Table of Contents Author Guidelines Submit a Manuscript
Computational and Mathematical Methods in Medicine
Volume 2014 (2014), Article ID 172923, 12 pages
http://dx.doi.org/10.1155/2014/172923
Research Article

A Mathematical Model of Cancer Treatment by Radiotherapy

1School of Science, Chongqing Jiaotong University, Chongqing 400074, China
2Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China
3School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China

Received 22 July 2014; Revised 14 October 2014; Accepted 25 October 2014; Published 13 November 2014

Academic Editor: Huaguang Zhang

Copyright © 2014 Zijian Liu and Chenxue Yang. 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.

Linked References

  1. C. A. Perez and J. A. Purdy, Levitt and Tapley's Technological Basis of Radiation Tehrapy: Clinical Applications, Williams and Wilkins, Philadelphia, Pa, USA, 3rd edition, 1999.
  2. R. L. Souhami, I. Tannock, P. Hohenberger, and J.-C. Horiot, Oxford Textbook of Oncology, vol. 1, Oxford University Press, Oxford, UK, 2nd edition, 2002.
  3. G. G. Steel, The Biological Basis of Radiotherapy, Elsevier, 1989.
  4. Z. Liu, M. Fan, and L. Chen, “Globally asymptotic stability in two periodic delayed competitive systems,” Applied Mathematics and Computation, vol. 197, no. 1, pp. 271–287, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. H. Zhang, Z. Wang, and D. Liu, “Global asymptotic stability of recurrent neural networks with multiple time-varying delays,” IEEE Transactions on Neural Networks, vol. 19, no. 5, pp. 855–873, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. L. V. Hien, T. T. Loan, B. T. Trang, and H. Trinh, “Existence and global asymptotic stability of positive periodic solution of delayed Cohen-Grossberg neural networks,” Applied Mathematics and Computation, vol. 240, no. 1, pp. 200–212, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. H. Zhang, W. Huang, Z. Wang, and T. Chai, “Adaptive synchronization between two different chaotic systems with unknown parameters,” Physics Letters A, vol. 350, no. 5-6, pp. 363–366, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. H. Gu, H. Jiang, and Z. Teng, “Existence and globally exponential stability of periodic solution of BAM neural networks with impulses and recent-history distributed delays,” Neurocomputing, vol. 71, no. 4–6, pp. 813–822, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. H. Zhang, Z. Wang, and D. Liu, “Robust exponential stability of recurrent neural networks with multiple time-varying delays,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 54, no. 8, pp. 730–734, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. Z. Liu, S. Zhong, C. Yin, and W. Chen, “Permanence, extinction and periodic solutions in a mathematical model of cell populations affected by periodic radiation,” Applied Mathematics Letters, vol. 24, no. 10, pp. 1745–1750, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. G. Belostotski, A control theory model for cancer treatment by radiotherapy [M.S. thesis], University of Alberta, 2004.
  12. G. Belostotski and H. I. Freedman, “A control theory model for cancer treatment by radiotherapy 1: no healthy cell damage,” International Journal of Applied Mechanics, vol. 25, no. 4, pp. 447–480, 2005. View at Google Scholar
  13. H. I. Freedman and G. Belostotski, “Perturbed models for cancer treatment by radiotherapy,” Differential Equations and Dynamical Systems, vol. 17, no. 1-2, pp. 115–133, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. H. I. Freedman, Deterministic Mathematical Models in Population Ecology, Marcel Dekker, New York, NY, USA, 1980. View at MathSciNet
  15. F. Nani and H. I. Freedman, “A mathematical model of cancer treatment by immunotherapy,” Mathematical Biosciences, vol. 163, no. 2, pp. 159–199, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. S. T. Pinho, H. I. Freedman, and F. Nani, “A chemotherapy model for the treatment of cancer with metastasis,” Mathematical and Computer Modelling, vol. 36, no. 7-8, pp. 773–803, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. Z. Ma, Mathematical Modeling and Research on the Population Ecology, Anhui Educational Press, Hefei, Hefei, 1996, (Chinese).
  18. V. Lakshmikantham, V. M. Matrosov, and S. Sivasundaram, Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991. View at MathSciNet
  19. T. Yoshizawa, Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Springer, New York, NY, USA, 1975.