Long time behaviour for a mixed reaction-diffusion-difference problem with distributed delay and non-local term

We investigate in this paper, the problem [GRAPHICS] . with Neumann boundary conditions. Such a problem takes its origin in modelling the dynamics of quiescent and proliferating hematopoietic stem cells. Our aim is to provide a complete asymptotic analysis, to ensure global attractiveness and exponential stability of trivial and positive steady states. To this end, chiefly, a good combination of a suitable choice of Lyapunov functional with some monotony techniques are used. A comparison principle applied to a well chosen deformation of our problem, permits us to obtain the aim. (c) 2023 Elsevier Inc. All rights reserved.