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Journal of Applied Mathematics
Volume 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.

Citations to this Article [9 citations]

The following is the list of published articles that have cited the current article.

  • Ralf Gallasch, Mirjana Efremova, Pornpimol Charoentong, Hubert Hackl, and Zlatko Trajanoski, “Mathematical models for translational and clinical oncology,” Journal of Clinical Bioinformatics, vol. 3, no. 1, 2013. View at Publisher · View at Google Scholar
  • Fathalla A. Rihan, “Numerical Modeling of Fractional-Order Biological Systems,” Abstract and Applied Analysis, vol. 2013, pp. 1–11, 2013. View at Publisher · View at Google Scholar
  • F.A. Rihan, D.H. Abdel Rahman, S. Lakshmanan, and A.S. Alkhajeh, “A time delay model of tumour–immune system interactions: Global dynamics, parameter estimation, sensitivity analysis,” Applied Mathematics and Computation, vol. 232, pp. 606–623, 2014. View at Publisher · View at Google Scholar
  • Gurpreet Kaur, and Naseem Ahmad, “On Study of Immune Response to Tumor Cells in Prey-Predator System,” International Scholarly Research Notices, vol. 2014, pp. 1–8, 2014. View at Publisher · View at Google Scholar
  • F. A. Rihan, D. H. Abdelrahman, F. Al-Maskari, F. Ibrahim, and M. A. Abdeen, “Delay Differential Model for Tumour-Immune Response with Chemoimmunotherapy and Optimal Control,” Computational and Mathematical Methods in Medicine, vol. 2014, pp. 1–15, 2014. View at Publisher · View at Google Scholar
  • Monika Joanna Piotrowska, “An immune system — tumour interactions model with discrete time delay: model analysis and validation,” Communications in Nonlinear Science and Numerical Simulation, 2015. View at Publisher · View at Google Scholar
  • Rachel Walker, and Heiko Enderling, “From concept to clinic: Mathematically informed immunotherapy,” Current Problems in Cancer, 2015. View at Publisher · View at Google Scholar
  • Fathalla A. Rihan, and Bassel F. Rihan, “Numerical modelling of biological systems with memory using delay differential equations,” Applied Mathematics and Information Sciences, vol. 9, no. 3, pp. 1645–1658, 2015. View at Publisher · View at Google Scholar
  • Fajar Adi-Kusumo, and Rara Sandhy Winanda, “Bifurcation analysis of the cervical cancer cells, effector cells, and IL-2 compounds interaction model with immunotherapy,” Far East Journal of Mathematical Sciences, vol. 99, no. 6, pp. 869–883, 2016. View at Publisher · View at Google Scholar