Mathematical Analysis of a Delayed Hematopoietic Stem Cell Model with Wazewska–Lasota Functional Production Type

  • Radouane YafiaEmail author
  • M. A. Aziz Alaoui
  • Abdessamad Tridane
  • Ali Moussaoui
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 14)


In this chapter, we consider a more general model describing the dynamics of a hematopoietic stem cell (HSC) model with Wazewska–Lasota functional production type describing the cycle of proliferating and quiescent phases. The model is governed by a system of two ordinary differential equations with discrete 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 the apoptosis rate of proliferating cells. We show that a sequence of Hopf bifurcations occurs at the positive steady state as the delay crosses some critical values. We illustrate our results with some numerical simulations.


Hematopoietic Stem Cell Hopf Bifurcation Daughter Cell Delay Differential Equation Autoimmune Hemolytic Anemia 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We are very grateful to the editors and to Professor M. C. Mackey for their valuable discussions.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Radouane Yafia
    • 1
    Email author
  • M. A. Aziz Alaoui
    • 2
    • 3
    • 4
  • Abdessamad Tridane
    • 5
  • Ali Moussaoui
    • 6
  1. 1.Polydisciplinary Faculty of OuarzazateIbn Zohr UniversityOuarzazateMorocco
  2. 2.Normandie UniversityLe HavreFrance
  3. 3.ULH, LMAHLe HavreFrance
  4. 4.FR CNRS 3335Le HavreFrance
  5. 5.Department of Mathematical SciencesUnited Arab Emirates UniversityAl AinUnited Arab Emirates
  6. 6.Department of MathematicsUniversity of TlemcenTlemcenAlgeria

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