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The main purpose of this paper is to study the existence of periodicsolutions for a nonautonomous differential-difference system describing thedynamics of hematopoietic stem cell (HSC) population under some externalperiodic regulatory factors at the cellular cycle level. The starting model isa nonautonomous system of two age-structured partial differential equationsdescribing 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 periodicallytime varying coefficients due for example to circadian rhythms or to theperiodic use of certain drugs, on the dynamics of HSC population. The method ofcharacteristics reduces the age-structured model to a nonautonomousdifferential-difference system. We prove under appropriate conditions on theparameters of the system, using topological degree techniques and fixed pointmethods, the existence of periodic solutions of our model.

Periodic solutions for a nonautonomous mathematical model of hematopoietic stem cell dynamics