Free Access
Math. Model. Nat. Phenom.
Volume 4, Number 2, 2009
Delay equations in biology
Page(s) 28 - 47
Published online 26 March 2009
  1. M. Adimy, F. Crauste. Global stability of a partial differential equation with distributed delay due to cellular replication. Nonlinear Analysis, 54 (2003), 1469–1491. [Google Scholar]
  2. M. Adimy, F. Crauste. Modelling and asymptotic stability of a growth factor-dependent stem cells dynamics model with distributed delay. Discret. Cont. Dyn. Sys. Ser. B, 8 (2007), No. 1, 19–38. [Google Scholar]
  3. M. Adimy, F. Crauste, L. Pujo-Menjouet. On the stability of a maturity structured model of cellular proliferation. Discret. Cont. Dyn. Sys. Ser. A, 12 (2005), No. 3, 501–522. [Google Scholar]
  4. 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]
  5. M. Adimy, F. Crauste, S. Ruan. Periodic Oscillations in Leukopoiesis Models with Two Delays. J. Theo. Biol., 242 (2006), 288–299. [Google Scholar]
  6. J. Bélair, M.C. Mackey, J.M. Mahaffy. Age-structured and two-delay models for erythropoiesis. Math. Biosci., 128 (1995), 317–346. [CrossRef] [PubMed] [Google Scholar]
  7. 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]
  8. S. Bernard, J. Bélair, M.C. Mackey. Oscillations in cyclical neutropenia: New evidence based on mathematical modeling. J. Theor. Biol., 223 (2003), 283–298. [CrossRef] [PubMed] [Google Scholar]
  9. F.J. Burns, I.F. Tannock. On the existence of a G0 phase in the cell cycle. Cell Tissue Kinet., 19 (1970), 321–334. [Google Scholar]
  10. C. Colijn, C. Foley, M.C. Mackey. G-CSF treatment of canine cyclical neutropenia: A comprehensive mathematical model. Exper. Hematol., 35 (2007), No. 6, 898–907. [CrossRef] [Google Scholar]
  11. F. Crauste. Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model. Math. Bio. Eng., 3 (2006), No. 2, 325–346. [Google Scholar]
  12. P. Fortin, M.C. Mackey. Periodic chronic myelogenous leukemia: Spectral analysis of blood cell counts and etiological implications. Brit. J. Haematol., 104 (1999), 336–345. [Google Scholar]
  13. J. Hale, S.M. Verduyn Lunel. Introduction to functional differential equations. Applied Mathematical Sciences 99. Springer-Verlag, New York, 1993. [Google Scholar]
  14. C. Haurie, D.C. Dale, M.C. Mackey. Cyclical neutropenia and other hematological disorders: A review of mechanisms and mathematical models. Blood, 92 (1998), No. 8, 2629–2640. [PubMed] [Google Scholar]
  15. L.G. Lajtha. On DNA labeling in the study of the dynamics of bone marrow cell populations, in: Stohlman, Jr., F. (Ed), The Kinetics of Cellular Proliferation, Grune and Stratton, New York (1959) 173–182. [Google Scholar]
  16. M.C. Mackey. Unified hypothesis of the origin of aplastic anaemia and periodic hematopoiesis. Blood, 51 (1978), 941–956. [PubMed] [Google Scholar]
  17. 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]
  18. 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]
  19. 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]
  20. L. Pujo-Menjouet, S. Bernard, M.C. Mackey. Long period oscillations in a G0 model of hematopoietic stem cells. SIAM J. Appl. Dyn. Systems, 4 (2005), No. 2, 312–332. [CrossRef] [Google Scholar]
  21. L. Pujo-Menjouet, M.C. Mackey. Contribution to the study of periodic chronic myelogenous leukemia. C. R. Biologies, 327 (2004), 235–244. [Google Scholar]
  22. L.F. Shampine, S. Thompson. Solving DDEs in Matlab. Appl. Numer. Math., 37 (2001), 441–458. [Google Scholar]

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.