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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 430486, 11 pages
http://dx.doi.org/10.1155/2013/430486
Research Article

A Class of Solutions for the Hybrid Kinetic Model in the Tumor-Immune System Competition

1Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy
2Depatment of Mathematics and Computer Science, University of Messina, Viale Ferdinando d'Alcontres 31, 98166 Messina, Italy

Received 6 March 2013; Accepted 7 April 2013

Academic Editor: Ezzat G. Bakhoum

Copyright © 2013 Carlo Cattani and Armando Ciancio. 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

In this paper, the hybrid kinetic models of tumor-immune system competition are studied under the assumption of pure competition. The solution of the coupled hybrid system depends on the symmetry of the state transition density which characterizes the probability of successful occurrences. Thus by defining a proper transition density function, the solutions of the hybrid system are explicitly computed and applied to a classical (realistic) model of competing populations.