.819-826, 2010.
DOI : 10.1016/j.nonrwa.2009.01.027

M. Iannelli, Mathematical theory of age-structured population dynamics, Giardini editori e stampatori, 1995.

D. Janet, R. Villella-bressan, and G. F. Webb, A singular transport equation modelling a proliferating maturity structured cell population, The Canadian Applied Mathematics Quarterly, vol.4, issue.1, 1996.

A. N. Kolmogorov, I. G. Petrovskii, and N. S. Piskunov, A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem, Bjul. Moskovskogo Gos. Univ, vol.1, pp.1-25, 1937.

D. S. Krause, Regulation of hematopoietic stem cell fate, Oncogene, vol.21, issue.21, pp.3262-3269, 2002.
DOI : 10.1038/sj.onc.1205316

Y. Kuang, Delay Differential Equations : With Applications in Population Dynamics, 1993.

K. Q. Lan and J. H. Wu, Travelling wavefronts of scalar reaction???diffusion equations with and without delays, Nonlinear Analysis: Real World Applications, vol.4, issue.1, pp.173-188, 2003.
DOI : 10.1016/S1468-1218(02)00020-2

Z. Ling and Z. Lin, Traveling wavefront in a Hematopoiesis model with time delay, Applied Mathematics Letters, vol.23, issue.4, pp.426-431, 2010.
DOI : 10.1016/j.aml.2009.11.011

S. Ma, Traveling Wavefronts for Delayed Reaction-Diffusion Systems via a Fixed Point Theorem, Journal of Differential Equations, vol.171, issue.2, pp.294-314, 2001.
DOI : 10.1006/jdeq.2000.3846

S. Ma, Traveling waves for non-local delayed diffusion equations via auxiliary equations, Journal of Differential Equations, vol.237, issue.2, pp.259-277, 2007.
DOI : 10.1016/j.jde.2007.03.014

Z. Ma, W. Li, and X. Yan, Stability and Hopf bifurcation for a three-species food chain model with time delay and spatial diffusion, Applied Mathematics and Computation, vol.219, issue.5, pp.2713-2731, 2012.
DOI : 10.1016/j.amc.2012.08.103

M. C. Mackey, Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis, Blood, vol.51, issue.5, pp.941-956, 1978.

M. C. Mackey, Dynamic Haematological Disorders of Stem Cell Origin, 1979.
DOI : 10.1007/978-1-4899-5330-8_33

M. C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science, vol.197, issue.4300, pp.287-289, 1977.
DOI : 10.1126/science.267326

M. C. Mackey and R. Rudnicki, Global stability in a delayed partial differential equation describing cellular replication, Journal of Mathematical Biology, vol.414, issue.1, pp.89-109, 1994.
DOI : 10.1007/BF00160175

M. C. Mackey and R. Rudnicki, A new criterion for the global stability of simultaneous cell replication and maturation processes, Journal of Mathematical Biology, vol.38, issue.3, pp.195-219, 1999.
DOI : 10.1007/s002850050146

J. Malfuson, Rôle de la niche mésenchymateuse dans la régulation du phénotype SP des progéniteurs hématopoïétiques humains, 2013.

C. Marquet and M. Adimy, On the stability of hematopoietic model with feedback control, Comptes Rendus Mathematique, vol.350, issue.3-4, pp.3-4173, 2012.
DOI : 10.1016/j.crma.2012.01.014
URL : https://hal.archives-ouvertes.fr/hal-00763154

R. H. Martin and H. L. Smith, Abstract functional-differential equations and reactiondiffusion systems, Trans. Amer. Math. Soc, vol.321, issue.1, pp.1-44, 1990.

P. Martinez-amores, Periodic solutions for coupled systems of differential-difference and difference equations, Annali di Matematica Pura ed Applicata, Series 4, vol.15, issue.2, pp.171-186, 1979.
DOI : 10.1007/BF02412000

A. Matsumura and K. Nishihara, Asymptotic stability of traveling waves for scalar viscous conservation laws with non-convex nonlinearity, Communications in Mathematical Physics, vol.7, issue.1, pp.83-96, 1994.
DOI : 10.1007/BF02099739

M. Mei, C. Lin, C. Lin, and J. W. So, Traveling wavefronts for time-delayed reaction???diffusion equation: (I) Local nonlinearity, Journal of Differential Equations, vol.247, issue.2, pp.495-510, 2009.
DOI : 10.1016/j.jde.2008.12.026

M. Mei, C. Lin, C. Lin, and J. W. So, Traveling wavefronts for time-delayed reaction???diffusion equation: (II) Nonlocal nonlinearity, Journal of Differential Equations, vol.247, issue.2, pp.511-529, 2009.
DOI : 10.1016/j.jde.2008.12.020

M. Mei, C. Ou, and X. Zhao, Global Stability of Monostable Traveling Waves For Nonlocal Time-Delayed Reaction-Diffusion Equations, SIAM Journal on Mathematical Analysis, vol.42, issue.6, pp.2762-2790, 2010.
DOI : 10.1137/090776342

M. Mei and J. W. So, Stability of strong travelling waves for a non-local time-delayed reaction???diffusion equation, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.138, issue.03, pp.551-568, 2008.
DOI : 10.1017/S0308210506000333

M. Mei, J. W. So, M. Y. Li, and S. P. Shen, Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.134, issue.03, pp.134579-594, 2004.
DOI : 10.1017/S0308210500003358

L. Meijer, Le cycle de division cellulaire et sa régulation, Oncologie, vol.5, pp.311-326, 2003.

J. A. Metz and O. Diekmann, The Dynamics of Physiologically Structured Populations, Lecture Notes in Biomathematics, vol.68, 1986.
DOI : 10.1007/978-3-662-13159-6

A. Morley, A. Baikie, and D. Galton, Cyclic leucocytosis as evidence for retention of normal homeostatic control in chronic granulocytic leukemia. The Lancet, pp.1320-1323, 1967.

J. D. Murray, Mathematical Biology : I. An Introduction, 2002.

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, 1983.
DOI : 10.1007/978-1-4612-5561-1

P. Pepe, On the asymptotic stability of coupled delay differential and continuous time difference equations, Automatica, vol.41, issue.1, pp.107-112, 2005.

P. Pepe, Z. Jiang, and E. Fridman, A new Lyapunov???Krasovskii methodology for coupled delay differential and difference equations, International Journal of Control, vol.13, issue.1, pp.107-115, 2008.
DOI : 10.1109/9.28018

P. Pepe and E. Verriest, On the stability of coupled delay differential and continuous time difference equations, IEEE Transactions on Automatic Control, vol.48, issue.8, pp.1422-1427, 2003.
DOI : 10.1109/TAC.2003.815036

B. Perthame, Transport Equations in Biology, 2006.

M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, 1984.
DOI : 10.1007/978-1-4612-5282-5

L. Pujo-menjouet, Contribution à l'étude d'une équation de transport à retards décrivant une dynamique de population cellulaire, 2001.

L. Pujo-menjouet, S. Bernard, and M. 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. 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

J. M. Roquejoffre, Convergence to Travelling Waves for Solutions of a Class of Semilinear Parabolic Equations, Journal of Differential Equations, vol.108, issue.2, pp.262-295, 1994.
DOI : 10.1006/jdeq.1994.1035

L. Roques, J. Garnier, F. Hamel, and E. K. Klein, Allee effect promotes diversity in traveling waves of colonization, Proceedings of the National Academy of Sciences, vol.109, issue.23, pp.8828-8833, 2012.
DOI : 10.1073/pnas.1201695109
URL : https://hal.archives-ouvertes.fr/hal-01257401

D. H. Sattinger, On the stability of waves of nonlinear parabolic systems, Advances in Mathematics, vol.22, issue.3, pp.312-355, 1976.
DOI : 10.1016/0001-8708(76)90098-0

K. W. Schaaf, Asymptotic behavior and traveling wave solutions for parabolic functional-differential equations, Trans. Amer. Math. Soc, vol.302, issue.2, pp.587-615, 1987.

P. Sciences, Parlons sciences 2011, feuille de renseignements : les cellules souches, pp.10-2015

R. Sipahi, T. Vyhlídal, S. Niculescu, and P. Pepe, Time Delay Systems : Methods, Applications and New Trends, Lecture Notes in Control and Information Sciences, vol.423, 2012.
DOI : 10.1007/978-3-642-25221-1
URL : https://hal.archives-ouvertes.fr/hal-00768435

H. Smith, Reduction of structured population models to threshold-type delay equations and functional differential equations: a case study, Mathematical Biosciences, vol.113, issue.1, pp.1-23, 1993.
DOI : 10.1016/0025-5564(93)90006-V

H. Smith, Monotone Dynamical Systems : An Introduction to the Theory of Competitive and Cooperative Systems, 1995.
DOI : 10.1090/surv/041

H. Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences, Texts in Applied Mathematics, 2011.
DOI : 10.1007/978-1-4419-7646-8

H. Smith and X. Zhao, Global Asymptotic Stability of Traveling Waves in Delayed Reaction-Diffusion Equations, SIAM Journal on Mathematical Analysis, vol.31, issue.3, pp.514-534, 2000.
DOI : 10.1137/S0036141098346785

J. W. So and X. Zou, Traveling waves for the diffusive Nicholson's blowflies equation, Applied Mathematics and Computation, vol.122, issue.3, pp.385-392, 2001.
DOI : 10.1016/S0096-3003(00)00055-2

Y. Su, J. Wei, and J. Shi, Hopf bifurcations in a reaction???diffusion population model with delay effect, Journal of Differential Equations, vol.247, issue.4, pp.1156-1184, 2009.
DOI : 10.1016/j.jde.2009.04.017

D. Tagliasacchi and G. Carboni, Observons les cellules sanguines 1997

H. Takizawa, R. R. Regoes, C. S. Boddupalli, S. Bonhoeffer, and M. G. Manz, Dynamic variation in cycling of hematopoietic stem cells in steady state and inflammation, The Journal of Experimental Medicine, vol.156, issue.2, pp.273-284, 2011.
DOI : 10.1016/j.stem.2007.10.020

H. R. Thieme, Mathematics in Population Biology, 2003.

H. R. Thieme and X. Zhao, A non-local delayed and diffusive predator???prey model, Nonlinear Analysis: Real World Applications, vol.2, issue.2, pp.145-160, 2001.
DOI : 10.1016/S0362-546X(00)00112-7

H. R. Thieme and X. Zhao, Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction???diffusion models, Journal of Differential Equations, vol.195, issue.2, pp.430-470, 2003.
DOI : 10.1016/S0022-0396(03)00175-X

P. Vegh, J. Winckler, and F. Melchers, Long-term ???in vitro??? proliferating mouse hematopoietic progenitor cell lines, Immunology Letters, vol.130, issue.1-2, pp.32-35, 2010.
DOI : 10.1016/j.imlet.2010.02.001

A. I. Volpert, V. A. Volpert, and V. A. Volpert, Traveling Wave Solutions of Parabolic Systems, 1994.

V. A. Volpert and S. Petrovskii, Reaction???diffusion waves in biology, Physics of Life Reviews, vol.6, issue.4, pp.267-310, 2009.
DOI : 10.1016/j.plrev.2009.10.002

Z. Wang, W. Li, and S. Ruan, Travelling wave fronts in reaction???diffusion systems with spatio-temporal delays, Journal of Differential Equations, vol.222, issue.1, pp.185-232, 2006.
DOI : 10.1016/j.jde.2005.08.010

Z. Wang, W. Li, and S. Ruan, Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay, Journal of Differential Equations, vol.238, issue.1, pp.153-200, 2007.
DOI : 10.1016/j.jde.2007.03.025

Z. Wang, W. Li, and S. Ruan, Traveling Fronts in Monostable Equations with Nonlocal Delayed Effects, Journal of Dynamics and Differential Equations, vol.146, issue.3, pp.573-607, 2008.
DOI : 10.1007/s10884-008-9103-8

G. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, 1985.

D. V. Widder, What is the Laplace Transform?, The American Mathematical Monthly, vol.52, issue.8, 1946.
DOI : 10.2307/2305640

J. Wu, Theory and Applications of Partial Functional Differential Equations, 1996.
DOI : 10.1007/978-1-4612-4050-1

J. Wu, D. Wei, and M. Mei, Analysis on the critical speed of traveling waves, Applied Mathematics Letters, vol.20, issue.6, pp.712-718, 2007.
DOI : 10.1016/j.aml.2006.08.006

J. Wu and X. Zou, Traveling wave fronts of reaction-diffusion systems with delay, Journal of Dynamics and Differential Equations, vol.13, issue.3, pp.651-687, 2001.
DOI : 10.1023/A:1016690424892

S. Wu, W. Li, and S. Liu, Asymptotic stability of traveling wave fronts in nonlocal reaction???diffusion equations with delay, Journal of Mathematical Analysis and Applications, vol.360, issue.2, pp.439-458, 2009.
DOI : 10.1016/j.jmaa.2009.06.061

J. Xin, Front Propagation in Heterogeneous Media, SIAM Review, vol.42, issue.2, pp.161-230, 2000.
DOI : 10.1137/S0036144599364296

D. Xu and X. Zhao, A nonlocal reaction-diffusion population model with stage structure, The Canadian Applied Mathematics Quarterly, vol.11, issue.3, pp.303-319, 2003.

X. Yan, Stability and Hopf bifurcation for a delayed prey???predator system with diffusion effects, Applied Mathematics and Computation, vol.192, issue.2, pp.552-566, 2007.
DOI : 10.1016/j.amc.2007.03.033

X. Zhao, Dynamical Systems in Population Biology, 2003.
DOI : 10.1007/978-0-387-21761-1

X. Zhao, Global attractivity in a class of nonmonotone reaction-diffusion equations with time delay, The Canadian Applied Mathematics Quarterly, vol.17, issue.1, pp.271-281, 2009.

X. Zhao and W. Wang, Fisher waves in an epidemic model. Discrete and Continuous Dynamical Systems, Series B, vol.4, issue.4, pp.1117-1128, 2004.

X. Zhao and D. Xiao, The Asymptotic Speed of Spread and Traveling Waves for a Vector Disease Model, Journal of Dynamics and Differential Equations, vol.4, issue.4, pp.1001-1019, 2006.
DOI : 10.1007/s10884-006-9044-z