Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 903678, 16 pages
doi:10.1155/2008/903678
Research Article

A Differential Equation Model of HIV Infection of CD4+ T-Cells with Delay

Junyuan Yang,1,2 Xiaoyan Wang,1 and Fengqin Zhang1

1Department of Applied Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, China
2Beijing Institute of Information and Control, Beijing 100037, China

Received 24 April 2008; Accepted 23 October 2008

Academic Editor: Leonid Berezansky

Copyright © 2008 Junyuan Yang 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.

Linked References

  1. R. J. De Boer and A. S. Perelson, “Target cell limited and immune control models of HIV infection: a comparison,” Journal of Theoretical Biology, vol. 190, no. 3, pp. 201–214, 1998. View at Publisher · View at Google Scholar
  2. T. B. Kepler and A. S. Perelson, “Cyclic re-entry of germinal center B cells and the efficiency of affinity maturation,” Immunology Today, vol. 14, no. 8, pp. 412–415, 1993. View at Publisher · View at Google Scholar
  3. J. K. Percus, O. E. Percus, and A. S. Perelson, “Predicting the size of the T-cell receptor and antibody combining region from consideration of efficient self-nonself discrimination,” Proceedings of the National Academy of Sciences of the United States of America, vol. 90, no. 5, pp. 1691–1695, 1993. View at Publisher · View at Google Scholar
  4. X. Zhou, X. Song, and X. Shi, “A differential equation model of HIV infection of CD4+T-cells with cure rate,” Journal of Mathematical Analysis and Applications, vol. 342, no. 2, pp. 1342–1355, 2008. View at Publisher · View at Google Scholar
  5. A. R. McLean, M. M. Rosado, F. Agenes, R. Vasconcellos, and A. A. Freitas, “Resource competition as a mechanism for B cell homeostasis,” Proceedings of the National Academy of Sciences of the United States of America, vol. 94, no. 11, pp. 5792–5797, 1997. View at Publisher · View at Google Scholar
  6. X. Song and A. U. Neumann, “Global stability and periodic solution of the viral dynamics,” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 281–297, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. L. Lloyd, “The dependence of viral parameter estimates on the assumed viral life cycle: limitations of studies of viral load data,” Proceedings of the Royal Society B, vol. 268, no. 1469, pp. 847–854, 2001. View at Publisher · View at Google Scholar · View at PubMed
  8. D. Li and W. Ma, “Asymptotic properties of a HIV-1 infection model with time delay,” Journal of Mathematical Analysis and Applications, vol. 335, no. 1, pp. 683–691, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. R. McLean and T. B. L. Kirkwood, “A model of human immunodeficiency virus infection in T helper cell clones,” Journal of Theoretical Biology, vol. 147, no. 2, pp. 177–203, 1990. View at Publisher · View at Google Scholar
  10. A. R. McLean and M. A. Nowak, “Models of interactions between HIV and other pathogens,” Journal of Theoretical Biology, vol. 155, no. 1, pp. 69–86, 1992. View at Publisher · View at Google Scholar
  11. J. E. Mittler, B. Sulzer, A. U. Neumann, and A. S. Perelson, “Influence of delayed viral production on viral dynamics in HIV-1 infected patients,” Mathematical Biosciences, vol. 152, no. 2, pp. 143–163, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. A. S. Perelson, P. Essunger, Y. Cao, et al., “Decay characteristics of HIV-1-infected compartments during combination therapy,” Nature, vol. 387, no. 6629, pp. 188–191, 1997. View at Publisher · View at Google Scholar · View at PubMed
  13. J. P. LaSalle, The Stability of Dynamical Systems, SIAM, Philadelphia, Pa, USA, 1976. View at Zentralblatt MATH · View at MathSciNet
  14. B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation, vol. 41 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, UK, 1981. View at Zentralblatt MATH · View at MathSciNet
  15. J. E. Marsden and M. McCracken, The Hopf Bifurcation and Its Applications, vol. 1 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1976. View at Zentralblatt MATH · View at MathSciNet
  16. S. N. Chow and J. K. Hale, Methods of Bifurcation Theory, vol. 251 of Grundlehren der Mathematischen Wissenschaften, Springer, New York, NY, USA, 1982. View at Zentralblatt MATH · View at MathSciNet