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Table of contents
1 General Introduction
Motivation
1.1 Hematopoietic Stem Cells
1.1.1 HSC dynamics : Mathematical modeling
1.1.2 Our contribution to HSC dynamics modeling
1.2 Immunosenescence, Cancer and Stem Cells
1.2.1 The Link Between Aging and Cancer : Mathematical modeling
1.2.2 Our contribution to the modeling of the interactions between aging and cancer
Organization of the thesis
I Hematopoietic Stem Cell Dynamics
2 Age-structured model of hematopoiesis dynamics with growth factordependent coefficients
Abstract
2.1 Introduction
2.2 Age-structured partial differential model
2.3 Reduction to a delay differential system
2.4 Positivity and boundedness of solutions
2.5 Existence of steady states
2.6 Global asymptotic stability of trivial steady state
2.7 Local asymptotic stability of the positive steady state
2.8 Numerical illustrations
3 Hematopoietic Stem Cells dynamics model with state dependant delay
Abstract
3.1 Age-structured partial differential model
3.2 Properties of the model and existence of steady states
3.3 Linearization and Characteristic Equation
3.4 Global Asymptotic Stability of the Trivial Steady State
3.5 Transcritical Bifurcation and Hopf Bifurcation
3.6 Numerical illustrations
3.6.1 Discussion
II Cancer cells Proliferation: Immune System Response
4 Interactions between immune challenges and cancer cells proliferation: timing does matter!
Abstract
4.1 Introduction
4.2 Materials and Methods
4.3 Results
Influence of timing and duration of a single immunosuppressive challenge
Combined effect of duration and the number of immunosuppressive challenges
Influence of immune activation challenges combined with immunosenescence
4.4 Discussion
Conclusion and Perspectives
Appendix A Supplementary data to Chapter 4
Bibliography
