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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 137015, 10 pages
http://dx.doi.org/10.1155/2014/137015
Research Article

Response of Immunotherapy to Tumour-TICLs Interactions: A Travelling Wave Analysis

School of Mathematics, Statistics, and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa

Received 19 March 2014; Revised 10 June 2014; Accepted 19 June 2014; Published 15 July 2014

Academic Editor: Igor Leite Freire

Copyright © 2014 Joseph Malinzi 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

There are several cancers for which effective treatment has not yet been identified. Mathematical modelling can nevertheless point out to clinicians tumour invasion properties that should be targeted to mitigate these cancers. We present a travelling wave analysis of a tumour-immune interaction model with immunotherapy. We use the geometric treatment of an apt-phase space to establish the intersection between stable and unstable manifolds. We calculate the minimum wave speed and numerical simulations are performed to support the analytical results.