DINAMIKA GLOBAL SEL INDUK HEMATOPOIETIK DAN SEL DIFERENSIASI PADA MODEL LEUKEMIA MIELOID KRONIK (LMK) - , Rapmaida Megawaty Pangaribuan, S.Si ([Yogyakarta] : Universitas Gadjah Mada, 2013)
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.