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

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 et al. in [35], 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 [20], 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. Key-words Age-structured equations, hematopoiesis, chronic myelogenous leukemia, model simplification. INRIA Paris-Rocquencourt, BANG, BP105, F78153 LeChesnay Cedex. Email: [email protected] Laboratoire J.-L. Lions, Université Pierre et Marie Curie, CNRS UMR7598, BC187, 4, place Jussieu, F75252 Paris cedex 05. Email: [email protected] Department of Mathematics, University of Utah, Salt Lake City, UT 84112-0090, USA. Email: [email protected] ∗Contributed comparably to this paper. 1