| Summary: | We propose and analyze an age-structured partial differential model for
hematopoietic stem cell dynamics, in which proliferation, differentiation
and apoptosis are regulated by growth factor concentrations.
By integrating the age-structured system over the age and
using the characteristics method, we reduce it to a delay differential system.
We investigate the existence and stability of the steady states of the reduced
delay differential system. By constructing a Lyapunov function, the trivial
steady state, describing cell's dying out, is proven to be globally
asymptotically stable when it is the only equilibrium of the system.
The asymptotic stability of the positive steady state, the most
biologically meaningful one, is analyzed using the characteristic equation.
This study may be helpful in understanding the uncontrolled proliferation
of blood cells in some hematological disorders.
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