Math. Model. Nat. Phenom.
Volume 4, Number 2, 2009Delay equations in biology
|Page(s)||28 - 47|
|Published online||26 March 2009|
- M. Adimy, F. Crauste. Global stability of a partial differential equation with distributed delay due to cellular replication. Nonlinear Analysis, 54 (2003), 1469–1491. [CrossRef] [MathSciNet]
- 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. [CrossRef] [MathSciNet]
- 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.
- 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]
- M. Adimy, F. Crauste, S. Ruan. Periodic Oscillations in Leukopoiesis Models with Two Delays. J. Theo. Biol., 242 (2006), 288–299. [CrossRef] [MathSciNet] [PubMed]
- J. Bélair, M.C. Mackey, J.M. Mahaffy. Age-structured and two-delay models for erythropoiesis. Math. Biosci., 128 (1995), 317–346. [CrossRef] [PubMed]
- 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]
- 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]
- F.J. Burns, I.F. Tannock. On the existence of a G0 phase in the cell cycle. Cell Tissue Kinet., 19 (1970), 321–334.
- 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]
- F. Crauste. Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model. Math. Bio. Eng., 3 (2006), No. 2, 325–346.
- 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. [CrossRef] [PubMed]
- J. Hale, S.M. Verduyn Lunel. Introduction to functional differential equations. Applied Mathematical Sciences 99. Springer-Verlag, New York, 1993.
- 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]
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- M.C. Mackey. Unified hypothesis of the origin of aplastic anaemia and periodic hematopoiesis. Blood, 51 (1978), 941–956. [PubMed]
- 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]
- 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]
- 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]
- 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]
- L. Pujo-Menjouet, M.C. Mackey. Contribution to the study of periodic chronic myelogenous leukemia. C. R. Biologies, 327 (2004), 235–244. [CrossRef] [PubMed]
- L.F. Shampine, S. Thompson. Solving DDEs in Matlab. Appl. Numer. Math., 37 (2001), 441–458. [CrossRef] [MathSciNet]
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