Global asymptotic stability for an age-structured model of hematopoietic stem cell dynamics

Abstract

We investigate a system of two nonlinear age-structured partial differential equations describing the dynamics of proliferating and quiescent hematopoietic stem cell (HSC) populations. The method of characteristics reduces the age-structured model to a system of coupled delay differential and renewal difference equations with continuous time and distributed delay. By constructing a Lyapunov–Krasovskii functional, we give a necessary and sufficient condition for the global asymptotic stability of the trivial steady state, which describes the population dying out. We also give sufficient conditions for the existence of unbounded solutions, which describe the uncontrolled proliferation of HSC population. This study may be helpful in understanding the behavior of hematopoietic cells in some hematological disorders.

Keywords:

• Age-structured PDE
• delay differential-difference system
• Lyapunov–Krasovskii functional
• cell dynamics
• hematopoietic stem cells

AMS Subject Classifications:

• 34D20
• 34D23
• 34K06
• 92C37

Notes

No potential conflict of interest was reported by the authors.