A nonlinear system of two delay differential equations is proposed to model
hematopoietic stem cell dynamics. Each equation describes the evolution of a
sub-population, either proliferating or nonproliferating. The nonlinearity
accounting for introduction of nonproliferating cells in the proliferating phase
is assumed to depend upon the total number of cells. Existence and stability
of steady states are investigated. A Lyapunov functional is built to obtain the
global asymptotic stability of the...
Plant growth occurs due to cell proliferation in the meristem. We model the case of
apical meristem specific for branch growth and the case of basal meristem specific for
bulbous plants and grass. In the case of apical growth, our model allows us to describe
the variety of plant forms and lifetimes, endogenous rhythms and apical domination. In the
case of basal growth, the spatial structure, which corresponds to the appearance of
leaves, results...
A hybrid model of red blood cell production, where cells are considered as discrete
objects while intra-cellular proteins and extra-cellular biochemical substances are
described with continuous models, is proposed. Spatial organization and regulation of red
blood cell production (erythropoiesis) are investigated. Normal erythropoiesis is
simulated in two dimensions, and the influence on the output of the model of some
parameters involved in cell...
The paper is devoted to mathematical modelling of erythropoiesis,
production of red blood cells in the bone marrow.
We discuss intra-cellular regulatory networks which determine
self-renewal and differentiation of erythroid progenitors.
In the case of excessive self-renewal, immature cells can fill
the bone marrow resulting in the development of leukemia.
We introduce a parameter characterizing the strength of mutation.
Depending on its value, leukemia will or will not develop.
The simplest...
We propose and analyze a mathematical model of hematopoietic stem cell dynamics. This model takes
into account a finite number of stages in blood production, characterized by cell maturity levels,
which enhance the difference, in the hematopoiesis process, between dividing cells that
differentiate (by going to the next stage) and dividing cells that keep the same maturity level (by
staying in the same stage). It is described by a system of nonlinear differential equations
with delays. We study...
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