Mathematical model of leukocyte formation with delays

Abstract

Leukopoiesis is the process of forming and developing different types of leukocyte in the bone marrow of adults and hematopoietic organs of the fetus. The process of leukopoiesis starts from inactivated stem cells originating from hematopoietic. When the process of differentiation of blood cells occurs, the sub-process of leukocyte production becomes slow-down. This can lead to serious illnesses such as cyclic neutropenia. For this purpose, the mathematical model for leukocyte formation with two consecutive delays proposed using more general continuous function as feedback control functions. The apoptosis rate of the neutrophil precursor also being replaced by a non-constant reduction function. The asymptotic stability of the equilibrium point is proved. The numerical simulation showed the illustration of solution behavior over time. We can conclude that the population of HSC daughter cells in the proliferation process tends to diverge in some critical cases.