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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 475720, 19 pages
http://dx.doi.org/10.1155/2012/475720
Research Article

Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions

1Department of Mathematical Sciences, Faculty of Science, United Arab Emirates University, Al-Ain 17551, United Arab Emirates
2Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
3Department of Mathematics, Faculty of Science, Helwan University, Cairo 11790, Egypt

Received 7 July 2011; Revised 15 October 2011; Accepted 28 October 2011

Academic Editor: Pedro Serranho

Copyright © 2012 F. A. Rihan et al. 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

We provide a family of ordinary and delay differential equations to model the dynamics of tumor-growth and immunotherapy interactions. We explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated. The possibility of clearing the tumor, with a strategy, is based on two parameters in the model: the rate of influx of the effector cells and the rate of influx of IL-2. The critical tumor-growth rate, below which endemic tumor does not exist, has been found. One can use the model to make predictions about tumor dormancy.