Table of Contents
International Scholarly Research Notices
Volume 2014, Article ID 346597, 8 pages
http://dx.doi.org/10.1155/2014/346597
Research Article

On Study of Immune Response to Tumor Cells in Prey-Predator System

1CIRBSc., Jamia Millia Islamia, Jamia Nagar, New Delhi 110025, India
2Department of Mathematics, Jamia Millia Islamia, Jamia Nagar, New Delhi 110025, India

Received 23 April 2014; Revised 9 June 2014; Accepted 9 June 2014; Published 22 September 2014

Academic Editor: Francesco Pappalardo

Copyright © 2014 Gurpreet Kaur and Naseem Ahmad. 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 aims to develop the mathematical model that explores the immune response to a tumor system as a prey-predator system. A deterministic model defining the dynamics of tumor growth progression and regression has been analyzed. Our analysis indicates the tumor recurring and dormancy on the cellular level in combination with resting and hunting cells. The model considered in the present study is a generalization of El-Gohary (2008) by introducing the Michaelis-Menten function. This function describes the stimulation process of the resting cells by the tumor cells in the presence of tumor specific antigens. Local and global stability analysis have been performed along with the numerical simulation to support our findings.