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All issues Volume 9 / No 1 (2014) Math. Model. Nat. Phenom., 9 1 (2014) 58-78 References
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Issue
Math. Model. Nat. Phenom.
Volume 9, Number 1, 2014
Issue dedicated to Michael Mackey
Page(s) 58 - 78
DOI https://doi.org/10.1051/mmnp/20149105
Published online 07 February 2014
  1. M. Adimy. Integrated semigroups and delay differential equations. J. of Math. Anal. and Appl., 177 (1993), no. 1, 125–134. [CrossRef] [Google Scholar]
  2. M. Adimy, F. Crauste, S. Ruan. Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics. Nonlinear Analysis: Real World Applications, 6 (2005), no. 4, 651–670. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Adimy, F. Crauste, S. Ruan. A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM Journal on Applied Mathematics, 65 (2005), no. 4, 1328–1352. [Google Scholar]
  4. M. Adimy, F. Crauste, S. Ruan. Periodic oscillations in leukopoiesis models with two delays. J. Theor. Biol., 242 (2006), 288-299. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  5. 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, 27 (2006), 4, 1091-1107. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Adimy, F. Crauste. Delay Differential Equations and Autonomous Oscillations in Hematopoietic Stem Cell Dynamics Modeling. Math. Model. Nat. Phenom., Vol. 7 (2012), No. 6, 1-22. [Google Scholar]
  7. J. Belair, M.C. Mackey. A model for the regulation of mammalian platelet production. Annals of the New York Academy of Sciences, 504 (1987), no. 1, 280–282. [Google Scholar]
  8. E. Beretta, Y. Kuang. Geometric stability switch criteria in delay differential systems with delay dependent parameters. SIAM J. Math. Anal., 33 (2002), no. 5, 1144-1165. [CrossRef] [MathSciNet] [Google Scholar]
  9. S. Bernard, J. Belair, M.C. Mackey. Oscillations in cyclical neutropenia: new evidence based on mathematical modelling. J. Theor. Biology, 223 (2003), 283-298. [Google Scholar]
  10. N. Chafee. A bifurcation problem for a functional differential equation of finitely retarded type. J. Math. Anal. and Appl., 35 (1991), 312-348. [CrossRef] [Google Scholar]
  11. C. Colijn, A.C. Fowler, M.C. Mackey. High frequency spikes in long period blood cell oscillations. Journal of mathematical biology, 53 (2006), no. 4, 499-519. [Google Scholar]
  12. C. Colijn, M.C. Mackey. A mathematical model of hematopoiesis I-Periodic chronic myelogenous leukemia. J. Theor. Biology, 237 (2005), 117-132. [Google Scholar]
  13. K. Cooke, Z. Grossman. Discrete Delay, Distributed Delay and Stability Switches. J. Math. Anal. Appl., 86 (1982), 592-627. [CrossRef] [MathSciNet] [Google Scholar]
  14. K. Cooke, P. van den Driessche. On zeros of some transcendental equations. Funkcialaj Ekvacioj, 29 (1986), 77-90. [MathSciNet] [Google Scholar]
  15. M.W.N. Deininger, J.M. Goldman, J.V. Melo. The molecular biology of chronic myeloid leukemia. Blood, 96 (2000), no. 10, 3343–3356. [PubMed] [Google Scholar]
  16. I. Drobnjak, A.C. Fowler. A Model of Oscillatory Blood Cell Counts in Chronic Myelogenous Leukaemia. Bulletin of mathematical biology, 73 (2011), no. 12, 2983–3007. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  17. L.E. El’sgol’ts, S.B. Norkin. Introduction to the theory of differential equations with deviating arguments. (in Russian). Nauka, Moscow, 1971. [Google Scholar]
  18. K. Engelborghs, T. Luzyanina, D. Roose. Numerical bifurcation analysis of delay differential equations using dde-biftool. ACM Transactions on Mathematical Software (TOMS), 28 (2002), no. 1, 1–21. [CrossRef] [MathSciNet] [Google Scholar]
  19. A. Friedman. Cancer as Multifaceted Disease. Math. Model. Nat. Phenom., Vol. 7 (2012), no. 1, 3–28. [CrossRef] [EDP Sciences] [Google Scholar]
  20. J.M. Goldman, J.V. Melo. Chronic myeloid leukemia—advances in biology and new approaches to treatment. New England Journal of Medicine, 349 (2003), no. 15, 1451–1464. [CrossRef] [Google Scholar]
  21. J. Hale. Introduction to Functional Differential Equations. Springer, New York, 1977. [Google Scholar]
  22. J. Hale, S.M. Verduyn Lunel. Theory of Functional Differential Equations, Springer, New York, 1993. [Google Scholar]
  23. B.D. Hassard, N.D. Kazarinoff, Y.H. Wan. Theory and Applications of Hopf Bifurcation. London Mathem. Soc. Lecture Note Series 41, Cambridge University Press, 1981. [Google Scholar]
  24. C. Haurie, D.C. Dale, R. Rudnicki, M.C. Mackey. Modeling complex neutrophil dynamics in the grey collie. Journal of theoretical biology, 204 (2000), no. 4, 505–519. [Google Scholar]
  25. N.L. Komarova, D. Wodarz. Drug resistance in cancer: principles of emergence and prevention. Proceedings of the National Academy of Sciences of the United States of America, 102 (2005), no. 27, 9714–9719. [Google Scholar]
  26. M.C. Mackey. Mathematical models of hematopoietic cell replication and control. Case Studies in Mathematical Modeling–Ecology, Physiology and Cell Biology. New Jersey, Prentice-Hall, 151-182, 1997. [Google Scholar]
  27. J.M. Mahaffy, J. Belair, M.C. Mackey. Hematopoietic model with moving boundary condition and state dependent delay: applications in erythropoiesis. Journal of theoretical biology, 190 (1998), no. 2, 135–146. [Google Scholar]
  28. A. Marciniak-Czochra, T. Stiehl, W. Wagner. Modeling of replicative senescence in hematopoietic development. Aging, 1 (2009), no. 8, 723–732. [Google Scholar]
  29. F. Michor, T.P. Hughes, Y. Iwasa, S. Branford, N.P. Shah, C.L. Sawyers, M.A. Nowak. Dynamics of chronic myeloid leukaemia. Nature, 435 (2005), 7046, 1267-1270. [CrossRef] [PubMed] [Google Scholar]
  30. F. Michor, Y. Iwasa, M.A. Nowak. Dynamics of cancer progression. Nature Reviews Cancer 4 (2004), no. 3, 197–205. [CrossRef] [PubMed] [Google Scholar]
  31. H. Ozbay, C. Bonnet, H. Benjelloun and J. Clairambault. Stability Analysis of Cell Dynamics in Leukemia. Math. Model. Nat. Phenom., Vol. 7 (2012), no. 1, 203–234. [Google Scholar]
  32. L. Pujo-Menjouet, S. Bernard, M. C. Mackey. Long period oscillations in a G0 model of hematopoietic stem cells. SIAM J. Appl. Dynam. Sys., 4 (2005), no. 2, 312–332. [Google Scholar]
  33. L. Pujo-Menjouet, M.C. Mackey. Contribution to the study of periodic chronic myelogenous leukemia. C. R. Biologies, 327 (2004), 235-244. [Google Scholar]
  34. 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), no. 10, 1181–1184. [Google Scholar]
  35. C.L. Sawyers. Chronic myeloid leukemia. New England Journal of Medicine, 340 (1999), no. 17, 1330–1340. [CrossRef] [Google Scholar]
  36. L. Shampine, S. Thompson. Solving ddes in matlab. Applied Numerical Mathematics, 37 (2001), no. 4, 441–458. [CrossRef] [MathSciNet] [Google Scholar]
  37. T. Stiehl, A. Marciniak-Czochra. Mathematical Modeling of Leukemogenesis and Cancer Stem Cell Dynamics. Math. Model. Nat. Phenom., Vol. 7 (2012), no. 1, 166–202. [Google Scholar]
  38. C. Tomasetti, D. Levy. Role of symmetric and asymmetric division of stem cells in developing drug resistance. PNAS, 107 (2010), 39, 16766-16771. [CrossRef] [Google Scholar]

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