Free Access
Math. Model. Nat. Phenom.
Volume 7, Number 1, 2012
Cancer modeling
Page(s) 235 - 244
Published online 25 January 2012
  1. L.H. Abbott, F. Michor. Mathematical models of targeted cancer therapy. British Journal of Cancer 95 (2006), 1136–1141. [CrossRef] [PubMed]
  2. M. Adimy, F. Crauste, A. Halanay, M. Neamţu, D. Opriş. Stability of Limit Cycles in a Pluripotent Stem Cell Dynamics Model. Chaos, Solitons&Fractals, 27(4) (2006), 1091–1107. [CrossRef] [MathSciNet]
  3. M. Adimy, F. Crauste, S. Ruan. A mathematical study of the hematopoiesis process with application to chronic myelogenous leukemia. SIAM J. Appl. Math. 65(4) (2005), 1328–1352. [CrossRef] [MathSciNet]
  4. M. Adimy, F. Crauste, S. Ruan. Periodic oscillations in leukopoiesis models with two delays. Journal of Theoretical Biology 242 (2006), 288-299. [CrossRef] [MathSciNet] [PubMed]
  5. S. Bernard, J. Belair, M.C. Mackey. Oscillations in cyclical neutropenia : new evidence based on mathematical modelling. J. Theor. Biology 223 (2003), 283–298. [CrossRef] [PubMed]
  6. B. Clarkson, A. Strife, D. Wisniewski, U. Lambek, C. Liu. Chronic myelogenous leukemia as a paradigm of early cancer and possible curative strategies. Leukemia 17 (2003), 1211–1262. [CrossRef] [PubMed]
  7. C. Colijn, M.C. Mackey. A mathematical model of hematopoiesis I-Periodic chronic myelogenous leukemia. J. Theor. Biology 237 (2005), 117–132. [CrossRef] [PubMed]
  8. Aristide Halanay, Differential Equations : stability, oscilations, time lags. Academic Press, 1966.
  9. A. Halanay. Periodic Solutions in Mathematical Models for Hematological Diseases under Treatment. IEEE Proceedings of the 8-th IFAC Workshop on Time-Delay Systems, Sept. 1-3, Sinaia, Romania, 2009.
  10. A. Halanay. Stability analysis for a mathematical model of chemotherapy action in hematological diseases. Bull. Sci. Soc. Roumaine Sci. Math. 53 (101) (2010), no. 1, 3-10.
  11. A. Halanay. Treatment induced periodic solutions in some mathematical models of tumoral cell dynamics. Mathematical Reports !2(62) (2010), no. 4, in press.
  12. J. Hale. Theory of Functional Differential Equations. Springer, New York, 1977.
  13. V. Kolmanovskii, A. Myshkis. Applied Theory of Functional Differential Equations. Kluwer Academic Publishers, Dordrecht, 1992.
  14. M.A. Krasnoselskii. Shift operator on orbits of differential equations. Nauka, Moskow, 1966 (in Russian).
  15. M.C. Mackey, A unified hypothesis of the origin of aplastic anemia and periodic hematopoiesis, Blood 51 (1978), 941–956. [PubMed]
  16. M.C. Mackey, C. Ou, L. Pujo-Menjouet, J. Wu. Periodic oscillations of blood cell population in chronic myelogenous leukemia. SIAM J. Math. Anal. 38 (2006), 166–187. [CrossRef] [MathSciNet]
  17. F. Michor, T. Hughes, Y. Iwasa, S. Branford, N.P. Shah, C. Sawyers, M. Novak. Dynamics of chronic myeloid leukemia. Nature 435 (2005), 1267–1270. [CrossRef] [PubMed]
  18. H. Moore, N.K. Li. A mathematical model for chronic myelogenous leukemia (CML) and T-cell interaction. J. Theor. Biol. 227 (2004), 513–523. [CrossRef] [PubMed]
  19. L. Pujo-Menjouet, C. Mackey. Contribution to the study of periodic chronic myelogenous leukemia. Comptes Rendus Biol, 327 (2004), 235–244. [CrossRef] [PubMed]
  20. C. Sawyers. Chronic Myeloid Leukemia. N. Engl. J. Med. 340 (2000), 1330–1340. [CrossRef]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.