Stability analysis of multi-compartment models for cell production systems

Abstract

We study two-and three-compartment models of a hierarchical cell production system with cell division regulated by the level of mature cells. We investigate the structure of equilibria with respect to parameters as well as local stability properties for the equilibria. To interpret the results we adapt the concept of reproduction numbers, which is well known in ecology, to stem cell population dynamics. In the twocompartment model, the positive equilibrium is stable wherever it exists. In the three-compartment model, we find that the intermediate stage of differentiation is responsible for the emergence of an instability region in the parameter plane. Moreover, we prove that this region shrinks as the mortality rate for mature cells increases and discuss this result.

Mathematical Modeling of Leukemogenesis and Cancer Stem Cell Dynamics

“…In the two-compartment model, the positive equilibrium is always stable. On the other hand, in the three-compartment model, emergence of an instability region in a parameter plane is possible [54]. These stability results were extended to a global stability in case of the two-compartment model [30].…”

“…[47] and analyzed in ref. [64,30,54]. In Section 3. we investigate the existence of multiple steady states and analyze which cell properties are necessary and sufficient to destabilize the physiological equilibrium of healthy cells.…”

A differential equation with state-dependent delay from cell population biology

“…For this parameterization they have analyzed the possibility of a unique positive equilibrium and computed representations of it. It is shown in [11,20] that for ODE variants of our model there is the possibility of destabilization of equilibria via Hopf bifurcation and the emergence of oscillations. As a future project we plan the stability analysis of equilibria in the general setting of the present paper.…”

Математическая Модель Клеточных Преобразований При Регенерации Костной Ткани В Условиях Изменяющейся Биохимической Среды С Возможной Механорегуляцией

“…Активно развиваются как детерминистские цепные модели [21,30], так и стохастические подходы [22] на их основе.…”