SOME MATHEMATICAL ASPECTS OF MODELING CELL-POPULATION DYNAMICS

The purpose of this paper is to discuss different types of models of cell population dynamics based on differential equations and to point out the connection between them. From the starting point of the McKendrick/Von Foerster type model we derive Lotka-Volterra type integral equations, and some delaying-differential equations. We establish a connection between the original partial differential equation model and the Takahashi ordinary differential equations model, based on compartmental analysis, by means of a numerical procedure named "the method of lines". © 1990.