Delayed nonlocal reaction–diffusion model for hematopoietic stem cell dynamics with Dirichlet boundary conditions

• Published in: Mathematical modelling of natural phenomena Vol. 12; no. 6; pp. 1 - 22
• Main Authors: Adimy, M., Chekroun, A., Kuniya, T.
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 01.01.2017
• Subjects: 34B18; 35B35; 37N25; 92C37; Age-space-structured PDE; Asymptotic properties; Blood cells; Boundary conditions; cell dynamics; Computer simulation; Dirichlet boundary conditions; Dirichlet problem; Dynamical Systems; Economic models; existence and uniqueness of positive steady state; Hematopoietic stem cells; Lyapunov functional; Mathematical models; Mathematics; Method of characteristics; Reaction-diffusion equations; Steady state; Stem cells; Time lag; time-delayed reaction–diffusion equation; Uniqueness; time-delayed reaction-diffusion equation; Lyapunov functional; existence and uniqueness of positive steady state; Dirichlet boundary conditions; Age-space-structured PDE; cell dynamics

The paper focuses on the mathematical analysis and modeling of hematopoietic stem cell (HSC) dynamics that lead to the production and regulation of blood cells in the bone morrow. The HSC population is seen as a continuous medium structured in age and space. Using the method of characteristics, we r...