Mathematics – Classical Analysis and ODEs
Scientific paper
2009-04-16
Bulletin of Mathematical Biology 68, 8 (2006) 2321-2351
Mathematics
Classical Analysis and ODEs
Scientific paper
10.1007/s11538-006-9121-9
Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed to carry out explanation on some blood diseases, characterized by oscillations in circulating blood cells. A system of three differential equations with delay, corresponding to the cell cycle duration, is analyzed. The existence of a Hopf bifurcation for a positive steady-state is obtained through the study of an exponential polynomial characteristic equation with delay-dependent coefficients. Numerical simulations show that long period oscillations can be obtained in this model, corresponding to a destabilization of the feedback regulation between blood cells and growth factors. This stresses the localization of periodic hematological diseases in the feedback loop.
Adimy Mostafa
Crauste Fabien
Ruan Shigui
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