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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...
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...
A large variety of complex
spatio-temporal patterns emerge from the processes occurring in
biological systems, one of them being the result of propagating
phenomena. This wave-like structures
can be modelled via reaction-diffusion equations. If a solution of
a reaction-diffusion equation represents a travelling wave, the
shape of the solution will be the same at all time and the speed
of propagation of this shape will be a constant. Travelling wave
solutions of reaction-diffusion systems have been...
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