Contribution to the Study of a Mathematical Model of Erythropoiesis

The asymptotic stability of a nonlinear system of three differential equations with delay is analyzed, describing the dynamics of red blood cell production. This process is based on the differentiation of stem cells, throughout divisions, into mature blood cells, that in turn control the dynamics of immature cells. Taking into account an explicit role of the mature cell population on the cell proliferation, a characteristic equation with delay dependent coefficients is studied. A necessary and sufficient condition for stability of the zero fixed point is determined. Finally, the existence of a Hopf bifurcation for the only positive fixed point is obtained, leading to the existence of periodic solutions.