Bulletin of Mathematical Biology

, Volume 72, Issue 7, pp 1732–1759 | Cite as

Stability Analysis of a Simplified Yet Complete Model for Chronic Myelogenous Leukemia

  • Marie Doumic-Jauffret
  • Peter S. Kim
  • Benoît Perthame
Original Article

Abstract

We analyze the asymptotic behavior of a partial differential equation (PDE) model for hematopoiesis. This PDE model is derived from the original agent-based model formulated by Roeder (Nat. Med. 12(10):1181–1184, 2006), and it describes the progression of blood cell development from the stem cell to the terminally differentiated state.

To conduct our analysis, we start with the PDE model of Kim et al. (J. Theor. Biol. 246(1):33–69, 2007), which coincides very well with the simulation results obtained by Roeder et al. We simplify the PDE model to make it amenable to analysis and justify our approximations using numerical simulations. An analysis of the simplified PDE model proves to exhibit very similar properties to those of the original agent-based model, even if for slightly different parameters. Hence, the simplified model is of value in understanding the dynamics of hematopoiesis and of chronic myelogenous leukemia, and it presents the advantage of having fewer parameters, which makes comparison with both experimental data and alternative models much easier.

Keywords

Age-structured equations Hematopoiesis Chronic myelogenous leukemia Model simplification 

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Copyright information

© Society for Mathematical Biology 2009

Authors and Affiliations

  • Marie Doumic-Jauffret
    • 1
    • 2
  • Peter S. Kim
    • 3
  • Benoît Perthame
    • 1
    • 2
  1. 1.INRIA Paris-RocquencourtBANGLeChesnay CedexFrance
  2. 2.Laboratoire J.-L. LionsUniversité Pierre et Marie Curie, CNRS UMR7598Paris Cedex 05France
  3. 3.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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