0000000000238402
AUTHOR
Najat M Omar Dabnoun
From the Classical Boltzmann Equation to the Generalized Kinetic models of Biological Systems
This paper deal with the classical Boltzmann Equation generalized to model populations in complex biological system. In particular, the populations refer to the cells of the immune system and to those of an aggressive host (cancer cells) in a human being. We will focus with the study of a spatially homogeneous continuous model, and derivation of the macroscopic model. The paper starts from a simple description of the classical Boltzmann equation and goes to the mathematical approach proposed to model the large systems of interacting entities focusing the competition between immune system and cancer cells.
A spatially homogeneous mathematical model of immune cancer competition
This paper deals with the modeling of interactions between the immune system and cancer cells, in the framework of the mathematical kinetic theory for active particles. The model assumes spatial homogeneity and continue values of the activity of cancer and immune cells.
On modeling the immune competition with Darwinian dynamics
Mathematical and computational models are increasingly used in this century to help modeling of living systems. Mathematical modeling presents many methods for studying and analyzing the behavior of biological systems, in particular, cellular systems. As Bellomo (2008), Bellouquid and Delitala (2006), suggest " The modeling of living systems is not an easy task, it requests technically complex mathematical methods to deal with the inner complexity of biological systems which exhibit features and behaviors very different from those of inert matter". The mathematical approach used in this dissertation is based on the Kinetic Theory of Active Particles (KTAP), that has been specifically develo…