Stability and existence results for a time-delayed nonlocal model of hematopoietic stem cells dynamics

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:463

Article

Chekroun, Abdennasser¹  Kuniya, Toshikazu² 

[1] Univ Abou Bakr Belkaid, Lab Anal Nonlineaire & Math Appl, Tilimsen 13000, Algeria

[2] Kobe Univ, Grad Sch Syst Informat, Nada Ku, 1-1 Rokkodai Cho, Kobe, Hyogo 6578501, Japan

关键词: Age-structured PDE;    Delayed nonlocal model;    Existence and uniqueness of positive solutions;    Lyapunov function;    Cell dynamics;   

DOI  :  10.1016/j.jmaa.2018.03.072

来源: Elsevier

【 摘 要 】

In this paper, we consider a time-delayed nonlocal model describing the dynamics of hematopoietic stem cells (HSCs), which represent the immature cells in the hematopoiesis process. By the method of characteristics, the nonlocal model is obtained from an age-structured reaction-diffusion system in bounded domain with Dirichlet boundary conditions. Along this paper, we focus on the mathematical analysis of it. Firstly, we give some results on the existence, uniqueness, positivity and boundedness of solutions. Next, we obtain a threshold value R-s and prove that the trivial steady state is globally asymptotically stable when R-s < 1. When R-s > 1, we prove the existence and uniqueness of positive stationary solution under the respective additional conditions on the monotonicity and non-monotonicity of the integral term. Finally, we prove the uniform weak persistence of the system when R-s > 1. Some numerical simulations are provided to verify the validity of our theoretical results. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free