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.

Autorentext

Ms. Rana Abu Eisheh is a mathematician and researcher. She has an interest in partial differential equations and simulation models of red blood cells production cycle .In 2010, she has obtained a master degree from a joint research program between Palestine Polytechnic University and Institute Camille Jordan, Claude Bernard Lyon 1 University.