Free Access
Math. Model. Nat. Phenom.
Volume 11, Number 1, 2016
Reviews in mathematical modelling
Page(s) 92 - 115
Published online 22 February 2016
  1. A. S. Ackleh, K. Deng, K. Ito, J. J. Thibodeaux. A structured poiesis model with nonlinear cell maturation velocity and hormone decay rate. Math Biosci. (2006), No. 204 (1), 21–48. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  2. A. S. Ackleh, J. J. Thibodeaux. Parameter estimation in a structured erythropoiesis model. Math Biosci Eng. (2008), No. 5 (4), 601–16. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  3. M. Adimy, O. Angulo, F. Crauste, J.C. Lopez-Marcos. Numerical integration of a mathematical model of hematopoietic stem cell dynamics, Computers Mathematics with Applications. (2008), Vol. 56 (3), 594–60. [CrossRef] [MathSciNet] [Google Scholar]
  4. M. Adimy, O. Angulo, J. Lopez-Marcos, M. L. Opez-Marcos. Asymptotic behaviour of a mathematical model of hematopoietic stem cell dynamics. International Journal of Computer Mathematics. (2014), Vol. 91, No. 2, 198–208. [CrossRef] [Google Scholar]
  5. M. Adimy, O. Angulo, C. Marquet, L. Sebaa. A mathematical model of multistage hematopoietic cell lineages. Discrete and Continuous Dynamical Systems - Series B (2014) Vol. 19, No. 1, 1–26. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Adimy, S. Bernard, J. Clairambault, F. Crauste, S. Génieys, L. Pujo-Menjouet. Modélisation de la dynamique de l’hématopoîèse normale et pathologique. Hématologie. (2008), 14 (5), 339–350. [Google Scholar]
  7. M. Adimy, A. Chekroun, T. M. Touaoula. Age structured and delay differential-difference model of hematopoietic stem cell dynamics. Discrete and Continuous Dynamical Systems - Series B. (2015), Vol. 20, No. 9, 2765–2791. [Google Scholar]
  8. M. Adimy, A. Chekroun, T. M. Touaoula. A delay differential-difference system of hematopoietic stem cell dynamics. Comptes Rendus Mathématiques. (2015), 353 (4), 303–307. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Adimy, F. Crauste. Un modèle non-linéaire de prolifération cellulaire : extinction des cellules et invariance. Comptes Rendus Mathématiques. (2003), 336, 559–564. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Adimy, F. Crauste. Global stability of a partial differential equation with distributed delay due to cellular replication. Nonlinear Analysis. (2003), TMA, 54 (8), 1469–1491. [Google Scholar]
  11. M. Adimy, F. Crauste. Stability and instability induced by time delay in an erythropoiesis model. Monografias del Seminario Matematico Garcia de Galdeano. (2004), 31, 3–12. [Google Scholar]
  12. M. Adimy, F. Crauste. Existence, positivity and stability for a nonlinear model of cellular proliferation. Nonlinear Analysis: Real World Applications. (2005), 6 (2), 337–366. [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Adimy, F. Crauste. Modelling and asymptotic stability of a growth factor-dependent stem cells dynamics model with distributed delay. Discrete and Continuous Dynamical Systems Series B. (2007), 8(1), 19–38. [CrossRef] [MathSciNet] [Google Scholar]
  14. M. Adimy, F. Crauste. Mathematical model of hematopoiesis dynamics with growth factor-dependent apoptosis and proliferation regulation. Mathematical and Computer Modelling. (2009), 49, 2128–2137. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Adimy, F. Crauste. Delay Differential Equations and Autonomous Oscillations in Hematopoietic Stem Cell Dynamics Modeling. Mathematical Modelling of Natural Phenomena (2012) 7 (6), 1–22. article [CrossRef] [EDP Sciences] [Google Scholar]
  16. M. Adimy, F. Crauste, A. El Abdllaoui. Asymptotic behavior of a discrete maturity structured system of hematopoietic stem cell dynamics with several delays. Journal of Mathematical Modelling and Natural Phenomena (2006), 1(2), 1–19. [CrossRef] [EDP Sciences] [Google Scholar]
  17. M. Adimy, F. Crauste, A. El Abdllaoui. Discrete maturity-structured model of cell differentiation with applications to acute myelogenous leukemia. Journal of Biological Systems (2008), Vol. 16 (3), 395–424. [CrossRef] [Google Scholar]
  18. M. Adimy, F. Crauste, A. El Abdllaoui. Boundedness and Lyapunov Function for a Nonlinear System of Hematopoietic Stem Cell Dynamics. Comptes Rendus Mathematique, (2010) 348 (7-8), 373–377. [CrossRef] [Google Scholar]
  19. M. Adimy, F. Crauste, A. Halanay, M. Neamtu, D. Opris. Stability of limit cycles in a pluripotent stem cell dynamics model. Chaos, Solitons and Fractals (2006), 27 (4), 1091–1107. [CrossRef] [MathSciNet] [Google Scholar]
  20. M. Adimy, F. Crauste, My L. Hbid, R. Qesmi. Stability and Hopf bifurcation for a cell population model with state-dependent delay. SIAM J. Appl. Math. (2010) 70 (5), 1611–1633. [CrossRef] [Google Scholar]
  21. M. Adimy, F. Crauste, C. Marquet. Asymptotic behavior and stability switch for a mature-immature model of cell differentiation. Nonlinear Analysis: Real World Applications (2010) 11 (4), 2913–2929. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Adimy, F. Crauste, L. Pujo-Menjouet. On the stability of a maturity structured model of cellular proliferation. Dis. Cont. Dyn. Sys. Ser. A (2005), 12 (3), 501–522. . [Google Scholar]
  23. M. Adimy, F. Crauste, S. Ruan. Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics. Nonlinear Analysis: Real World Applications (2005), 6 (4), 651–670. [CrossRef] [MathSciNet] [Google Scholar]
  24. M. Adimy, F. Crauste, S. Ruan. A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J. Appl. Math. (2005), 65 (4), 1328–1352. [CrossRef] [MathSciNet] [Google Scholar]
  25. M. Adimy, F. Crauste, S. Ruan. Periodic Oscillations in Leukopoiesis Models with Two Delays. Journal of Theoretical Biology (2006), 242, 288–299. [Google Scholar]
  26. M. Adimy, F. Crauste, S. Ruan. Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases. Bulletin of Mathematical Biology (2006), 68 (8), 2321–2351. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  27. M. Adimy, K. Ezzinbi, C. Marquet. Ergodic and weighted pseudo-almost periodic solutions for partial functional differential equations in fading memory spaces. Journal of Applied Mathematics and Computing (2014) 44, No. 1-2, 147-165. [CrossRef] [MathSciNet] [Google Scholar]
  28. M. Adimy, C. Marquet. On the stability of hematopoietic model with feedback control. C. R. Math. Acad. Sci. Paris. (2012) 350, 173–176. [CrossRef] [MathSciNet] [Google Scholar]
  29. M. Adimy, L. Pujo-Menjouet. A singular transport model describing cellular division. C.R. Acad. Sci. Paris (2001), 332 (12), 1071–1076. [CrossRef] [MathSciNet] [Google Scholar]
  30. M. Adimy, L. Pujo-Menjouet. A mathematical model describing cellular division with a proliferating phase duration depending on the maturity of cells. Electron. J. Diff. Equ. (2003), 107, 1–14. [Google Scholar]
  31. M. Adimy, L. Pujo-Menjouet. Asymptotic behavior of a singular transport equation modelling cell division. Dis. Cont. Dyn. Sys. Ser. B (2003), 3 (3), 439-456. [CrossRef] [Google Scholar]
  32. E. Afenya, S. Mundle. Hematologic Disorders and Bone Marrow Peripheral Blood Dynamics. Math. Model. Nat. Phenom. (2010) Vol. 5, No. 3, 15–27. DOI: 10.1051/mmnp/20105302. [CrossRef] [EDP Sciences] [Google Scholar]
  33. T. Alarcon, P. Getto, A. Marciniak-Czochra, M. D. Vivanco. A model for stem cell population dynamics with regulated maturation delay. Disc. Cont. Dyn. Syst. Suppl. (2011), 32–43. [Google Scholar]
  34. U. an der Heiden, M.C. Mackey. Mixed feedback: A paradigm for regular and irregular oscillations. Temporal Disorder in Human Oscillatory Systems (eds. L. Rensing, U. an der Heiden, and M.C. Mackey), Springer-Verlag, New York, Berlin, Heidelberg 1987, 30–36. [Google Scholar]
  35. E.S. Antoniou, C. L. Mouser, M. E. Rosar, J. Tadros, E. K. Vassiliou. Hematopoietic stem cell proliferation modeling under the influence of hematopoietic-inducing agent. Shock. (2009) Nov;32(5):471-7. doi: 10.1097/SHK.0b013e3181a1a05f. [CrossRef] [PubMed] [Google Scholar]
  36. R. Apostu, M.C. Mackey. Understanding cyclical thrombocytopenia: A mathematical modeling approach. J. Theor. Biol. (2008), 251, 297–316. [CrossRef] [PubMed] [Google Scholar]
  37. O. Arino, M. Kimmel. Asymptotic analysis of a functional-integral equation related to cell population kinetics, North-Holland Mathematics Studies, Proceedings of the VIth International Conference on Trends in the Theory and Practice of Non-Linear Analysis (1985), 110:27–32. [Google Scholar]
  38. O. Arino, M. Kimmel. Stability analysis of models of cell production systems, Math. Modelling, (1986), 7, 9–12. [CrossRef] [MathSciNet] [Google Scholar]
  39. O. Arino, M. Kimmel. Asymptotic analysis of a cell cycle model based on unequal division, SIAM J. Appl. Math., (1987), 47(1):128–145. [CrossRef] [Google Scholar]
  40. O. Arino, M. Kimmel, M. Zerner. Analysis of a cell population model with unequal division and random transition, Lecture Notes in Pure and Appl. Math., 131 (1991), 3–12. [Google Scholar]
  41. O. Arino, A. Mortabit. Slow oscillations in a model of cell population dynamics, Lecture Notes in Pure and Appl. Math., 131 (1991), 13–25. [Google Scholar]
  42. O. Arino, M. Kimmel. Comparison of approaches to modeling of cell population dynamics, SIAM J. Appl. Math., 53 (1993) (5):1480–1504. [CrossRef] [MathSciNet] [Google Scholar]
  43. O. Arino, M. Kimmel, G. F. Webb. Mathematical modelling of the loss of telomere sequences, J. Theoretical Biology, 177 (1995), 45–57. [CrossRef] [PubMed] [Google Scholar]
  44. O. Arino, E. Sánchez. A survey of cell population dynamics, J. Theor. Med., 1 (1997)(1):35–51. [CrossRef] [Google Scholar]
  45. O. Arino, E. Sánchez, G. F. Webb. Necessary and sufficient conditions for asynchronous exponential growth in age structured cell populations with quiescence, J. Math. Anal. Appl., 215 (1997), (2):499–513. [CrossRef] [MathSciNet] [Google Scholar]
  46. O. Arino, E. Sánchez, G. F. Webb. Polynomial growth dynamics of telomere loss in a heterogeneous cell population, Dynam. Contin. Discrete Impuls. Systems, Arino, O., Axelrod, D. and Kimmel, M., editors., 3(1997) (3):263–282. [Google Scholar]
  47. J.L. Avila Alonso, C. Bonnet, J. Clairambault, H. Özbay, S.-I. Niculescu, F. Merhi, A. Ballesta, R. P. Tang, J. P. Marie. Delay Systems : From Theory to Numerics and Applications, T. Vyhlídal, J.-F. Lafay, R. Sipahi eds., Advances in Delays and Dynamics series, Springer, New York (2014), 315–328. Analysis of a New Model of Cell Population Dynamics in Acute Myeloid Leukemia [Google Scholar]
  48. S. Balea, A. Halanay, D. Jardan, M. Neamţu, C. A. Safta. Stability Analysis of a Feedback Model for the Action of the Immune System in Leukemia. Math. Model. Nat. Phenom. (2014) Vol. 9, No. 1, 108–32. DOI: 10.1051/mmnp/20149108. [CrossRef] [EDP Sciences] [Google Scholar]
  49. H. T. Banks, C. E. Cole, P. M. Schlosser, H. T. Tran. Modeling and optimal regulation of erythropoiesis subject to benzene intoxication. Math Biosci Eng. (2004);1(1):15–48. Jun [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  50. A. J. Becker, E. A. McCulloch, J. E. Till. Cytological demonstration of the clonal nature of spleen colonies derived from transplanted mouse marrow cells. Nature, (1963), 197(4866), 452–4. (Bibcode:1963Natur.197.452B. doi:10.1038/197452a0) [CrossRef] [PubMed] [Google Scholar]
  51. F. Bekkal Brikci, J. Clairambault, B. Ribba, B. Perthame. An age-and-cyclin-structured cell population model for healthy and tumoral tissues, Journal of Mathematical Biology (2008) 57(1):91–110. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  52. F. Bekkal Brikci, J. Clairambault, B. Ribba, B. Perthame. Analysis of a molecular structured population model with polynomial growth for the cell cycle. Mathematical and Computer Modelling (2008), 47(7-8): 699–713. [CrossRef] [MathSciNet] [Google Scholar]
  53. J. Bélair, M.C. Mackey. A model for the regulation of mammalian platelet production, Ann. N.Y. Acad. Sci. (1987), 504, 280–282. [CrossRef] [Google Scholar]
  54. J. Bélair, M.C. Mackey, J.M. Mahaffy. Age-structured and two delay models for erythropoiesis, Math. Biosci. (1995), 128, 317–346. [CrossRef] [PubMed] [Google Scholar]
  55. J. Bélair, J.M. Mahaffy. Variable maturation velocity and parameter sensitivity in a model of haematopoiesis. IMA J. Math. Appl. Med Biol. (2001);18(2):193–211. Jun [CrossRef] [PubMed] [Google Scholar]
  56. S. Bernard, J. Bélair, M.C. Mackey. Sufficient conditions for stability of linear differential equations with distributed delay, Discr. Contin. Dyn. Sys. B (2001), 1:233–256. [CrossRef] [MathSciNet] [Google Scholar]
  57. S. Bernard, J. Bélair, M.C. Mackey. Oscillations in cyclical neutropenia: new evidence based on mathematical modeling, J. Theor. Biol. (2003), 223:283–298. [CrossRef] [PubMed] [Google Scholar]
  58. S. Bernard, J. Bélair, M.C. Mackey. Bifurcations in a white-blood-cell production model. C. R. Biologies (2004), 327:201–210. [Google Scholar]
  59. S. Bernard, F. Crauste. Optimal linear stability condition for scalar differential equations with distributed delay. Discrete and Continuous Dynamical Systems Series B (2015) 20 (7), 1855-1876. [CrossRef] [Google Scholar]
  60. S. Bernard, D. Gonze, B. C˘ajavec, H. Herzel, A. Kramer. Synchronization-induced rhythmicity of circadian oscillators in the suprachiasmatic nucleus. PLOS Comput Biol. (2007) 3:e68. [CrossRef] [Google Scholar]
  61. S. Bernard, L. Pujo-Menjouet, M.C. Mackey. Analysis of cell kinetics using a cell division marker: mathematical modeling of experimental data, Biophys. J. (2003), 84:3414–3424. [CrossRef] [PubMed] [Google Scholar]
  62. N. Bessonov, E. Babushkina, S. F. Golovashchenko, A. Tosenberger, F. Ataullakhanov, M. Panteleev, A. Tokarev, V. Volpert. Numerical Modelling of Cell Distribution in Blood Flow. Math. Model. Nat. Phenom., 9 (2014), no. 6, 69–84. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  63. N. Bessonov, F. Crauste, I. Demin, V. Volpert. Dynamics of erythroid progenitors and erythroleukemia. Mathematical Modeling of Natural Phenomena (2009), 4 (3), 210–232. [Google Scholar]
  64. N. Bessonov, F. Crauste, S. Fischer, P. Kurbatova, V. Volpert. Application of Hybrid Models to Blood Cell Production in the Bone Marrow. Math. Model. Nat. Phenom. (2011) 6 (7), 2–12. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  65. N. Bessonov, L. Pujo-Menjouet, V. Volpert. Cell Modelling of Hematopoiesis. Math. Model. Nat. Phenom. (2006) Vol. 1, No. 2, 81–103. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  66. D. Bonnet, J.E. Dick. Human acute myeloid leukemia is organized as a hierarchy that originates from a primitive hematopoietic cell. Nature Medicine, (1997), 3 (7), 730–737. doi:10.1038/nm0797-730. PMID 9212098. [CrossRef] [PubMed] [Google Scholar]
  67. R. Borges, A. Calsina, S. Cuadrado, O. Diekmann. Delay equation formulation of a cyclin-structured cell population model. Journal of Evolution Equations (2014) 14 (4-5), 841–862. [CrossRef] [MathSciNet] [Google Scholar]
  68. A. Bouchnita, N. Eymard, M. Koury, V. Volpert. Initiation of erythropoiesis by BFU-E cells. ITM Web of Conferences 4, 01002 (2015) DOI: 10.1051/itmconf/20150401002. [Google Scholar]
  69. A. Bouzinab, O. Arino. On the existence and uniqueness for an age-dependent population model with nonlinear growth, Facta Univ. Ser. Math. Inform., (1993) (8):55–68. [Google Scholar]
  70. D. Breda, O. Diekmann, S. Maset, R. Vermiglio. A numerical approach to investigate the stability of equilibria for structured population models. Journal of biological dynamics (2013) 7 (Suppl. 1), 4–20. [Google Scholar]
  71. G. Brooks, G. Provencher Langlois, J. Lei, M.C. Mackey. Neutrophil dynamics after chemotherapy and G-CSF: The role of pharmacokinetics in shaping the response. J. Theor. Biol. (2012), 315, 97–109. [CrossRef] [PubMed] [Google Scholar]
  72. B. Bungart, M. Loeffler, H. Goris, B. Dontje, V. Diehl, W. Nijhof. Differential effects of rekombinant human colony stimulating factor (rh G-CSF) on stem cells in marrow, spleen and peripheral blood in mice, Br. J. Haematol. 76 (1990) 174–179. [CrossRef] [PubMed] [Google Scholar]
  73. F. J. Burns, J. F. Tannock, On the existence of a G0-phase in the cell cycle. Cell Tissue Kinet. (1970), 3:321–334. [PubMed] [Google Scholar]
  74. C. Calmelet, A. Prokop, J. Mensah, L. J. McCawley, P. S. Crooke. Modeling the Cancer Stem Cell Hypothesis. Math. Model. Nat. Phenom. (2010) Vol. 5, No. 3, 40–62. DOI: 10.1051/mmnp/20105304. [CrossRef] [EDP Sciences] [Google Scholar]
  75. P. Carnot, C. Deflandre. Sur l’activité hémopoïétique du sérum au cours de la régénération du sang. Comptes rendus hebdomadaires des séances de l’Académie des sciences, (1906), 143: 384–432. [Google Scholar]
  76. V. Chickarmane, T. Enver, C. Peterson. Computational modeling of the hematopoietic erythroid- myeloid switch reveals insights into cooperativity. PLoS Comput. Biol. (2009) 5, doi:10.1371/journal.pcbi.1000268. [Google Scholar]
  77. J. Clairambault. A Step Toward Optimization of Cancer Therapeutics. Physiologically Based Modeling of Circadian Control on Cell Proliferation. IEEE-EMB Magazine (2008), 27(1):20-24. [Google Scholar]
  78. J. Clairambault. Modelling physiological and pharmacological control on cell proliferation to optimise cancer treatments. Mathematical Modelling of Natural Phenomena (2009), 4(3) : 12–67. [CrossRef] [EDP Sciences] [Google Scholar]
  79. J. Clairambault, S. Gaubert, T. Lepoutre. Comparison of Perron and Floquet eigenvalues in age structured cell division models. Mathematical Modelling of Natural Phenomena (2009), 4(3) : 183–209. [CrossRef] [MathSciNet] [Google Scholar]
  80. C. Colijn, D.C. Dale, C. Foley, M.C. Mackey. Observations on the pathophysiology and mechanisms for cyclic neutropenia. Math. Model. Natur. Phenom. (2006), 1(2), 45–69. [CrossRef] [EDP Sciences] [Google Scholar]
  81. C. Colijn, C. Foley, M.C. Mackey. G-CSF treatment of canine cyclical neutropenia: A comprehensive mathematical model. Exper. Hematol. (2007), 35, 898–907. [CrossRef] [Google Scholar]
  82. C. Colijn, A.C. Fowler, M.C. Mackey. High frequency spikes in long period blood cell oscillations. J. Math. Biol. (2006), 53(4), 499–519. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  83. C. Colijn, M.C. Mackey. A mathematical model of hematopoiesis: Periodic chronic myelogenous leukemia, part I. J. Theor. Biol. (2005), 237, 117–132. [CrossRef] [PubMed] [Google Scholar]
  84. C. Colijn, M.C. Mackey. A mathematical model of hematopoiesis: Cyclical neutropenia, part II. J. Theor. Biol. (2005), 237, 133–146. [CrossRef] [PubMed] [Google Scholar]
  85. C. Colijn, M.C. Mackey. Bifurcation and bistability in a model of hematopoietic regulation, SIAM J. App. Dynam. Sys. (2007), 6(2), 378–394. [CrossRef] [Google Scholar]
  86. F. Crauste. Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model. Mathematical Biosciences and Engineering (2006), 3 (2), 325–346. [CrossRef] [MathSciNet] [Google Scholar]
  87. F. Crauste. Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch. Math. Model. Nat. Phenom. (2009) Vol. 4, No. 2, 28–47. [CrossRef] [EDP Sciences] [Google Scholar]
  88. F. Crauste. Stability and Hopf bifurcation for a first-order linear delay differential equation with distributed delay, in Complex Time Delay Systems (Ed. F. Atay), Springer, 1st edition, (2010) 320 p., ISBN: 978-3-642-02328-6. [Google Scholar]
  89. F. Crauste. A review on local asymptotic stability analysis for mathematical models of hematopoietic with delay and delay-dependent coefficients. Annals of the Tiberiu Popoviciu Seminar of functionnal equations, approximation and convexity (2011) 9, 121-143. [Google Scholar]
  90. F. Crauste, I. Demin, O. Gandrillon, V. Volpert. Mathematical study of feedback control roles and relevance in stress erythropoiesis. Journal of Theoretical Biology, (2010) 263 (3), 303–316. [Google Scholar]
  91. F. Crauste, L. Pujo-Menjouet, S. GÃľnieys, C. Molina, O. Gandrillon. Adding Self-Renewal in Committed Erythroid Progenitors Improves the Biological Relevance of a Mathematical Model of Erythropoiesis. Journal of Theoretical Biology (2008), 250, 322–338. [Google Scholar]
  92. F. Crauste, M. Adimy. Bifurcation dans un modÃĺle non-linÃľaire de production du sang. Comptes-rendus de la 7ième Rencontre du Non-linéaire, Non-linéaire Publications, Paris (2004), 73–78. [Google Scholar]
  93. R. Crabb, M.C. Mackey, A. Rey. Propagating fronts, chaos and multistability in a cell replication model, Chaos (1996) 6, 477–492. [CrossRef] [PubMed] [Google Scholar]
  94. M. Craig, A.R. Humphries, F. Nekka, J. Belair, J. Li, M.C. Mackey. Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: Mathematical modelling guides dose optimisation to minimize neutropenia. J. Theor. Biol. (2015), 385, 77–89. [CrossRef] [PubMed] [Google Scholar]
  95. J. M. Cushing. Existence and stability of equilibria in age-structured population dynamics. Math. Biol. (1984), 20, 259–276. [CrossRef] [MathSciNet] [Google Scholar]
  96. D.C. Dale, M.C. Mackey. Understanding, treating and avoiding hematological disease: Better medicine through mathematics?. Bulletin of Mathematical Biology (2015), 77, 739–757. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  97. G. De Haan, C. H. Engel, B. Dontje, W. Nijhof, M. Loeffler. Mutual inhibition of murine erythropoiesis and granulopoiesis during combined erythropoietin, granulocyte colony-stimulating factor and stem cell factor adminstration: In vivo interactions and dose response surfaces. Blood 12 Vol 84 (1994) 4157–4163. [Google Scholar]
  98. G. De Haan, B. Dontje, W. Nijhof, M. Loeffler. Effects of Continuous Stem Cell Factor Administration on Normal and Erythropoietin- Stimulated Murine Hemopoiesis. Experimental Results and Model Analysis, Stem Cells (Dayt) 13 (1995) 65-76 [CrossRef] [Google Scholar]
  99. G. De Haan, C. Engel, B. Dontje, M. Loeffler, W. Nijhof. Hematoxicity by prolonged etoposide adminstration to mice can be prevented by simultaneous growth factor therapy, Cancer Research 55 (1995) 324–329. [PubMed] [Google Scholar]
  100. G. De Haan, B. Dontje, C. Engel, M. Loeffler, W. Nijhof. The kinetics of murine hemopoietic stem cells in vivo in response to prolonged increased mature blood cell production, induced by granulocyte colony-stimulating factor. Blood 86: 8 (1995) 2986–2992. [Google Scholar]
  101. G. De Haan, B. Dontje, C. Engel, M. Loeffler, W. Nijhof. In vivo effects of interleukin-11 and stem cell factor in combination with erythropoietin in the regulation of erythropoiesis. British Journal of Hematology (1995) 90: 4, 783–790. [CrossRef] [Google Scholar]
  102. I. Demin, F. Crauste, O. Gandrillon, V. Volpert. A multi-scale model of erythropoiesis. Journal of Biological Dynamics, (2010) 4 (1), 59–70. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  103. P. K. Dhar, A. Mukherjee, D. Majumder. Difference Delay Equation-Based Analytical Model of Hematopoiesis. Automatic Control of Physiological State and Function Vol. 1 (2012), Article ID 235488, 11 pages doi:10.4303/acpsf/235488. [Google Scholar]
  104. W. Desch, W. Schappacher, G. F. Webb. Hypercyclic and chaotic semigroups of linear operators, Ergodic Theory and Dynamical Systems 17, (1997), 1–27. [CrossRef] [MathSciNet] [Google Scholar]
  105. O. Diekmann, H. J. A. M. Heijmans, H. R. Thieme. On the stability of the cell size distribution. J. Math. Biol., (1984) 19:227–248. [CrossRef] [Google Scholar]
  106. O. Diekmann, K. Korvasovà. A didactical note on the advantage of using two parameters in Hopf bifurcation studies. Journal of biological dynamics (2013) 7 (Suppl. 1), 21–30. [CrossRef] [PubMed] [Google Scholar]
  107. D. Dingli, A. Traulsen, J. M. Pacheco. Stochastic dynamics of hematopoietic tumor stem cells. Cell Cycle (2007), 6 : 461–6. [CrossRef] [PubMed] [Google Scholar]
  108. D. Dingli, J. M. Pacheco. Ontogenic growth of the haemopoietic stem cell pool in humans. Proc R Sci B (2007), 274 : 2497–501. [CrossRef] [Google Scholar]
  109. M. D’Inverno, R. Saunders. Agent-Based Modelling of Stem Cell Self-organisation in a Niche. In : Lecture Notes in Computer Science. Berlin/Heidelberg : Springer, (volume 3464/2005), 2008. [Google Scholar]
  110. M. Doumic. Analysis of a Population Model Structured by the Cells Molecular Content. Math. Model. Nat. Phenom. (2007) Vol. 2, No. 3, 121–152. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  111. M. Doumic, A. Marciniak-Czochra, B. Perthame, J.P. Zubelli. A structured population model of cell differentiation. SIAM Journal on Applied Mathematics (2011) 71 (6), 1918–1940. [CrossRef] [Google Scholar]
  112. I. Drobnjak, A.C. Fowler, M.C. Mackey. Oscillations in a maturation model of blood cell production. SIAM J. Appl. Math. (2006), 66(6), 2027–2048. [CrossRef] [Google Scholar]
  113. A. Ducrot, V. Volpert. On a Model of Leukemia Development with a Spatial Cell Distribution. Math. Model. Nat. Phenom. (2007) Vol. 2, No. 3, pp. 101–120. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  114. A. Ducrot, F. LeFoll, P. Magal, H. Murakawa, J. Pasquier, G. F. Webb. An in vitro cell population dynamics model incorporating cell size, quiescence, and contact inhibition, Math. Mod. Meth. Appl. Sci. Vol.21 (2011), DOI No: 10.1142/S0218202511005404, 871–892. [Google Scholar]
  115. X. Dupuis. Optimal Control of Leukemic Cell Population Dynamics. Math. Model. Nat. Phenom. (2014) Vol. 9, No. 1, pp. 4–26. DOI: 10.1051/mmnp/20149102. [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  116. J. Dyson, E. Sanchez, R. Villella-Bressan, G. F. Webb. Stabilization of telomeres in nonlinear models of proliferating cell lines. J Theor Biol. (2007);244(3):400–8. Feb 7 [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  117. J. Dyson, R. Villella-Bressan, G. F. Webb. A singular transport equation modelling a proliferating maturity structured cell population, Canadian Appl. Math. Quart., Vol.4, No.1 (1996), 65–95. [MathSciNet] [Google Scholar]
  118. J. Dyson, R. Villella-Bressan, G. F. Webb. Hypercyclicity of a transport equation with delays, J. Nonl. Anal. Theory Meth. Appl., Vol. 29, No. 12 (1997), 1343–1351. [CrossRef] [Google Scholar]
  119. J. Dyson, R. Villella-Bressan, G. F. Webb. A maturity structured model of a population of proliferating and quiescent cells, Archives of Control Sciences, Vol. 9 (XLV) No. 1-2 (1999), 201–225. [Google Scholar]
  120. J. Dyson, R. Villella-Bressan, G. F. Webb. An age and maturity structured model of cell population dynamics, Mathematical Models in Medical and Health Science, Proceedings of the Conference on Mathematical Models in Medical and Health Sciences, Vanderbilt University Press, (1999), 99–116. [Google Scholar]
  121. J. Dyson, R. Villella-Bressan, G. F. Webb. A Nonlinear age and maturity structured model of population dynamics. I. Basic Theory. J. Math. Anal. Appl. Vol. 242 (2000), 93–104. [CrossRef] [Google Scholar]
  122. J. Dyson, R. Villella-Bressan, G. F. Webb. A Nonlinear age and maturity structured model of population dynamics. II. Chaos. J. Math. Anal. Appl. Vol. 242 (2000), 255–270. [CrossRef] [Google Scholar]
  123. J. Dyson, R. Villella-Bressan, G. F. Webb. Asynchronous exponential growth in an age structured population of proliferating and quiescent cells. Math. Biosci., Vol. 177-178 (2002), 73–83. [CrossRef] [PubMed] [Google Scholar]
  124. J. Dyson, R. Villella-Bressan, G. F. Webb. A semilinear transport equation with delays. Int. J. Math. Math. Sci. Vol. 6, No. 32 (2003), 2011–2026. [CrossRef] [Google Scholar]
  125. C. Engel, M. Loeffler, H. Franke, S. T. Schmitz. Endogenous thrombopoietin serum levels during multicycle chemotherapy British Journal of Haematology (1999) 105, 832–838. [CrossRef] [PubMed] [Google Scholar]
  126. C. Engel, M. Scholz, M. Loeffler. A computational model of human granulopoiesis to simulate the hematotoxic effects of multicycle polychemotherapy. BLOOD (2004), 104 (8) 2323–2331. [CrossRef] [PubMed] [Google Scholar]
  127. N. Eymard · N. Bessonov O. Gandrillon · M. J. Koury V. Volpert. The role of spatial organization of cells in erythropoiesis J Math Biol. (2015) Jan;70(1-2):71-97. doi: 10.1007/s00285-014-0758-y. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  128. S. Fischer, P. Kurbatova, N. Bessonov, O. Gandrillon, V. Volpert, F. Crauste. Modelling erythroblastic islands: using a hybrid model to assess the function of central macrophage. J. Theo. Biol., (2012) 298, 92–106. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  129. C. Foley, S. Bernard, M.C. Mackey. Cost-effective G-CSF therapy strategies for cyclical neutropenia: Mathematical modelling based hypotheses. J. Theor. Biol. (2006), 238:754–763. [CrossRef] [PubMed] [Google Scholar]
  130. C. Foley, M.C. Mackey. Dynamic hematological disease: A review. J. Math. Biol. (2009), 58, 1, 285–322. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  131. C. Foley, M.C. Mackey. Mathematical model for G-CSF administration after chemotherapy. J. Theor. Biol. (2009), 257, 27–44. DOI:10.1016/j.jtbi.2008.09.043. [CrossRef] [PubMed] [Google Scholar]
  132. J. Foo, M. W. Drummond, B. Clarkson, T. Holyoke, F. Michor. Eradication of chronic myeloid leukemia stem cells: a novel mathematical model predicts no therapeutic benefit of adding G-CSF to imatinib. PLoS Computational Biology (2009) 5, e10000503. (PDF) [Google Scholar]
  133. P. Fortin M.C. Mackey. Periodic chronic myelogenous leukemia: Spectral analysis of blood cell counts and etiological implications, Br. J. Haematol. (1999), 104, 336–345. [CrossRef] [PubMed] [Google Scholar]
  134. A. Fowler, M.C. Mackey. Relaxation oscillations in a class of delay differential equations. SIAM J. Appl. Math. (2002), 63, 299–323. [CrossRef] [Google Scholar]
  135. J. Galle J, G. Aust, G. Schaller, T. Beyer, D. Drasdo. Individual cell-based models of the spatio-temporal organisation of multicellular systems - achievements and limitations. Cytometry (2006) 69A : 704–10. [Google Scholar]
  136. P. Getto, A. Marciniak-Czochra. Mathematical Modelling as a Tool to Understand Cell Self-renewal and Differentiation Mammary Stem Cells: Methods and Protocols (2015) 247–266. [Google Scholar]
  137. I. Glauche, M. Cross, M. Loeffler, I. Roeder. Lineage specification of hematopoietic stem cells: mathematical modeling and biological implications. Stem cells (Dayton, Ohio) 25 (2007), 1791–9. [CrossRef] [PubMed] [Google Scholar]
  138. I. Glauche, M. Horn, I. Roeder. Leukaemia stem cells: hit or miss? British Journal of Cancer 96 (2007), 677–9. [CrossRef] [PubMed] [Google Scholar]
  139. I. Glauche, K. Horn, M. Horn, L. Thielecke, M. A. Essers, A. Trumpp, I. Roeder. Therapy of chronic myeloid leukaemia can benefit from the activation of stem cells: simulation studies of different treatment combinations. British journal of cancer 106 (2012) 1742–52. [CrossRef] [PubMed] [Google Scholar]
  140. I. Glauche, I. Roeder. In silico hematology. 42 (2014) 19. [Google Scholar]
  141. H. Goris, M. Loeffler, B. Bungart, S. Schmitz, W. Nijhof, Hemopoiesis during thiamphenicol treatment. I. Stimulation of stem cells during eradication of intermediate cell stages, Exp. Hematol., 17 (1989), 957–961. [PubMed] [Google Scholar]
  142. H. Goris, B. Bungart, M. Loeffler, W. Nijhof. Migration of stem cells and progenitors between marrow and spleen following a thiamphenicol treatment of mice, Exp. Hematol. 18 (1990) 400–407. [PubMed] [Google Scholar]
  143. A. Grabosch, G. F. Webb. Asynchronous exponential growth in transition probability models of the cell cycle, SIAM J. Math. Anal. 18, (1987), 4, 897–907. No. [Google Scholar]
  144. M. Gyllenberg. The age structure of populations of cells reproducing by asymmetric division, in Mathematics in biology and medicine, V. Capasso, E. Grosso and S.L. Paveri-Fontana (Eds.), Springer Lecture Notes in Biomathematics, (1985), 57, 320–327. [Google Scholar]
  145. M. Gyllenberg, H. J. A. M. Heijmans. An abstract delay-differential equation modelling size dependent cell growth and division, SIAM J. Math. Anal. (1987), 18, 74–88. [CrossRef] [MathSciNet] [Google Scholar]
  146. M. Gyllenberg, G. F. Webb. Age-size structure in populations with quiescence. Math. Biosci., (1987) 86(1):67–95. [CrossRef] [Google Scholar]
  147. M. Gyllenberg, G. F. Webb. Asynchronous exponential growth of semigroups of nonlinear operators, J. Math. Anal. Appl. 167, 2 (1992), 443–467. No. [CrossRef] [Google Scholar]
  148. H. Haeno, R. L. Levine, D. G. Gilliland, F. Michor. A progenitor cell origin of myeloid malignancies. Proc. Natl. Acad. Sci. U S A (2009) 106, 16616–16621. [CrossRef] [PubMed] [Google Scholar]
  149. A. Halanay, D. Cândea, I. R. Rădulescu. Existence and Stability of Limit Cycles in a Two-delays Model of Hematopoiesis Including Asymmetric Division. Math. Model. Nat. Phenom. (2014) Vol. 9, No. 1, 58–78. DOI: 10.1051/mmnp/20149105. [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  150. D. Hasenclever, O. Brosteanu, T. Gerike, M. Loeffler. Modelling of chemotherapy: The effective dose approach. Ann. Hematol. (2001), 80: B89–B94. [PubMed] [Google Scholar]
  151. C. Haurie, D.C. Dale, M.C. Mackey. Cyclical neutropenia and other periodic hematological disorders: A review of mechanisms and mathematical models, Blood (1998), 92, 2629–2640. [PubMed] [Google Scholar]
  152. C. Haurie, D.C. Dale, M.C. Mackey. Cyclical neutropenia and other periodic hematological disorders: A review of mechanisms and mathematical models, Blood (1998), 92, 2629–2640. [PubMed] [Google Scholar]
  153. C. Haurie, D.C. Dale, 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, Exper. Hematol. (1999), 27, 401–409. [CrossRef] [PubMed] [Google Scholar]
  154. C. Haurie, D.C. Dale, R. Rudnicki, M.C. Mackey. Modeling of complex neutrophil dynamics in the grey collie. J. theor. Biol. (2000), 204, 505–519. [CrossRef] [PubMed] [Google Scholar]
  155. C. Haurie, R. Person, D.C. Dale, M.C. Mackey. Hematopoietic dynamics in grey collies, Exper. Hematol. (1999), 27, 1139–1148. [CrossRef] [PubMed] [Google Scholar]
  156. T. Hearn, C. Haurie, M.C. Mackey. Cyclical neutropenia and the peripheral control of white blood cell production, J. Theor. Biol. (1998), 192, 167–181. [CrossRef] [PubMed] [Google Scholar]
  157. R. Hoffman, E.J. Benz, L.E. Silberstein, H. Heslop, J. Weitz and J. Anastasi. Hematology: Basic Principles and Practice, 6th edition. Churchill Livingstone, Elsevier, 2102. [Google Scholar]
  158. M. Horn, I. Glauche, M. C. Müller, R. Hehlmann, A. Hochhaus, M. Loeffler, I. Roeder. Model-based decision rules reduce the risk of molecular relapse after cessation of tyrosine kinase inhibitor therapy in chronic myeloid leukemia. Blood 121 (2013) 378–84. [CrossRef] [PubMed] [Google Scholar]
  159. M. Horn, M. Loeffler, I. Roeder. Mathematical modeling of genesis and treatment of chronic myeloid leukemia. Cells, tissues, organs 188 (2008), 236-47. [CrossRef] [PubMed] [Google Scholar]
  160. S. Huang, Y. P. Guo, G. May, T. Enver. Bifurcation dynamics in lineage-commitment in bipotent progenitor cells. Dev. biol. (2007), 305, 695–713. [Google Scholar]
  161. E. V. Hulse. Recovery of Erythropoiesis after Irradiation: A Quantitative Study in the Rat. Brit. J. Haemat., (1963), 9, 365–375. [CrossRef] [Google Scholar]
  162. A. Krinner, I. Roeder, M. Loeffler, M. Scholz. Merging concepts - coupling an agent-based model of hematopoietic stem cells with an ODE model of granulopoiesis. BMC systems biology 7 (2013) 117. [CrossRef] [PubMed] [Google Scholar]
  163. M. Johnson, G. F. Webb. Resonances in age structured cell population models of periodic chemotherapy, Internat. J. Appl. Sci. Comp., Vol. 3, No. 1 (1996), 57–67. [Google Scholar]
  164. N. D. Kazarinoff, P. van den Driessche, P. Control of oscillations in hematopoiesis, Science (1979), 203, 1348–1350. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  165. E. Kelemen, I. Cserhati, B. Tanos. Demonstration and some properties of human thrombopoietin in thrombocythemic sera, Acta Haematol., (1958), 20, 350–355. [CrossRef] [PubMed] [Google Scholar]
  166. E. A. King-Smith, A. Morley. Computer simulation of granulopoiesis: normal and impaired granulopoiesis, Blood (1970), 36, 254–262. [PubMed] [Google Scholar]
  167. J. Kirk, J. S. Orr, C. S. Hope. A Mathematical Analysis of Red Blood Cell and Bone Marrow Stem Cell Control Mechanisms. British Journal of Haematology, (1968), 15, 1, 35–46. [CrossRef] [PubMed] [Google Scholar]
  168. L. Kold-Andersen, M.C. Mackey. Resonance in periodic chemotherapy: A case study of acute myelogenous leukemia. J. Theor. Biol. (2001), 209, 113–130. [CrossRef] [PubMed] [Google Scholar]
  169. C. Kou, M. Adimy, A. Ducrot. On the dynamics of an impulsive model of hematopoiesis. Journal of Mathematical Modelling and Natural Phenomena (2009) 4(2), 89–112. [CrossRef] [EDP Sciences] [Google Scholar]
  170. M. Koury, M. Bondurant, Erythropoietin retards DNA breakdown and prevents pro- grammed death in erythroid progenitor cells, Science, 248 (1990), pp. 378–381. [CrossRef] [PubMed] [Google Scholar]
  171. P. Kurbatova, S. Bernard, N. Bessonov, F. Crauste, I. Demin, C. Dumontet, S. Fischer, V. Volpert. Hybrid model of erythropoiesis and leukemia treatment with cytosine arabinoside. SIAM J. App. Math. (2011) 71 (6), 2246-2268. [CrossRef] [MathSciNet] [Google Scholar]
  172. A. Lasota, M. C. Mackey, The Extinction of Slowly Evolving Dynamical Systems, J. Math. Biology (1980), 10, 333–345 [CrossRef] [MathSciNet] [Google Scholar]
  173. A. Lasota, M.C. Mackey, M. Wazewska-Czyzewska, Minimizing therapeutically induced anemia, J. Math. Biol. (1981) 13, 149–158. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  174. A. Lasota, M.C. Mackey, Globally asymptotic properties of proliferating cell populations, J. Math. Biol. (1984) 19, 43–62. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  175. A. Lasota, M. Ważewska-Czyżewska, Matematyczne problemy dynamiki układu krwinek czerwonych (Mathematical problems of the dynamics of red blood cell population), (in Polish), Matematyka Stosowana (1976), 6:23–40. [Google Scholar]
  176. A. Lasota, K. Loskot, M.C. Mackey. Stability properties of proliferatively coupled cell replication models, Acta Biotheor., 39 (1991), 1–14. [CrossRef] [PubMed] [Google Scholar]
  177. A. Lasota, M.C. Mackey. Cell division and the stability of cellular replication, J. Math. Biol., 38, (1999), 241–261. [CrossRef] [Google Scholar]
  178. U. Ledzewicz, H. Schättler. A Review of Optimal Chemotherapy Protocols: From MTD towards Metronomic Therapy. Math. Model. Nat. Phenom. Vol. 9, No. 4, (2014), 131–152. DOI: 10.1051/mmnp/20149409. [CrossRef] [EDP Sciences] [Google Scholar]
  179. F. Lévi, A. Altinok, J. Clairambault, A. Goldbeter. Implications of circadian clocks for the rhythmic delivery of cancer therapeutics. Phil. Trans. Roy. Soc. A (2008), 366 (1880), 3575–3598. [CrossRef] [Google Scholar]
  180. J. Lei, M.C. Mackey. Stochastic differential delay equation, moment stability, and appplication to hematopoietic stem cell regulation system. SIAM J. Appl. Math., 67(2) (2007), 387–407. [CrossRef] [Google Scholar]
  181. J. Lei, M. C. Mackey. Multistability in an age-structured model of hematopoiesis: Cyclical neutropenia. J. Theor. Biol., 270 (2011), 143–153. [CrossRef] [PubMed] [Google Scholar]
  182. J. Lei, M. C. Mackey. Understanding and treating cytopenia through mathematical modeling in Systems Biology Approach to Blood (ed. S. Corey, M. Kimmel, J. Leonard), Springer-Verlag (2013). [Google Scholar]
  183. A. Liso, F. Castiglione, A. Cappuccio, F. Stracci, R. F. Schlenk, S. Amadori, C. Thiede, S. Schnittger, P. J. M. Valk, K. Doehner, M. F. Martelli, M. Schaich, J. Krauter, A. Ganser, M. P. Martelli, N. Bolli, B. Loewenberg, T. Haferlach, G. Ehninger, F. Mandelli, H. Doehner, F. Michor, B. Falini. A one-mutation mathematical model can explain the age incidence of AML with mutated nucleophosmin (NPM1). Haematologica, 93 (2008), 1219–1226. [CrossRef] [PubMed] [Google Scholar]
  184. M. Loeffler. Modelling the effects of continuous irradiation on murine haematopoiesis. British Journal of Radiology, (S26) (2002), 188–197. [Google Scholar]
  185. M. Loeffler, H. E. Wichmann, A comprehensive mathematical model of stem cell proliferation which reproduces most of the published experimental results, Cell Tissue Kinet., 13 (1980), 543–561. [PubMed] [Google Scholar]
  186. M. Loeffler, P. Herkenrath, H. E. Wichmann, B.I. Lord, M.J. Murphy, The kinetics of hematopoietic stem cells during and after hypoxia - A model analysis, Blood, 49, (1984), 427–439. [Google Scholar]
  187. M. Loeffler, B. Bungart, H. Goris, S. Schmitz, W. Nijhof, Hemopoiesis during thiamphenicol treatment. II. A theoretical analysis shows consistency of new new data with a previously hypothesized model of stem cell regulation. Exp. Hematol. 17 (1989), 962–967. [PubMed] [Google Scholar]
  188. M. Loeffler, K. Pantel, H. Wulff, H. E. Wichmann, A mathematical model of erythropoiesis in mice and rats, Part 1. Structure of the model, Cell Tissue Kinet., 22 (1989), 13–30. [PubMed] [Google Scholar]
  189. M. Loeffler, K. Pantel, A mathematical model of erythropoiesis suggests an altered plasma volume control as cause for anemia in aged mice. Exp. Gerontology, 25 (1990), 483–495. [CrossRef] [Google Scholar]
  190. M. Loeffler, I. Roeder. Tissue Stem Cells: definition, plasticity, heterogeneity, self organization and models - a conceptual approach. Cells Tissues Organs, 171 (1) (2002), 8–26. [CrossRef] [PubMed] [Google Scholar]
  191. M. Loeffler, I. Roeder. Conceptual models to understand tissue stem cell organization. Current Opinion in Hematology, 11, (2004), 81–87 . [CrossRef] [PubMed] [Google Scholar]
  192. M. Loeffler, A. D. Tsodikov, A. Y. U. Yakolev, A cure model with time-changing risk factor: An application to the analysis of secondary leukemia. Statistics in Medicine, 17 (1998), 27–40. [CrossRef] [PubMed] [Google Scholar]
  193. M.C. Mackey. Mathematical models of hematopoietic cell replication and control, pp. 149-178 in The Art of Mathematical Modelling: Case Studies in Ecology, Physiology and Biofluids (H.G. Othmer, F.R. Adler, M.A. Lewis, and J.C. Dallon eds.) Prentice Hall, 1997. [Google Scholar]
  194. M.C. Mackey. Cell kinetic status of hematopoietic stem cells. Cell Prolif., 34, (2001), 71–83. [CrossRef] [PubMed] [Google Scholar]
  195. M.C. Mackey, U. an der Heiden. Dynamic diseases and bifurcations in physiological control systems, Funk. Biol. Med., 1 (1982), 156–164. [Google Scholar]
  196. M. C. Mackey, A.A.G. Aprikyan, D.C. Dale. The rate of apoptosis in post mitotic neutrophil precursors of normal and neutropenic humans. Cell Prolif., 36 (2003), 27–34. [CrossRef] [PubMed] [Google Scholar]
  197. M.C. Mackey, P. Dörmer. Enigmatic hemopoiesis, in Biomathematics and Cell Kinetics (ed. M. Rotenberg), Elsevier/North Holland, (1981), 87–103. [Google Scholar]
  198. M. C. Mackey, L. Glass, Oscillation and chaos in physiological control systems. Science, 197 (1977), 287–289. [CrossRef] [PubMed] [Google Scholar]
  199. M.C. Mackey, P. Dörmer, Continuous maturation of proliferating erythroid precursors. Cell and Tissue Kinetics, 15, (1982), 381–392. [PubMed] [Google Scholar]
  200. M.C. Mackey, J. Milton. Feedback, delays, and the origins of blood cell dynamics. Comm. on Theor. Biol., 1 (1990), 299–327. [Google Scholar]
  201. M.C. Mackey, C. Ou, L. Pujo-Menjouet, J. Wu. Periodic oscillations of blood cell populations in chronic myelogenous leukemia. SIAM J. Math. Anal., 38(1), (2006), 166–187. [CrossRef] [MathSciNet] [Google Scholar]
  202. M.C. Mackey, R. Rudnicki. Global stability in a delayed partial differential equation describing cellular replication. J. Math. Biol., 33 (1994), 89–109. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  203. M.C. Mackey, R. Rudnicki. A new criterion for the global stability of simultaneous cell replication and maturation processes. J. Math. Biol., 38 (1999), 195–219. [CrossRef] [Google Scholar]
  204. J.M. Mahaffy, J. Bélair, M.C. Mackey. Hematopoietic model with moving boundary condition and state dependent delay. J. Theor. Biol., 190, (1998), 135–146. [CrossRef] [PubMed] [Google Scholar]
  205. A. Marciniak-Czochra, A. D. Ho, W. Jäger T. Stiehl, W. Wagner. Modeling of asymmetric cell division in hematopoietic stem cells–regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev., 18(3) (2009), 377–85. doi: 10.1089/scd.2008.0143. [CrossRef] [PubMed] [Google Scholar]
  206. A. Marciniak-Czochra, T. Stiehl, W. Wagner. Modeling of replicative senescence in hematopoietic development. Aging (Albany NY), 1 (8) (2009), 723–732. [CrossRef] [PubMed] [Google Scholar]
  207. A. Marciniak-Czochra, T. Stiehl. Mathematical models of hematopoietic reconstitution after stem cell transplantation Model Based Parameter Estimation. Bock, H.G., Carraro, T., äger, W., Körkel, S., Rannacher, R., Schlöder, J.P., (Eds.) Contributions in Mathematical and Computational Sciences, Vol. 3, Springer Verlag, (2013), 191–206. [Google Scholar]
  208. A. Maximow. The Lymphocyte as a stem cell common to different blood elements in embryonic development and during the post-fetal life of mammals. Originally in German: Folia Haematologica 8. (1909), 125–134. (English translation: Cell Ther. Transplant.(2009), 1:e.000032.01. doi:10.3205/ctt-2009-en-000032.01). [Google Scholar]
  209. D. Metcalf. The granulocyte-macrophage colony-stimulating factors. Science, (1985), 229(4708): 16–22. doi:10.1126/science.2990035, PMID 2990035. [CrossRef] [PubMed] [Google Scholar]
  210. J. A. J. Metz, O. Diekmann, editors. The dynamics of physiologically structured populations, volume 68 of Lecture Notes in Biomathematics. Springer-Verlag, Berlin, 1986. Papers from the colloquium held in Amsterdam, 1983. [Google Scholar]
  211. P. Michel. Optimal Proliferation Rate in a Cell Division Model. Math. Model. Nat. Phenom. Vol. 1, No. 2, (2006), 23–44. [CrossRef] [EDP Sciences] [Google Scholar]
  212. F. Michor. Quantitative approaches to analyzing imatinib-treated chronic myeloid leukemia. Trends in Pharmacological. Sciences, 28 (2007), 197–199. [Google Scholar]
  213. F. Michor. Chronic myeloid leukemia blast crisis arises from progenitors. Stem Cells, 25 (2007), 1114–1118. [CrossRef] [PubMed] [Google Scholar]
  214. F. Michor. The long-term response to imatinib treatment of CML. British Journal of Cancer, 96 (2007), 679–680. [Google Scholar]
  215. F. Michor, T. P. Hughes, Y. Iwasa, S. Branford, N.P. Shah, C. L Sawyers, M. A. Nowak Dynamics of chronic myeloid leukemia. Nature, 435 (2005), 1267–1270. [CrossRef] [PubMed] [Google Scholar]
  216. F. Michor, Y. Iwasa, M. A. Nowak. The age incidence of chronic myeloid leukemia can be explained by a one-mutation model. Proc. Natl. Acad. Sci. U S A (2006) 103, 14931–14934. [CrossRef] [PubMed] [Google Scholar]
  217. J. Milton, M.C. Mackey. Periodic haematological diseases: Mystical entities or dynamical disorders?, J. Roy. Coll. Phys. (Lond) 23 (1989), 236–241. [Google Scholar]
  218. C. L. Mouser, E. S. Antoniou, J. Tadros, E. K. Vassiliou, A model of hematopoietic stem cell proliferation under the influence of a chemotherapeutic agent in combination with a hematopoietic inducing agent. Theoretical Biology and Medical Modelling (2014) 11:4 DOI: 10.1186/1742-4682-11-4. [CrossRef] [Google Scholar]
  219. T. Niederberger, H. Failmezger, D. Uskat, D. Poron, I. Glauche, N. Scherf, I. Roeder, T. Schroeder, A. Tresch. Factor graph analysis of live cell imaging data reveals mechanisms of cell fate decisions. Bioinformatics (Oxford, England) (2015). [Google Scholar]
  220. W. Nijhof, H. Goris, B. Dontje, J. Dresz, M. Loeffler. Quantification of the cell kinetic effects of G-CSF using a model of human granulopoiesis, Experimental Hematology 21 (1993), 496–501. [PubMed] [Google Scholar]
  221. G. C. Nooney. Iron kinetics and erythron development. Biophysical Journal, vol. 5, (1965), 755–765. [CrossRef] [PubMed] [Google Scholar]
  222. I. Østby, L. S. Rusten, G. Kvalheim, P. Grøttum. A mathematical model for reconstitution of granulopoiesis after high dose chemotherapy with autologous stem cell transplantation. J. Math. Biol., 47(2) (2003), 101–36. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  223. I. Østby, R. Winther. Stability of a model of human granulopoiesis using continuous maturation. J. Math. Biol., 49(5) (2004), 501–36. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  224. H. Özbay, C. Bonnet, H. Benjelloun, J. Clairambault. Stability analysis of cell dynamics in leukemia. Mathematical Modelling of Natural Phenomena, 7(1) (2012), 203–234. [Google Scholar]
  225. K. Pantel, M. Loeffler, B. Bungart, H. E. Wichmann, A mathematical model of erythropoiesis in mice and rats. Part 4. Differences between bone marrow and spleen, Cell Tissue Kinet. 23 (1990), 283–297. [PubMed] [Google Scholar]
  226. J. F. Perez, C. P. Malta, C. P., F. A. B. Coutinho. Qualitative analysis of oscillations in isolated populations of flies. J. Theoret. Biol., 71 (1978), 505–514. [CrossRef] [MathSciNet] [Google Scholar]
  227. J. Pimentel. Agent Based Model for the Production Mechanism and Control of Blood Cells in the Human Body. Proceedings of The National Conference On Undergraduate Research (NCUR), The University of North Carolina at Asheville, North Carolina, 2006. [Google Scholar]
  228. A. Plesa, G. Ciuperca V. Louvet, L. Pujo-Menjouet, S. Génieys, C. Dumontet, X. Thomas, V. Volpert. Diagnostics of the AML with immunophenotypical data. Math. Model. Nat. Phenom. Vol. 1, No. 2, (2006), 104–123. [CrossRef] [EDP Sciences] [Google Scholar]
  229. G. Prindull, B. Prindull, N. Meulen. Haematopoietic stem cells (CFUc) in human cord blood. Acta Paediatr Scand. 67(4) (1978), 413–6. [CrossRef] [PubMed] [Google Scholar]
  230. L. Pujo-Menjouet, M. C. Mackey. Contribution to the study of periodic chronic myelogenous leukemia. Comptes Rendus Biologiques (2004), 327, 235–244. [Google Scholar]
  231. L. Pujo-Menjouet, S. Bernard, M.C. Mackey. Long period oscillations in a G0 model of hematopoietic stem cells. SIAM J. Appl. Dyn. Sys., (2005), 4:312–332. [Google Scholar]
  232. H. Quastler. The analysis of cell population kinetics. Cell Proliferation, Ed. by L. T. Lanierton and R. J . M. Fry, p. 18. Blackwell Scientific Publications, Oxford (1963), 18–34. [Google Scholar]
  233. H. Quastler, F. G. Sherman. Cell population kinetics in the intestinal epithelium of the mouse. Exp Cell Res., Jun; 17(3) (1959), 420–438. [CrossRef] [PubMed] [Google Scholar]
  234. N. M. Rashidi, M. K. Scott, N. Scherf, A. Krinner, J. S. Kalchschmidt, K. Gounaris, M.E. Selkirk, I. Roeder, C. Lo Celso. In vivo time-lapse imaging of mouse bone marrow reveals differential niche engagement by quiescent and naturally activated hematopoietic stem cells. Blood, 124(1) (2014), 79–83. [CrossRef] [PubMed] [Google Scholar]
  235. U. Reincke, M. Loeffler, H. E. Wichmann, B. Harrisson. The kinetics of granulopoiesis in long term mouse bone marrow culture. Part I. Int.J.Cell Cloning, 2 (1984), 394–407. [CrossRef] [Google Scholar]
  236. C. Roberts, L. Kean, D. Archer, C. Balkan, L. L. Hsu. Murine and math models for the level of stable mixed chimerism to cure beta-thalassemia by nonmyeloablative bone marrow transplantation. Ann. N.Y. Acad. Sci. 1054 (2005), 423–8. [CrossRef] [Google Scholar]
  237. I. Roeder. Quantitative stem cell biology - Computational studies in the hematopoietic system. Curr. Opin. Hematol., 13 (4) (2006), 222–228. [CrossRef] [PubMed] [Google Scholar]
  238. I. Roeder, K. Braesel, R. Lorenz, M. Loeffler. Stem cell fate analysis revisited: interpretation of individual clone dynamics in the light of a new paradigm of stem cell organization. Journal of biomedicine, biotechnology, (2007), 84656. [Google Scholar]
  239. I. Roeder, G. de Haan, C. Engel, W. Nijhof, B. Dontje, M. Loeffler. Interactions of Erythropoietin, Granulocyte Colony-Stimulating Factor, Stem Cell Factor, and Interleukin-11 on Murine Hematopoiesis During Simultaneous Administration, Blood, 91 9 (1998), 3222–3229. [PubMed] [Google Scholar]
  240. I. Roeder I, M. d’Inverno. New experimental and theoretical investigations of hematopoietic stem cells and chronic myeloid leukemia. Blood cells, molecules and diseases 43 (2009), 88–97. [CrossRef] [Google Scholar]
  241. I. Roeder, J. Galle, M. Loeffler. Theoretical concepts of tissue stem cell organization. Tissue Stem Cells, Edited by Christopher S . Potten, Robert B . Clarke, James Wilson, Andrew G . Renehan CRC Press (2006), 17–35. [Google Scholar]
  242. I. Roeder and I. Glauche. Towards an understanding of lineage specification in hematopoietic stem cells: A mathematical model for the interaction of transcription factors GATA-1 and PU.1. J. Theor. Biol., 241 4 (2006), 852–865. [CrossRef] [PubMed] [Google Scholar]
  243. I. Roeder, I. Glauche. Towards an understanding of lineage specification in hematopoietic stem cells: a mathematical model for the interaction of transcription factors GATA-1 and PU.1. Journal of theoretical biology, 241 (2006), 852–65. [Google Scholar]
  244. I. Roeder, I. Glauche Pathogenesis, treatment effects, and resistance dynamics in chronic myeloid leukemia–insights from mathematical model analyses. Journal of molecular medicine (Berlin Germany), 86 (2008), 17–27. [CrossRef] [Google Scholar]
  245. I. Roeder, M. Herberg, M. Horn. An “age”-structured model of hematopoietic stem cell organization with application to chronic myeloid leukemia. Bulletin of mathematical biology, 71 (2009), 602–26. [Google Scholar]
  246. I. Roeder, M. Kamminga, K. Braesel, B. Dontje, G. de Haan, M. Loeffler. Competitive clonal hematopoiesis in mouse chimeras explained by a stochastic model of stem cell organization. Blood, 15 2 (2005), 609–616. [CrossRef] [Google Scholar]
  247. I. Roeder, M. Horn, I. Glauche, A. Hochhaus, M. C. Mueller, M. Loeffler. Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications. Nature medicine, 12 (2006), 1181–4. [Google Scholar]
  248. I. Roeder, K. Horn, H. B. Sieburg, R. Cho, C. Muller-Sieburg, M. Loeffler. Characterization and quantification of clonal heterogeneity among hematopoietic stem cells: a model-based approach. Blood, 112 (2008), 4874–83 [CrossRef] [PubMed] [Google Scholar]
  249. I. Roeder, M. Loeffler. A Novel Dynamic Model of Hematopoietic Stem Cell Organization Based on the Concept of Within-Tissue Plasticity. Experimental Hematology, 30 (8) (2002), 853–861. [CrossRef] [PubMed] [Google Scholar]
  250. I. Roeder, M. Loeffler, P. J. Quesenberry, G. A. Colvin, J. F. Lambert. Quantitative tissue stem cell modeling. Blood, 102 (3) (2003), 1143–1144. [CrossRef] [Google Scholar]
  251. I. Roeder, R. Lorenz. Asymmetry of stem cell fate and the potential impact of the niche: observations, simulations, and interpretations. Stem cell reviews 2 (2006), 171–80. [CrossRef] [PubMed] [Google Scholar]
  252. S. I. Rubinow. A Maturity-Time Representation for Cell Populations. Biophys J., Oct; 8(10) (1968), 1055–1073. doi: 10.1016/S0006-3495(68)86539-7 [CrossRef] [PubMed] [Google Scholar]
  253. S. I. Rubinow, J. L. Lebowitz. A mathematical model of neutrophil production and control in normal man. J. Math. Biol., 1 (1975), 187–225. [CrossRef] [PubMed] [Google Scholar]
  254. R. Rudnicki. Global stability of a nonlinear model of cellular populations, J. Tech. Phys., 38 (1997), 333–336. [Google Scholar]
  255. R. Rudnicki. Chaoticity of the blood cell production system. Chaos, 19(4) (2009), 043112. doi: 10.1063/1.3258364. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  256. R. Rudnicki, K. Pichór. Asymptotic behaviour of Markov semigroups and applications to transport equations, Bull. Polish Acad. Sci. Math., 45 (1997), 379–397. [MathSciNet] [Google Scholar]
  257. A. Safarishahrbijari, A. Gaffari. Parameter identification of hematopoiesis mathematical model – periodic chronic myelogenous leukemia. Wspolczesna Onkol, 17 (1) (2013), 73–77, DOI: 10.5114/wo.2013.33778. [CrossRef] [Google Scholar]
  258. E. Sánchez, O. Arino, M. Kimmel. Noncompact semigroups of operators generated by cell kinetics models, Differential Integral Equations, 4 (6) (1991), 1233–1249. [MathSciNet] [Google Scholar]
  259. M. Santillan, J.M. Mahaffy, J. Bélair, M.C. Mackey. Regulation of platelet production: The normal response to perturbation and cyclical platelet disease. J. theor. Biol., 206, (2000), 585–603. [CrossRef] [PubMed] [Google Scholar]
  260. S. Scheding, M. Loeffler, V. Anselsetter, H. E. Wichmann. A mathematical approach to benzo[a]pyrene-induced hematotoxicity, Arch Toxicology, 66 (1992), 546–550. [CrossRef] [Google Scholar]
  261. S. Schirm, C. Engel, M. Loeffler, M. Scholz. A biomathematical model of human erythropoiesis under erythropoietin and chemotherapy administration. PLOS ONE, Vol. 8 (6), (2013), e65630. [CrossRef] [PubMed] [Google Scholar]
  262. S. Schirm, C. Engel, M. Loeffler, M. Scholz. A combined model of human erythropoiesis and granulopoiesis under growth factor and chemotherapy treatment. Theoretical Biology and Medical Modelling, 11, (2014), 24. [CrossRef] [Google Scholar]
  263. S.Schirm, C. Engel, M. Loeffler, M. Scholz. Modelling chemotherapy effects on granulopoiesis. BMC Syst Biol., (2014) 8(1), 138. [CrossRef] [Google Scholar]
  264. S. Schmitz, M. Loeffler, J. B. Jones, R. D. Lange, H. E. Wichmann. Synchrony of marrow maturation as origin of cyclic hemopoiesis, Cell Tissue Kinet., 23 (1990), 425–441. [PubMed] [Google Scholar]
  265. S. Schmitz, H. Franke, M. Loeffler, H. E. Wichmann, V. Diehl. Reduced variance of bone-marrow transit time of granulopoiesis - a possible pathomechanism of human cyclic neutropenia. Cell Prolif., 27 (1994), 655–667. [CrossRef] [Google Scholar]
  266. S. Schmitz, H. Franke, M. Loeffler, H. E. Wichmann, V. Diehl. Model analysis of the contrasting effects of GM-CSF and G-CSF treatment on peripheral blood neutrophils observed in three patients with childhood-onset cyclic neutropenia. British Journal of Hematology, 95 4 (1996), 616–625. [CrossRef] [Google Scholar]
  267. M. Scholz, C. Engel, M. Loeffler. Modelling Human Granulopoiesis under Polychemotherapy with G-CSF Support. Journal of Mathematical Biology, 10.1007 (2004), 285–295. [Google Scholar]
  268. M. Scholz, C. Engel, M. Loeffler. Model-based design of chemotherapeutic regimens that account for heterogeneity in leucopoenia. British Journal of Haematology, 132 (2006), 723–735. [CrossRef] [PubMed] [Google Scholar]
  269. M. Scholz, A. Gross, M. Loeffler. A biomathematical model of human thrombopoiesis under chemotherapy. Journal of Theoretical Biology, Vol. 264 (2), (2010), 287–300. [CrossRef] [PubMed] [Google Scholar]
  270. H. Schwegler, M.C. Mackey. Fluctuations in circulating cell numbers following chemotherapy or bone marrow transplant, J. Math. Biol., 32 (1994), 761–770. [CrossRef] [PubMed] [Google Scholar]
  271. L. Sharney, L. R. Wasserman, L. Schwartz, D. Tendler. Multiple pool analysis as applied to erythro-kinetics. Ann. N. Y. Acad. Sci., 10 108 (1963), 230–49. [Google Scholar]
  272. E. Shochat, V. Rom-Kedar, L. A. Segel. G-CSF control of neutrophils dynamics in the blood. Bull Math Biol., 69(7) (2007), 2299–338. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  273. J. A. Smith, L. Martin. Do cells cycle?, Proc. Natl. Acad. Sci. USA, 70 (1973), 1263–1267. [CrossRef] [PubMed] [Google Scholar]
  274. T. Stiehl, N. Baran, A. D. Ho, A. Marciniak-Czochra. Clonal selection and therapy resistance in acute leukaemias: mathematical modelling explains different proliferation patterns at diagnosis and relapse. Journal of The Royal Society Interface, 11 (2014) (94), 20140079. [Google Scholar]
  275. T. Stiehl, N. Baran, A. D. Ho, A. Marciniak-Czochra. Cell division patterns in acute myeloid leukemia stem-like cells determine clinical course: a model to predict patient survival. Cancer research, 75 (6), (2015), 940–949. [CrossRef] [PubMed] [Google Scholar]
  276. T. Stiehl, A. Marciniak-Czochra. Characterization of stem cells using mathematical models of multistage cell lineages. Mathematical and Computer Modelling, 53 (7), (2011), 1505–1517. [CrossRef] [Google Scholar]
  277. T. Stiehl, A. Marciniak-Czochra. Mathematical modeling of leukemogenesis and cancer stem cell dynamics. Mathematical Modelling of Natural Phenomena, 7 (01) (2012), 166–202. [Google Scholar]
  278. A. Świerniak, J. Klamka. Local Controllability of Models of Combined Anticancer Therapy with Delays in Control. Math. Model. Nat. Phenom. (2014) Vol. 9, No. 4, 216–226. DOI: 10.1051/mmnp/20149413. [CrossRef] [EDP Sciences] [Google Scholar]
  279. J. Swinburne, M.C. Mackey. Cyclical thrombocytopenia: Characterization by spectral analysis and a review. J. Theor. Med. (2000), 2, 81–91. [CrossRef] [Google Scholar]
  280. H. Talibi Alaoui, R. Yafia. Stability and Hopf bifurcation in an approachable haematopoietic stem cells model. Math Biosci. (2007) 206(2), 176–84. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  281. T. Tian, K. Smith-Miles. Mathematical modeling of GATA-switching for regulating the differentiation of hematopoietic stem cell. BMC Systems Biology (2014), 8(Suppl 1):S8 [CrossRef] [Google Scholar]
  282. J. E. Till, E. A. McCulloch, L. Siminovitch. A Stochastic Model of Stem Cell Proliferation, Based on the Growth of Spleen Colony-Forming Cells. Proceedings of the National Academy of Sciences of the United States of America, (1964), 15, Vol. 51, No. 1, 29–36. [Google Scholar]
  283. A. D. Tsodikov, D. Hasenclever, M. Loeffler. Regression with bounted outcome score: Evaluation of power by bootstrap and simulation in a chronic myelogenous leukemia clinical trial, Statistics in Medicine 17 (1998), 1909–1922. [CrossRef] [PubMed] [Google Scholar]
  284. V. Vainstein, Y. Ginosar, M. Shoham, A. Ianovski A. Rabinovich, Y. Kogan, V. Selitser, Z. Agur. Improving Cancer Therapy by Doxorubicin and Granulocyte Colony-Stimulating Factor: Insights from a Computerized Model of Human Granulopoiesis. Math. Model. Nat. Phenom. (2006), Vol. 1, No. 2, 70–80. [CrossRef] [EDP Sciences] [Google Scholar]
  285. H. von Foerster. (1959), Some remarks on changing populations. F. Stohlman, ed., The kinetics of cell proliferation, Grune and Stratton, New York, 1959), 382–407. [Google Scholar]
  286. G. F. Webb. Theory of nonlinear age-dependent population dynamics, volume 89 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker Inc., New York, 1985. [Google Scholar]
  287. G. F. Webb. An operator-theoretic formulation of asynchronous exponential growth. Trans. Amer. Math. Soc., (1987) 303(2) 751–763. [CrossRef] [MathSciNet] [Google Scholar]
  288. G. F. Webb. Semigroup methods in populations dynamics: Proliferating cell populations, Semigroup Theory and Applications, Lecture Notes in Pure and Applied Mathematics Series, Vol. 116, Marcel Dekker, New York, 1989, 441–449. [Google Scholar]
  289. G. F. Webb. Asynchronous exponential growth in differential equations with homogeneous nonlinearities, Differential Equations in Banach Spaces, Lecture Notes in Pure and Applied Mathematics Series, Vol. 148, Marcel Dekker, New York, (1993), 225–233. [Google Scholar]
  290. G. F. Webb. Asynchronous exponential growth in differential equations with asymptotically homogeneous nonlinearities, Adv. Math. Sci. Appl., Vol. 3 (1994), 43–55. [Google Scholar]
  291. G. F. Webb. Periodic and chaotic behavior in structured models of cell population dynamics, Recent Developments in Evolution Equations, Pitman Res. Notes Math. Series. 324 (1995), 40–49. [Google Scholar]
  292. G. F. Webb. Structured population dynamics, Banach Center Publications, Polish Academy of Sciences Institute of Mathematics, Mathematical Modelling of Population Dynamics, Vol. 63 (2004), 123-163. [Google Scholar]
  293. G. F. Webb. Population models structured by age, size, and spatial position, in Structured Population Models in Biology and Epidemiology. Lecture Notes in Mathematics, Vol. 1936, Springer-Verlag, Berlin-New York (2008), 1–49. [Google Scholar]
  294. Z. L. Whichard, C. A. Sarkar, M. Kimmel, S. J. Corey. Hematopoiesis and its disorders: a systems biology approach. Blood (2010) 115: 2339-2347 doi:10.1182/blood-2009-08-215798. [CrossRef] [PubMed] [Google Scholar]
  295. H. E. Wichmann, M. Loeffler, Probability of self-renewal: Assumptions and limitations. A commentary. Blood Cells, 9, (1983), 475–483. [Google Scholar]
  296. H. E. Wichmann, M. Loeffler, U. Reincke, The kinetics of granulopoiesis in long term mouse bone marrow culture. Part II. Int.J.Cell Cloning, 2 (1984), 408–424. [CrossRef] [Google Scholar]
  297. H. E. Wichmann, M. Loeffler, S. Schmitz, A concept of hemopoietic regulation and its biomathematical realisation. Blood Cells, 14 (1988), 411–429. [PubMed] [Google Scholar]
  298. H. E. Wichmann, M. Loeffler, K. Pantel, H. Wulff, A mathematical model of erythropoiesis in mice and rats. Part 2. Stimulated erythropoiesis. Cell Tissue Kinet., 22, (1989), 31–49. [PubMed] [Google Scholar]
  299. O. Wolkenhauer, C. Auffray, O. Brass, J. Clairambault, A. Deutsch, D. Drasdo, F. Gervasio, L. Preziosi, P. Maini, A. Marciniak-Czochra, C. Kossow, L. Kuepfer, K. Rateitschak, I. Ramis-Conde, B. Ribba, A. Schuppert, R.Smallwood, G. Stamatakos, F. Winter, H. Byrne. Enabling multiscale modeling in systems medicine. Genome Med (2014) 6, 3 pages. [Google Scholar]
  300. H. Wulff, H. E. Wichmann, M. Loeffler, K. Pantel, A mathematical model of erythropoiesis in mice and rats. Part 3. Suppressed erythropoiesis. Cell Tissue Kinet., 22 (1989), 51–61. [PubMed] [Google Scholar]
  301. C. Zhuge, J. Lei, M.C. Mackey. Neutrophil dynamics in response to chemotherapy and G-CSF. J. Theor. Biol. (2012) 293, 111–120. [CrossRef] [PubMed] [Google Scholar]

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