M. Adimy, O. Angulo, C. Marquet, and L. Sebaa, A mathematical model of multistage hematopoietic cell lineages. Discrete and Continuous Dynamical Systems, Series B, vol.19, pp.1-26, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00993751

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.
DOI : 10.3934/dcdsb.2015.20.2765
URL : https://hal.archives-ouvertes.fr/hal-01249892

M. Adimy and F. Crauste, Global stability of a partial differential equation with distributed delay due to cellular replication. Nonlinear Analysis: Theory, Methods & Applications, vol.54, pp.1469-1491, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00375926

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

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.70-1611, 2010.
DOI : 10.1137/080742713
URL : https://hal.archives-ouvertes.fr/hal-00542655

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.65-1328, 2005.
DOI : 10.1137/040604698
URL : https://hal.archives-ouvertes.fr/hal-00375977

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

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. 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

G. Bocharov and K. Hadeler, Structured Population Models, Conservation Laws, and Delay Equations, Journal of Differential Equations, vol.168, issue.1, pp.212-237, 2000.
DOI : 10.1006/jdeq.2000.3885
URL : http://doi.org/10.1006/jdeq.2000.3885

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, pp.217-571, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00849405

K. J. Brown and J. Carr, Deterministic epidemic waves of critical velocity, Mathematical Proceedings of the Cambridge Philosophical Society, vol.80, issue.03, pp.81-431, 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-00000736

O. Diekmann, Thresholds and travelling waves for the geographical spread of infection, Journal of Mathematical Biology, vol.4, issue.2, pp.109-130, 1978.
DOI : 10.2307/2342829

J. Fang and X. Q. Zhao, Traveling Waves for Monotone Semiflows with Weak Compactness, SIAM Journal on Mathematical Analysis, vol.46, issue.6, pp.3678-3704, 2014.
DOI : 10.1137/140953939

J. Fang, K. Lan, G. Seo, and J. Wu, Spatial Dynamics of an Age-Structured Population Model of Asian Clams, SIAM Journal on Applied Mathematics, vol.74, issue.4, pp.959-979, 2014.
DOI : 10.1137/130930273

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

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.74-453, 2012.
DOI : 10.1090/S0894-0347-05-00504-7
URL : https://hal.archives-ouvertes.fr/hal-01257398

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

X. Liang and X. Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Communications on Pure and Applied Mathematics, vol.105, issue.1, pp.1-40, 2007.
DOI : 10.1007/978-0-387-21761-1

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

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

M. C. Mackey, Dynamic Haematological Disorders of Stem Cell Origin, Biophysical and Biochemical Information Transfer in Recognition, pp.373-409, 1979.
DOI : 10.1007/978-1-4899-5330-8_33

M. C. Mackey, C. Ou, L. Pujo-menjouet, and J. Wu, Periodic Oscillations of Blood Cell Populations in Chronic Myelogenous Leukemia, SIAM Journal on Mathematical Analysis, vol.38, issue.1, pp.38-166, 2006.
DOI : 10.1137/04061578X

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

M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, 1999.
DOI : 10.1007/978-1-4612-5282-5

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

L. Roques, J. Garnier, F. Hamel, and E. K. Klein, Allee effect promotes diversity in traveling waves of colonization, Proc. Natl. Acad. Sci. USA, pp.8828-8833, 2012.
DOI : 10.1016/0001-8708(78)90130-5
URL : https://hal.archives-ouvertes.fr/hal-01257401

J. W. So, J. Wu, and X. Zou, A reaction-diffusion model for a single species with age structure. I Travelling wavefronts on unbounded domains, Proc. R. Soc. Lond. A, pp.457-1841, 2001.
DOI : 10.1098/rspa.2001.0789

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, Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations, J. Reine Angew. Math, vol.306, pp.94-121, 1979.

H. R. Thieme and X. Q. 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.195-430, 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.

Z. C. Wang, W. T. Li, and S. Ruan, Traveling Fronts in Monostable Equations with Nonlocal Delayed Effects, Journal of Dynamics and Differential Equations, vol.146, issue.3, pp.20-573, 2008.
DOI : 10.1007/978-1-4612-4050-1

I. L. Weissman, Stem Cells, Cell, vol.100, issue.1, pp.157-168, 2000.
DOI : 10.1016/S0092-8674(00)81692-X

A. Wilson, E. Laurenti, G. Oser, R. C. Van-der-wath, W. Blanco-bose et al., Hematopoietic stem cells reversibly switch from dormancy to self-renewal during homeostasis and repair, Cell, pp.135-1118, 2008.
DOI : 10.1016/j.cell.2009.06.020
URL : http://doi.org/10.1016/j.cell.2009.06.020

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

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

X. Q. Zhao and W. Wang, Fisher waves in an epidemic model. Discrete and Continuous Dynamical Systems, Series B, vol.4, pp.1117-1128, 2004.
DOI : 10.3934/dcdsb.2004.4.1117

X. Q. 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