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Mathematical model of hematopoiesis dynamics with growth factor-dependent apoptosis and proliferation regulations. (English) Zbl 1171.34344
Summary: We consider a nonlinear mathematical model of hematopoietic stem cell dynamics, in which proliferation and apoptosis are controlled by growth factor concentrations. Cell proliferation is positively regulated, while apoptosis is negatively regulated. The resulting age-structured model is reduced to a system of three differential equations, with three independent delays, and existence of steady states is investigated. The stability of the trivial steady state, describing cells dying out with a saturation of growth factor concentrations is proven to be asymptotically stable when it is the only equilibrium. The stability analysis of the unique positive steady state allows the determination of a stability area, and shows that instability may occur through a Hopf bifurcation, mainly as a destabilization of the proliferative capacity control, when cell cycle durations are very short. Numerical simulations are carried out and result in a stability diagram that stresses the lead role of the introduction rate compared to the apoptosis rate in the system stability.
MSC:
34K20Stability theory of functional-differential equations
34K60Qualitative investigation and simulation of models
92C37Cell biology
37N25Dynamical systems in biology
References:
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