Journal of Theoretical Medicine
Volume 4 (2002), Issue 1, Pages 39-50

A Kinetic Model of Tumor/Immune System Cellular Interactions

1Department of Civil Engineering, University of Udine, via delle Scienze, 208, 33100 Udine, Italy
2Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Turin, Italy
3Department of Mathematics, Warsaw University, Banacha 2, 02097 Warsaw, Poland

Received 1 August 2000; Accepted 23 April 2001

Copyright © 2002 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.


In this paper, a model of cellular tumor dynamics in competition with the immune system is proposed. The characteristic scale of the phenomenon is the cellular one and the model is developed with probabilistic methods analogous to those of the kinetic theory. The interacting individuals are the cells of the populations involved in the competition between the tumor and the immune system. Interactions can change the activation state of the tumor and cause tumor proliferation or destruction. The model is expressed in terms of a bi-linear system of integro-differential equations. Some preliminary mathematical analysis of the model as well as computational simulations are presented.