Rad HAZU, Matematičke znanosti, Vol. 26 (2022), 201-227.

MATHEMATICAL ANALYSIS OF A MODEL FOR CHRONIC MYELOID LEUKEMIA

Fatima Zohra Elouchdi Derrar, Djamila Benmerzouk and Bedr'Eddine Ainesba

Bordeaux Mathematics Institute, UMR CNRS 52 51, Case 36, Université Victor Segalen Bordeaux 2,3 ter place de la victoire, F 33076 Bordeaux Cedex, France
e-mail: Bedreddine.ainseba@u-bordeaux.fr

Abstract.   In this paper, a mathematical analysis of a model describing the evolution of chronic myeloid leukemic with effect of growth factors is considered. The corresponding dynamics are represented by a system of ordinary differential equations of dimension 5. This system described the interactions between hematopoietic stem cells (H.S.C), hematopoietic mature cells (M.C), cancer hematopoietic stem cells, cancer hematopoietic mature cells and the associated growth factor concentration. Our research is, henceforth, carried out on the existence and the uniqueness of the solution of this system. The next substantive concern will be a discussion on the local and global stability of the corresponding steady states. Three scenarios, however, corresponding to different actions of hematopoiesis on stem cells (differentiate cells or both cells) are considered.

2020 Mathematics Subject Classification.   92B05, 34A34.

Key words and phrases.   Myeloid chronic leukemia model, cancer modeling, existence of solutions, global stability analysis, Lyapunov stability.

DOI: https://doi.org/10.21857/y6zolb6gzm

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