| Summary: | In this thesis, we consider a mathematical model describing the dynamics of
normal and leukemic hematopoietic stam cells and differentiated cells in bone
marrow. We focus on a chronic myeloid leukemia, a cancer of blood cells
resulting from a malignant transformation of hematopoietic stem cells.
Homeostatis regulates the proliferation of normal hematopoietic stem cells and
leads the dynamics to an equilibrium. This mechanism is partially efficient for
leukemic cells. We define homeostatis by a functional of either hematopoietic
stem cells, differentiated cells or both cells line.
We determine the equilibrium points for each scenario, and each scenario
provides three equilibrium points, there are the chronic equilibrium, the blastic
equilibrium and the non-pathological equilibrium. Then we analyse the stability of
the equilibrium points. We prove that normal and leukemic cells can not coexist
for a long time. Numerical simulations is given to illustrate the stability of the
equilibrium points.
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