Abstract
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 Rs and prove that the trivial steady state is globally asymptotically stable when Rs<1. When Rs>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 Rs>1. Some numerical simulations are provided to verify the validity of our theoretical results.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
