Mathematical problems of the dynamics of the red blood cells
Treść / Zawartość
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.