Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods

P Getto, M Gyllenberg, Y Nakata, F Scarabel - Journal of mathematical …, 2019 - Springer
We consider a mathematical model describing the maturation process of stem cells up to
fully mature cells. The model is formulated as a differential equation with state-dependent …

Asymptotic behavior and stability switch for a mature–immature model of cell differentiation

M Adimy, F Crauste, C Marquet - Nonlinear Analysis: Real World …, 2010 - Elsevier
We consider a nonlinear age-structured model, inspired by hematopoiesis modelling,
describing the dynamics of a cell population divided into mature and immature cells …

A model for stem cell population dynamics with regulated maturation delay

T Alarcon, P Getto, A Marciniak-Czochra… - Conference …, 2011 - aimsciences.org
We develop a structured population model for the maturation process of stem cells in the
form of a state-dependent delay differential equation. Moreover, results on existence …

Delay model of hematopoietic stem cell dynamics: asymptotic stability and stability switch

F Crauste - Mathematical Modelling of Natural Phenomena, 2009 - cambridge.org
A nonlinear system of two delay differential equations is proposed to model hematopoietic
stem cell dynamics. Each equation describes the evolution of a sub-population, either …

Stability of limit cycles in a pluripotent stem cell dynamics model

M Adimy, F Crauste, A Halanay, M Neamţu… - Chaos, Solitons & …, 2006 - Elsevier
This paper is devoted to the study of the stability of limit cycles of a nonlinear delay
differential equation with a distributed delay. The equation arises from a model of population …

Asymptotic behavior of a discrete maturity structured system of hematopoietic stem cell dynamics with several delays

M Adimy, F Crauste, A El Abdllaoui - Mathematical Modelling of …, 2006 - cambridge.org
We propose and analyze a mathematical model of hematopoietic stem cell dynamics. This
model takes into account a finite number of stages in blood production, characterized by cell …

Modelling and asymptotic stability of a growth factor-dependent stem cells dynamics model with distributed delay

M Adimy, F Crauste - … and Continuous Dynamical Systems-Series B, 2007 - hal.science
Under the action of growth factors, proliferating and nonproliferating hematopoietic stem
cells differentiate and divide, so as to produce blood cells. Growth factors act at different …

Discrete-maturity structured model of cell differentiation with applications to acute myelogenous leukemia

M Adimy, F Crauste, A El Abdllaoui - Journal of Biological Systems, 2008 - World Scientific
We propose and analyze a mathematical model of hematopoietic stem cell dynamics, that
takes two cell populations into account, an immature and a mature one. All cells are able to …

Stability and Hopf bifurcation for a cell population model with state-dependent delay

M Adimy, F Crauste, ML Hbid, R Qesmi - SIAM Journal on Applied …, 2010 - SIAM
We propose a mathematical model describing the dynamics of a hematopoietic stem cell
population. The method of characteristics reduces the age-structured model to a system of …

Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics

M Adimy, F Crauste, S Ruan - Nonlinear Analysis: Real World Applications, 2005 - Elsevier
We study a mathematical model describing the dynamics of a pluripotent stem cell
population involved in the blood production process in the bone marrow. This model is a …