On a Mathematical Model for the Formation of HemoDoiesis

A basic model in immunology, that of the formation of hemopoiesis, and the corresponding initial and boundary value problem for a reaction-diffusion system with time delay is studied. By using the upper and lower method and a well-defined iterated scheme, the existence, uniqueness, boundedness, and non-negativeness of the global solutions are proved. Especially the uniqueness of equilibrium solutions under some conditions are proved . The asymptotic behavior of the equilibrium solutions are discussed. The sufficient conditions for stabiMty of the equilibrium solutions are given.