Free Access
Math. Model. Nat. Phenom.
Volume 9, Number 1, 2014
Issue dedicated to Michael Mackey
Page(s) 108 - 132
Published online 07 February 2014
  1. A. K. Abass, A. H. Lichtman, S. Pillai. Cellular and molecular immunolgy. 7th edition, Elsevier (2012). [Google Scholar]
  2. L.H. Abbott, F. Michor. Mathematical models of targeted cancer therapy. British Journal of Cancer 95 (2006), 1136–1141. [CrossRef] [PubMed] [Google Scholar]
  3. M. Adimy, F. Crauste. Delay differential equations and autonomous oscillations in Hematopoietic stem cell dynamics modeling. Math. Model. Nat. Phenom., (2012), 7(6), 1–22. [Google Scholar]
  4. M. Adimy, F. Crauste, A. Halanay, M. Neamţu, D. Opriş. Stability of limit cycles in a pluripotent stem cell dynamics model. Chaos, Solitons&Fractals (2006), 27(4), 1091–1107. [Google Scholar]
  5. M. Adimy, F. Crauste, S. Ruan. A mathematical study of the hematopoiesis process with application to chronic myelogenous leukemia. SIAM J. Appl. Math. (2005), 65(4), 1328–1352. [CrossRef] [MathSciNet] [Google Scholar]
  6. J. Beckman, S. Scheitza, P. Wernet, J. Fischer, B. Giebel. Asymmetric cell division within the human hematopoietic stem and progenitor cell compartment: identification of asymetrically segregating proteins. Blood (2007), No. 12, 109, 5494–5501. [Google Scholar]
  7. R. Bellman, K. L. Cooke. Differential-Difference equations. Academic Press New York, (1963). [Google Scholar]
  8. E. Beretta, Y. Kuang. Geometric stability switch criteria in delay differential dystems with delay-dependent darameters. SIAM J. Math. Anal. (2002), 33(5), 1144-1165. [CrossRef] [MathSciNet] [Google Scholar]
  9. E. Burger. On stability of certain economic systems. Econometrica (1956), 24, 488–493. [CrossRef] [Google Scholar]
  10. C. Colijn, M.C. Mackey. A mathematical model of hematopoiesis I-Periodic chronic myelogenous leukemia. J. Theor. Biology (2005), 237, 117–132. [Google Scholar]
  11. K. Cooke, Z. Grossman. Discrete Delay, Distribution delay and stability switches. J. Math. Anal. Appl. (1982), 86, 592–627. [CrossRef] [MathSciNet] [Google Scholar]
  12. K. Cooke, P. van den Driessche. On zeros of some transcendental equations. Funkcialaj Ekvacioj (1986), 29, 77–90. [MathSciNet] [Google Scholar]
  13. 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]
  14. A. Fridman. Cancer as multifaceted disease. Math. Model. Nat. Phenom (2012), 7, No.1, 3–28. [CrossRef] [EDP Sciences] [Google Scholar]
  15. A. Halanay. Periodic solutions in mathematical models for the treatment of chronic myelogenous leukemia. Math. Model. Nat. Phenom (2012), 7, No.1, 235–244. [Google Scholar]
  16. J. Hale. Theory of functional differential equations. Springer, New York, 1977. [Google Scholar]
  17. P. Kim, P. Lee, D. Levy. Dynamics and potential impact of the immune response to chronic myelogenous leukemia. PLoS Comput.Biol. (2008), 4(6):e1000095. [Google Scholar]
  18. P. Kim, P.Lee, D. Levy.A theory of immunodominance and adaptive regulation,Bull. Math. Biol. (2010), DOI 10.1007/s11538-010-9585-5. [Google Scholar]
  19. M.C. Mackey, C. Ou, L. Pujo-Menjouet, J. Wu. Periodic oscillations of blood cell population in chronic myelogenous leukemia. SIAM J. Math. Anal. (2006), 38, 166–187. [CrossRef] [MathSciNet] [Google Scholar]
  20. A. Marciniak-Czochra, T. Stiehl, W. Wagner. Modeling of replicative senescence in hematopoietic development. Aging (2009), 1(8), 723–732. [Google Scholar]
  21. F. Michor, T. Hughes, Y. Iwasa, S. Branford, N.P. Shah, C. Sawyers, M. Novak. Dynamics of chronic myeloid leukemia. Nature (2005), 435, 1267–1270. [CrossRef] [PubMed] [Google Scholar]
  22. H. Moore, N.K. Li. A mathematical model for chronic myelogenous leukemia (CML) and T-cell interaction. J. Theor. Biol. (2004), 227, 513–523. [CrossRef] [PubMed] [Google Scholar]
  23. S. I. Niculescu, P. S. Kim, K. Gu, P. Lee, D. Levy. Stability crossing boundaries of delay systems modeling immune dynamics in leukemia. Discrete and Continuous Dynamical Systems (2010), Series B Volume 13, No. 1, pp. 129–156. [Google Scholar]
  24. H. Ozbay, C. Bonnet, H. Benjelloun, J. Clairambault. Stability analysis of cell dynamcis in leukemia. Math. Model. Nat. Phenom. (2012), Volume 7, No. 1, 203–234. [Google Scholar]
  25. R. Radulescu, D. Candea, A. Halanay. Stability and bifurcation in a model for the dynamics of stem-like cells in leukemia under treatment. American Institute of Physics Proceedings (2012), 1493, 758–763. [Google Scholar]
  26. T. Reya. Regulation of hematopoietic stem cell self-Renewal. Recent Progress in Hormone Research (2003), 58, 283–295. [CrossRef] [PubMed] [Google Scholar]
  27. T. Stiehl, A. Marciniak-Czochra. Mathematical modeling of leukemogenesis and cancer stem cell dynamics. Math. Model. Nat. Phenom. (2012), Vol. 7, No. 1, 166–202. [Google Scholar]
  28. C. Tomasetti, D. Levi. Role of symmetric and asymmetric division of stem cells in developing drug resistance. PNAS (2010), Vol. 17 , No. 39, 16766–16771. [CrossRef] [Google Scholar]
  29. J. Zajac, L. E. Harrington. Immune response to viruses: antibody-mediated immunity. University of Alabama at Birmingham, Birmingham, AL, USA, Elsevier Ltd, 2008. [Google Scholar]

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