Sur certains modèles mathématiques en biologie et médecine.

Abstract

The main objective of this thesis is to analyze two mathematical models that describes the dynamics of cellular population in the case of chronic myeloid leukemia disease. To answer this biological problem, our work was devided into two parts : In the first part, we started with an quantitative and qualitative study for an hybrid mathematical model ([51]) that describes the dynamics of hematopoietic stem cell population in the chronic myeloid leukemia disease. First, we formulate the basic model as a one which contain two equations, one of them represent an age structured equation and the other one is an ordinary differential equation. Next to understand behaviour of our solutions we study the existence of steady state and their stability. In the second part, we studied the existence of steady states and their stability for an age structured model of leukemic diseases wich has developped by the authors ([13], [3]) in the case that the normal and leukemic stem cells proliferate from the ages a1 and a2 respectively. Then we transforme the (PDE) system to an (ODE) system in the case that the division rates and the death rates of normal stem cells and leukemia cells are constant.