Traveling wavefront in a Hematopoiesis model with time delay

AbstractThis paper is concerned with a reaction–diffusion equation with time delay, which describes the dynamics of the blood cell production. The existence of the traveling wavefront is given by using the upper–lower solution technique and the monotone iteration

Existence and asymptotics of traveling wave fronts for a coupled nonlocal diffusion and difference system with delay

In this paper, we consider a general study of a recent proposed hematopoietic stem cells model. This model is a combination of nonlocal diffusion equation and difference equation with delay. We deal with the properties of traveling waves for this system such as the existence and asymptotic behavior. By using the Schauder’s fixed point theorem combined with the method based on the construction of upper and lower solutions, we obtain the existence of traveling wave fronts for a speed c > c . The case c = c is studied by using a limit argument. We prove also that c is the critical value. We finally prove that the nonlocality increases the minimal wave speed

Stability analysis of cell dynamics in leukemia

In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized system around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations. © 2012 EDP Sciences

Stability Analysis of Cell Dynamics in Leukemia

Cataloged from PDF version of article.In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized system around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations

Existence and asymptotics of traveling wave fronts for a coupled nonlocal diffusion and difference system with delay

In this paper, we consider a general study of a recent proposed hematopoietic stem cells model. This model is a combination of nonlocal diffusion equation and difference equation with delay. We deal with the properties of traveling waves for this system such as the existence and asymptotic behavior. By using the Schauder’s fixed point theorem combined with the method based on the construction of upper and lower solutions, we obtain the existence of traveling wave fronts for a speed c > c . The case c = c is studied by using a limit argument. We prove also that c is the critical value. We finally prove that the nonlocality increases the minimal wave speed