Asymptotic behaviour of a mathematical model of hematopoietic stem cell dynamics

Abstract

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.

Keywords:

• hematopoietic stem cell
• population dynamics
• age-structured model
• asymptotic analysis
• numerical integration

2000 AMS Subject Classifications:

• 35Q80
• 35L50
• 65M25
• 92C37

Acknowledgements

O. Angulo, J.C. López-Marcos and M.A. López-Marcos were supported in part by the Ministerio de Ciencia e Innovación (Spain) project MTM2011-25238.