Analysis of a System Describing Proliferative-Quiescent Cell Dynamics

Abstract

Systems describing the dynamics of proliferative and quiescent cells are commonly used as computational models, for instance for tumor growth and hematopoiesis. Focusing on the very earliest stages of hematopoiesis, stem cells and early progenitors, the authors introduce a new method, based on an energy/Lyapunov functional to analyze the long time behavior of solutions. Compared to existing works, the method in this paper has the advantage that it can be extended to more complex situations. The authors treat a system with space variable and diffusion, and then adapt the energy functional to models with three equations.

Keywords

Stability analysis / Lyapunov functional / Energy method / Parabolic systems / Proliferative and quiescent cells / Tumor growth / Hematopoiesis

References

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