Abstract
A cell differentiation model with maturity structure in progenitor cells is described by a system of nonlinear ODEs coupled to a PDE. The work mainly discusses Hopf-bifurcation for the model when the maturation rate of progenitor cells only depends on the number of mature cells, and is a continuation of the previous work (Doumic et al., 2011). Using the methods of characteristics and a change in variable, the system can be transformed into one of state-dependent delay differential equations and then into constant delay differential equations. A qualitative analysis of the solutions is performed, which includes well-posedness, non-negativity, uniform boundedness and linearized stability. Furthermore, we conduct Hopf-bifurcation analysis by taking the maturation level of progenitor as the bifurcation parameter, which means that the levels of stem and mature cells may vary with persistent oscillations. A numerical analysis stresses the role of some important parameters on the stability and Hopf-bifurcation.
Published Version
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