Mathematical Analysis of a Delayed Hematopoietic Stem Cell Model with Wazewska–Lasota Functional Production Type
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.
KeywordsHematopoietic Stem Cell Hopf Bifurcation Daughter Cell Delay Differential Equation Autoimmune Hemolytic Anemia
We are very grateful to the editors and to Professor M. C. Mackey for their valuable discussions.
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