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In this paper, we consider a more general model describing the dynamics of Hematopoietic  Stem Cells (HSC) model with one delay. Its dynamics are studied in terms of local  stability and Hopf bifurcation. We prove the existence of the possible steady state and  their stability with respect to the time delay and without delay. We show that a sequence  of Hopf bifurcations occur at the positive steady state as the delay crosses some critical  values. We illustrate our results by some numerical simulations

Qualitative Properties in a More General Delayed Hematopoietic Stem Cells Model