Asymptotic behaviour of a mathematical model of hematopoietic stem cell dynamics

We deeply researched into the asymptotic behaviour of a numerical method adapted for the solution of mathematical model of hematopoiesis which describes the dynamics of a stem cell population. We investigated the stationary solutions of the original model by their numerical approximation: we proved the existence of a numerical stationary solution that provides a good approximation to the nontrivial equilibrium solution of the problem. Also, we presented a numerical simulation which confirms this behaviour.

[1]  Smith Br.  Regulation of hematopoiesis. , 1990 .

[2]  I. Weissman,et al.  Stem Cells Units of Development, Units of Regeneration, and Units in Evolution , 2000, Cell.

[3]  Fabien Crauste,et al.  Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics , 2005, 0904.2491.

[4]  Oscar Angulo,et al.  Size-structured population dynamics models and their numerical solutions , 2004 .

[5]  Oscar Angulo,et al.  A numerical method for nonlinear age-structured population models with finite maximum age , 2010 .

[6]  Oscar Angulo,et al.  Mass Structured Systems with Boundary Delay: Oscillations and the Effect of Selective Predation , 2012, J. Nonlinear Sci..

[7]  Oscar Angulo,et al.  Age-structured population models and their numerical solution , 2005 .

[8]  G. Webb.  Theory of Nonlinear Age-Dependent Population Dynamics , 1985 .

[9]  Richard H. Elderkin.  Theory of nonlinear age-dependent population dynamics (Monographs and textbooks in pure and applied mathematics, vol. 89): By G.F. Webb. Dekker, New York (1985). vi+294 pp. $65.00 , 1987 .

[10]  Juan C. López-Marcos,et al.  Numerical integration of a mathematical model of hematopoietic stem cell dynamics , 2008, Comput. Math. Appl..

[11]  Oscar Angulo,et al.  Numerical investigation of the recruitment process in open marine population models , 2011 .

[12]  Oscar Angulo,et al.  Numerical approximation of singular asymptotic states for a size-structured population model with a dynamical resource , 2011, Math. Comput. Model..

[13]  Michael C Mackey,et al.  Dynamic hematological disease: a review , 2009, Journal of mathematical biology.

[14]  Juan C. López-Marcos,et al.  Numerical analysis of an open marine population model with spaced-limited recruitment , 2010, Math. Comput. Model..

[15]  Ahmet Yildirim,et al.  An efficient algorithm for solving nonlinear age-structured population models by combining homotopy perturbation and Padé techniques , 2011, Int. J. Comput. Math..

[16]  Oscar Angulo,et al.  Numerical study on the proliferation cells fraction of a tumour cord model , 2010, Math. Comput. Model..

[17]  Michael C. Mackey,et al.  Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis , 1978 .

[18]  Mimmo Iannelli,et al.  Mathematical Theory of Age-Structured Population Dynamics , 1995 .

[19]  Fabien Crauste,et al.  A Mathematical Study of the Hematopoiesis Process with Applications to Chronic Myelogenous Leukemia , 2009, SIAM J. Appl. Math..

[20]  D. Nathan.  Regulation of Hematopoiesis , 1990, Pediatric Research.

[21]  M C Mackey,et al.  Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. , 1978, Blood.