Year: 2026
Type: article
Abstract: We consider an age-structured partial differential equation model for cell population dynamics in which the cell cycle duration depends on the total number of quiescent cells. Using the method of characteristics, the model is reduced to a state-dependent delay differential equation. We analyze the stability properties of the resulting equation. By constructing a Lyapunov function, we obtain a sufficient condition for the global asymptotic stability of the trivial equilibrium, corresponding to cell extinction. We further prove the existence of a unique positive equilibrium emerging from a transcritical bifurcation of the trivial equilibrium. The analysis of the positive equilibrium reveals the possible occurrence of a Hopf bifurcation and provides criteria for stability switches. Numerical simulations illustrate the theoretical results. This modeling framework is motivated by periodic hematological diseases, characterized by pathological oscillations in blood cell populations, and captures the influence of the physiological state on cell cycle durations.
Authors: Mostafa Adimy, Nohayla Alaoui, My Lhassan Hbid
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Université Cadi Ayyad
OpenAlex ID: W7214116521