Mathematical problems of the dynamics of the red blood cells

M. Ważewska-Czyżewska, and A. Lasota. "Mathematical problems of the dynamics of the red blood cells." Mathematica Applicanda 4.6 (1976): null. <http://eudml.org/doc/292703>.

@article{M1976,
abstract = {The purpose of this paper is to construct a model for the process of generation and degeneration of red blood cells, taking into account biological-medical experimental data. The paper contains four sections. The first section presents basic biological facts enabling the reader who is not a specialist to understand this process. Section 2 is devoted to constructing an analytic model which uses a first order linear partial differential equation and a nonlinear integral equation. Section 3 lists some of the simplest mathematical properties of this model and the biological consequences arising from it. Section 4 gives a simplified model which can be described in terms of a nonlinear ordinary differential equation with a delayed parameter. The properties of this simple equation are of interest from both a mathematical and a biological point of view. In particular, the proof of the existence of periodic equations requires the application of a nontrivial version of a theorem on fixed points. The problem of the stability of this periodic solution is open. The problem is important in that the existence of a stable periodic solution gives a theoretical explanation of certain types of blood diseases.},
author = {M. Ważewska-Czyżewska, A. Lasota},
journal = {Mathematica Applicanda},
keywords = {97M60},
language = {eng},
number = {6},
pages = {null},
title = {Mathematical problems of the dynamics of the red blood cells},
url = {http://eudml.org/doc/292703},
volume = {4},
year = {1976},
}

TY - JOUR
AU - M. Ważewska-Czyżewska
AU - A. Lasota
TI - Mathematical problems of the dynamics of the red blood cells
JO - Mathematica Applicanda
PY - 1976
VL - 4
IS - 6
SP - null
AB - The purpose of this paper is to construct a model for the process of generation and degeneration of red blood cells, taking into account biological-medical experimental data. The paper contains four sections. The first section presents basic biological facts enabling the reader who is not a specialist to understand this process. Section 2 is devoted to constructing an analytic model which uses a first order linear partial differential equation and a nonlinear integral equation. Section 3 lists some of the simplest mathematical properties of this model and the biological consequences arising from it. Section 4 gives a simplified model which can be described in terms of a nonlinear ordinary differential equation with a delayed parameter. The properties of this simple equation are of interest from both a mathematical and a biological point of view. In particular, the proof of the existence of periodic equations requires the application of a nontrivial version of a theorem on fixed points. The problem of the stability of this periodic solution is open. The problem is important in that the existence of a stable periodic solution gives a theoretical explanation of certain types of blood diseases.
LA - eng
KW - 97M60
UR - http://eudml.org/doc/292703
ER -