L. M. Abia, O. Angulo, and J. C. López-marcos, Age-structured population models and their numerical solution, Ecological Modelling, vol.188, issue.1, pp.112-136, 2005.
DOI : 10.1016/j.ecolmodel.2005.05.007

A. S. Ackleh, K. Deng, K. Ito, and J. Thibodeaux, A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate, Mathematical Biosciences, vol.204, issue.1, pp.21-48, 2006.
DOI : 10.1016/j.mbs.2006.08.004

A. S. Ackleh and J. Thibodeaux, Parameter estimation in a structured erythropoiesis model, Mathematical Biosciences and Engineering, vol.5, issue.4, pp.601-616, 2008.
DOI : 10.3934/mbe.2008.5.601

M. Adimy, F. Crauste, and L. Pujo-menjouet, On the stability of a maturity structured model of cellular proliferation, Discret. Cont. Dyn. Sys. Ser. A, vol.12, issue.3, pp.501-522, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00375940

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.328-1352, 2005.
DOI : 10.1137/040604698

URL : https://hal.archives-ouvertes.fr/hal-00375977

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, O. Angulo, F. Crauste, and J. C. López-marcos, Numerical integration of a mathematical model of hematopoietic stem cell dynamics, Computers & Mathematics with Applications, vol.56, issue.3, pp.56-594, 2008.
DOI : 10.1016/j.camwa.2008.01.003

URL : https://hal.archives-ouvertes.fr/hal-00750283

O. Angulo and F. Crauste, Investigating the Roles of the Experimental Protocol in Phenylhidrazine-Induced Anemia in Mice, J. Theor. Biol

O. Angulo, J. C. López-marcos, and M. A. Bees, Mass Structured Systems with Boundary Delay: Oscillations and the Effect of Selective Predation, Journal of Nonlinear Science, vol.244, issue.178, pp.961-984, 2012.
DOI : 10.1016/j.jtbi.2006.08.024

O. Angulo, J. C. López-marcos, and M. A. , López-Marcos, A numerical integrator for a model with a discontinuous sink term: the dynamics of the sexual phase of monogonont rotifera, pp.6-935, 2005.

O. Angulo, J. C. López-marcos, and M. A. López-marcos, Numerical approximation of singular asymptotic states for a size-structured population model with a dynamical resource, Mathematical and Computer Modelling, vol.54, issue.7-8, pp.54-1693, 2011.
DOI : 10.1016/j.mcm.2010.12.006

O. Angulo, J. C. López-marcos, and M. A. , A semi-Lagrangian method for a cell population model in a dynamical environment, Mathematical and Computer Modelling, vol.57, issue.7-8, pp.1860-1866, 2013.
DOI : 10.1016/j.mcm.2011.12.016

O. Angulo, J. C. López-marcos, M. A. López-marcos, and J. , Numerical analysis of a population model of marine invertebrates with different life stages, Communications in Nonlinear Science and Numerical Simulation, vol.18, issue.8, pp.2153-2163, 2013.
DOI : 10.1016/j.cnsns.2013.01.009

O. Angulo, J. C. López-marcos, M. A. López-marcos, and F. A. Milner, A numerical method for nonlinear age-structured population models with finite maximum age, Journal of Mathematical Analysis and Applications, vol.361, issue.1, pp.361-150, 2010.
DOI : 10.1016/j.jmaa.2009.09.001

URL : https://doi.org/10.1016/j.jmaa.2009.09.001

A. Bauer, F. Tronche, O. Wessely, C. Kellendonk, H. M. Reichardt et al., The glucocorticoid receptor is required for stress erythropoiesis, Genes & Development, vol.13, issue.22, pp.2996-3002, 1999.
DOI : 10.1101/gad.13.22.2996

URL : http://genesdev.cshlp.org/content/13/22/2996.full.pdf

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.317-34610, 1995.
DOI : 10.1016/0025-5564(94)00078-E

N. I. Berlin and C. Lotz, Life Span of the Red Blood Cell of the Rat Following Acute Hemorrhage., Experimental Biology and Medicine, vol.78, issue.3, pp.78-788, 1951.
DOI : 10.3181/00379727-78-19220

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

C. Colijn and M. C. Mackey, A mathematical model of hematopoiesis: II. Cyclical neutropenia, Journal of Theoretical Biology, vol.237, issue.2, pp.133-146, 2005.
DOI : 10.1016/j.jtbi.2005.03.034

F. Crauste, I. Demin, O. Gandrillon, and V. Volpert, Mathematical study of feedback control roles and relevance in stress erythropoiesis, Journal of Theoretical Biology, vol.263, issue.3, pp.303-316, 2010.
DOI : 10.1016/j.jtbi.2009.12.026

URL : https://hal.archives-ouvertes.fr/hal-00567288

F. Crauste, L. Pujo-menjouet, S. Génieys, C. Molina, and O. Gandrillon, Adding self-renewal in committed erythroid progenitors improves the biological relevance of a mathematical model of erythropoiesis, Journal of Theoretical Biology, vol.250, issue.2, pp.250-322, 2008.
DOI : 10.1016/j.jtbi.2007.09.041

URL : https://hal.archives-ouvertes.fr/hal-00194422

O. Gandrillon, U. Schmidt, H. Beug, and J. Samarut, TGF-?? cooperates with TGF-?? to induce the self???renewal of normal erythrocytic progenitors: evidence for an autocrine mechanism, The EMBO Journal, vol.18, issue.10, pp.2764-2781, 1999.
DOI : 10.1093/emboj/18.10.2764

URL : https://hal.archives-ouvertes.fr/hal-00194310

S. M. Hattangadi, K. A. Burke, and H. F. Lodish, Homeodomain-interacting protein kinase 2 plays an important role in normal terminal erythroid differentiation, Blood, vol.115, issue.23, pp.4853-4861, 2010.
DOI : 10.1182/blood-2009-07-235093

URL : http://www.bloodjournal.org/content/bloodjournal/115/23/4853.full.pdf

M. J. Koury and M. C. Bondurant, Erythropoietin retards DNA breakdown and prevents programmed death in erythroid progenitor cells, Science, vol.248, issue.4953, pp.378-381, 1990.
DOI : 10.1126/science.2326648

M. Loeffler, K. Pantel, H. Wulff, and H. E. Wichmann, A mathematical model of erythropoiesis in mice and rats Part 1: Structure of the model, Cell Proliferation, vol.22, issue.1, pp.3-30, 1989.
DOI : 10.1016/0014-4827(67)90370-9

M. C. Mackey, Unified hypothesis of the origin of aplastic anaemia and periodic hematopo¨?esishematopo¨?esis, Blood, vol.51, pp.941-956, 1978.

J. M. Mahaffy, J. Belair, and M. C. Mackey, Hematopoietic Model with Moving Boundary Condition and State Dependent Delay: Applications in Erythropoiesis, Journal of Theoretical Biology, vol.190, issue.2, pp.135-146, 1998.
DOI : 10.1006/jtbi.1997.0537

K. Nagai, K. Oue, and H. Kawagoe, Studies on the short-lived reticulocytes by use of the in vitro labeling method, Acta Haematol. Jpn, pp.31-967, 1968.

K. Nagai, K. Ishizu, and E. Kakishita, Studies on the erythroblast dynamics based on the production of fetal hemoglobin, Acta Haematol. Jpn, vol.34, 1971.

M. Iannelli and F. A. Milner, On the approximation of the Lotka???McKendrick equation with finite life-span, Journal of Computational and Applied Mathematics, vol.136, issue.1-2, pp.245-254, 2001.
DOI : 10.1016/S0377-0427(00)00616-6

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

I. Roeder, Quantitative stem cell biology: computational studies in the hematopoietic system, Current Opinion in Hematology, vol.13, issue.4, pp.222-228, 2006.
DOI : 10.1097/01.moh.0000231418.08031.48

I. Roeder and M. Loeffler, A novel dynamic model of hematopoietic stem cell organization based on the concept of within-tissue plasticity, Experimental Hematology, vol.30, issue.8, pp.853-861, 2002.
DOI : 10.1016/S0301-472X(02)00832-9

A. Shimada, The maturation of reticulocytes. II. Life-span of red cells originating from stress reticulocytes, Acta Med. Okayama, vol.29, issue.4, pp.283-289, 1975.

F. Stohlman, Humoral regulation of erythropoiesis. VII. Shortened survival of erythrocytes by erythropoietin or severe anemia, Proc. Soc. Exp. Biol. Med, vol.107, issue.884, 1961.

G. Webb, Theory of nonlinear age-dependent population dynamics, Monographs and textbooks in Pure and Appl, Math, vol.89, 1985.