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

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.