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Computational and Mathematical Methods in Medicine
Volume 7 (2006), Issue 2-3, Pages 143-157
http://dx.doi.org/10.1080/10273660600968911

On the Discrete Kinetic Theory for Active Particles. Modelling the Immune Competition

Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy

Received 14 July 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with the application of the mathematical kinetic theory for active particles, with discrete activity states, to the modelling of the immune competition between immune and cancer cells. The first part of the paper deals with the assessment of the mathematical framework suitable for the derivation of the models. Two specific models are derived in the second part, while some simulations visualize the applicability of the model to the description of biological events characterizing the immune competition. A final critical outlines some research perspectives.