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In this paper, we investigate a time-delayed model describing the dynamics of the hematopoietic stem cell population with treatment. First, we give some property results of the solutions. Second, we analyze the asymptotic behavior of the model, and study the local asymptotic stability of each equilibrium: trivial and positive ones. Next, a necessary and sufficient condition is given for the trivial steady state to be globally asymptotically stable. Moreover, the uniform persistence is obtained in the case of instability. Finally, we prove that this system can exhibits a periodic solutions around the positive equilibrium through a Hopf bifurcation.

Mathematical analysis and global dynamics for a time-delayed Chronic Myeloid Leukemia model with treatment