Table of Contents
International Scholarly Research Notices
Volume 2014 (2014), Article ID 260379, 10 pages
http://dx.doi.org/10.1155/2014/260379
Research Article

Global Stability of an HIV-1 Infection Model with General Incidence Rate and Distributed Delays

Department of Mathematics and Informatics, Faculty of Sciences, Chouaib Doukkali University, BP 20, 24000 El Jadida, Morocco

Received 6 March 2014; Accepted 8 July 2014; Published 29 October 2014

Academic Editor: Shengqiang Liu

Copyright © 2014 Abdoul Samba Ndongo and Hamad Talibi Alaoui. 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. A. Murase, T. Sasaki, and T. Kajiwara, “Stability analysis of pathogen-immune interaction dynamics,” Journal of Mathematical Biology, vol. 51, no. 3, pp. 247–267, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. R. M. Anderson, R. M. May, and S. Gupta, “Non-linear phenomena in host-parasite interactions,” Parasitology, vol. 99, pp. S59–S79, 1989. View at Publisher · View at Google Scholar · View at Scopus
  3. R. A. Arnaout, M. A. Nowak, and D. Wodarz, “HIV-1 dynamics revisited: biphasic decay by cytotoxic T lymphocyte killing?” Proceedings of the Royal Society B: Biological Sciences, vol. 267, no. 1450, pp. 1347–1354, 2000. View at Publisher · View at Google Scholar · View at Scopus
  4. C. Chiyaka, W. Garira, and S. Dube, “Modelling immune response and drug therapy in human malaria infection,” Computational and Mathematical Methods in Medicine, vol. 9, no. 2, pp. 143–163, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. A. M. Elaiw, A. Alhejelan, and M. A. Alghamdi, “Global dynamics of virus infection model with antibody immune response and distributed delays,” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 781407, 9 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  6. H.-F. Huo, Y.-L. Tang, and L.-X. Feng, “A virus dynamics model with saturation infection and humoral immunity,” International Journal of Mathematical Analysis, vol. 6, no. 37–40, pp. 1977–1983, 2012. View at Google Scholar · View at Scopus
  7. M. A. Nowak and C. R. M. Bangham, “Population dynamics of immune responses to persistent viruses,” Science, vol. 272, no. 5258, pp. 74–79, 1996. View at Publisher · View at Google Scholar · View at Scopus
  8. A. S. Perelson, “Modelling viral and immune system dynamics,” Nature Reviews Immunology, vol. 2, no. 1, pp. 28–36, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Wang and D. Zou, “Global stability of in-host viral models with humoral immunity and intracellular delays,” Applied Mathematical Modelling, vol. 36, no. 3, pp. 1313–1322, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. T. Wang, Z. Hu, F. Liao, and W. Ma, “Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity,” Mathematics and Computers in Simulation, vol. 89, pp. 13–22, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. X. Wang and S. Liu, “A class of delayed viral models with saturation infection rate and immune response,” Mathematical Methods in the Applied Sciences, vol. 36, no. 2, pp. 125–142, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. D. Wodarz, R. M. May, and M. A. Nowak, “The role of antigen-independent persistence of memory cytotoxic T lymphocytes,” International Immunology, vol. 12, no. 4, pp. 467–477, 2000. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. Yang, H. Wang, Z. Hu, and F. Liao, “Global stability of in-host viral model with humoral immunity and Beddington-Deangelis functional response,” International Journal of Life Science and Medical Research, vol. 3, no. 5, pp. 200–209, 2013. View at Google Scholar
  14. X. Yang, L. Chen, and J. Chen, “Permanence and positive periodic solution for the single-species nonautonomous delay diffusive models,” Computers & Mathematics with Applications, vol. 32, no. 4, pp. 109–116, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  15. J. P. LaSalle, The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1976. View at MathSciNet
  16. C. C. McCluskey, “Complete global stability for an SIR epidemic model with delay—distributed or discrete,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 55–59, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus