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., Nat. Med., 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, JTB, 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.
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