  The main purpose of this paper is to study the existence of periodic
solutions for a nonautonomous differential-difference system describing the
dynamics of hematopoietic stem cell (HSC) population under some external
periodic regulatory factors at the cellular cycle level. The starting model is
a nonautonomous system of two age-structured partial differential equations
describing the HSC population in quiescent ($G_0$) and proliferating ($G_1$,
$S$, $G_2$ and $M$) phase. We are interested on the effects of a periodically
time varying coefficients due for example to circadian rhythms or to the
periodic use of certain drugs, on the dynamics of HSC population. The method of
characteristics reduces the age-structured model to a nonautonomous
differential-difference system. We prove under appropriate conditions on the
parameters of the system, using topological degree techniques and fixed point
methods, the existence of periodic solutions of our model.
