Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 7, Number 1, 2012
Cancer modeling
|
|
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Page(s) | 235 - 244 | |
DOI | https://doi.org/10.1051/mmnp/20127110 | |
Published online | 25 January 2012 |
- L.H. Abbott, F. Michor. Mathematical models of targeted cancer therapy. British Journal of Cancer 95 (2006), 1136–1141. [CrossRef] [PubMed] [Google Scholar]
- 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. [Google Scholar]
- 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] [Google Scholar]
- M. Adimy, F. Crauste, S. Ruan. Periodic oscillations in leukopoiesis models with two delays. Journal of Theoretical Biology 242 (2006), 288-299. [Google Scholar]
- 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]
- 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] [Google Scholar]
- C. Colijn, M.C. Mackey. A mathematical model of hematopoiesis I-Periodic chronic myelogenous leukemia. J. Theor. Biology 237 (2005), 117–132. [Google Scholar]
- Aristide Halanay, Differential Equations : stability, oscilations, time lags. Academic Press, 1966. [Google Scholar]
- 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. [Google Scholar]
- 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. [Google Scholar]
- A. Halanay. Treatment induced periodic solutions in some mathematical models of tumoral cell dynamics. Mathematical Reports !2(62) (2010), no. 4, in press. [Google Scholar]
- J. Hale. Theory of Functional Differential Equations. Springer, New York, 1977. [Google Scholar]
- V. Kolmanovskii, A. Myshkis. Applied Theory of Functional Differential Equations. Kluwer Academic Publishers, Dordrecht, 1992. [Google Scholar]
- M.A. Krasnoselskii. Shift operator on orbits of differential equations. Nauka, Moskow, 1966 (in Russian). [Google Scholar]
- M.C. Mackey, A unified hypothesis of the origin of aplastic anemia and periodic hematopoiesis, Blood 51 (1978), 941–956. [PubMed] [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- L. Pujo-Menjouet, C. Mackey. Contribution to the study of periodic chronic myelogenous leukemia. Comptes Rendus Biol, 327 (2004), 235–244. [Google Scholar]
- C. Sawyers. Chronic Myeloid Leukemia. N. Engl. J. Med. 340 (2000), 1330–1340. [Google Scholar]
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