173
Views
3
CrossRef citations to date
0
Altmetric
Section B

Asymptotic behaviour of a mathematical model of hematopoietic stem cell dynamics

, , &
Pages 198-208 | Received 19 Oct 2012, Accepted 18 Feb 2013, Published online: 12 Apr 2013

References

  • L.M. Abia, O. Angulo, and J.C. López-Marcos, Size-structured population dynamics models and their numerical solutions, Discrete Contin. Dyn. Syst. Ser. B 4 (2004), pp. 1203–1222. doi: 10.3934/dcdsb.2004.4.1203
  • L.M. Abia, O. Angulo, and J.C. López-Marcos, Age-structured population models and their numerical solution, Ecol. Model. 188 (2005), pp. 112–136. doi: 10.1016/j.ecolmodel.2005.05.007
  • L.M. Abia, O. Angulo, J.C. López-Marcos, and M.A. López-Marcos, Numerical study on the proliferation cells fraction of a tumour cord model, Math. Comput. Model. 52 (2010), pp. 992–998. doi: 10.1016/j.mcm.2010.02.038
  • M. Adimy, F. Crauste, and S. Ruan, A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia, SIAM J. Appl. Math. 65 (2005), pp. 1328–1352. doi: 10.1137/040604698
  • M. Adimy, F. Crauste, and S. Ruan, Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics, Nonlinear Anal. Real World Appl. 6 (2005), pp. 651–670. doi: 10.1016/j.nonrwa.2004.12.010
  • M. Adimy, O. Angulo, F. Crauste, and J.C. López-Marcos, Numerical integration of a mathematical model of hematopoietic stem cell dynamics, Comput. Math. Appl. 55 (2008), pp. 337–366.
  • O. Angulo, J.C. López-Marcos, M.A. López-Marcos, and F.A. Milner, A numerical method for nonlinear age-structured population models with finite maximum age, J. Math. Anal. Appl. 361 (2010), pp. 150–160. doi: 10.1016/j.jmaa.2009.09.001
  • O. Angulo, J.C. López-Marcos, M.A. López-Marcos, and J. Martínez-Rodríguez, Numerical analysis of an open marine population model with spaced-limited recruitment, Math. Comput. Model. 52 (2010), pp. 1037–1044. doi: 10.1016/j.mcm.2010.02.020
  • O. Angulo, J.C. López-Marcos, and M.A. López-Marcos, Numerical approximation of singular asymptotic states for a size-structured population model with a dynamical resource, Math. Comput. Model. 54 (2011), pp. 1693–1698. doi: 10.1016/j.mcm.2010.12.006
  • O. Angulo, J.C. López-Marcos, M.A. López-Marcos, and J. Martínez-Rodríguez, Numerical investigation of the recruitment process in open marine population models, J. Stat. Mech. Theory Exp. (2011), pp. 1–11. doi:10.1088/1742-5468/2011/01/P01003
  • O. Angulo, J.C. López-Marcos, and M.A. Bees, Mass structured systems with boundary delay: oscillations and the effect of selective predation, J. Nonlinear Sci. 22 (2012), pp. 961–984. doi: 10.1007/s00332-012-9133-6
  • B. Bialecki, G. Fairweather, and J.C. López-Marcos, Orthogonal spline collocation for quasilinear problems with nonlocal boundary conditions, Adv. Appl. Math. Mech. (in press).
  • C. Foley and M.C. Mackey, Dynamic hematological disease: a review, J. Math. Biol. 58 (2009), pp. 285–322. doi: 10.1007/s00285-008-0165-3
  • M. Iannelli, Mathematical Theory of Age-Structured Population Dynamics, Applied Mathematics Monographs, C.N.R., Giardini Editori e Stampatori, Pisa, 1994.
  • Y. Kocak and A. Yildirim, An efficient algorithm for solving nonlinear age-structured population models by combining homotopy perturbation and Padé techniques, Int. J. Comput. Math. 88 (2011), pp. 491–500. doi: 10.1080/00207160903477159
  • M.C. Mackey, Unified hypothesis of the origin of aplastic anaemia and periodic hematopoiesis, Blood 51 (1978), pp. 941–956.
  • B.R. Smith, Regulation of hematopoiesis, Yale J. Biol. Med. 63(5) (1990), pp. 371–380.
  • W. Vainchenker, Hématopoïèse et facteurs de croissance, Encycl. Med. Chir. Hematologie, 13000 M85, Editions Techniques, Paris, 1991.
  • G.F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 89, Marcel Dekker Inc., New-York, 1985.
  • I.L. Weissman, Stem cells: units of development, units of regeneration, and units in evolution, Cell 100 (2002), pp. 157–168. doi: 10.1016/S0092-8674(00)81692-X

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.