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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 264759, 8 pages
http://dx.doi.org/10.1155/2013/264759
Research Article

Global Dynamics of HIV Infection of CD4+ T Cells and Macrophages

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71511, Egypt
3Department of Mathematics, Science and Literature College in Namas, King Khalid University, Abha 61431, Saudi Arabia

Received 16 May 2013; Revised 7 July 2013; Accepted 8 July 2013

Academic Editor: Zhengqiu Zhang

Copyright © 2013 A. M. Elaiw and A. S. Alsheri. 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. M. A. Nowak and R. M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, Oxford, UK, 2000. View at Zentralblatt MATH · View at MathSciNet
  2. Z. Yuan and X. Zou, “Global threshold dynamics in an HIV virus model with nonlinear infection rate and distributed invasion and production delays,” Mathematical Biosciences and Engineering, vol. 10, no. 2, pp. 483–498, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. 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 Scopus
  4. 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
  5. G. Huang, H. Yokoi, Y. Takeuchi, T. Kajiwara, and T. Sasaki, “Impact of intracellular delay, immune activation delay and nonlinear incidence on viral dynamics,” Japan Journal of Industrial and Applied Mathematics, vol. 28, no. 3, pp. 383–411, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. Huang, W. Ma, and Y. Takeuchi, “Global properties for virus dynamics model with Beddington-DeAngelis functional response,” Applied Mathematics Letters, vol. 22, no. 11, pp. 1690–1693, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. Xu, “Global stability of the virus dynamics model with Crowley-Martin functional response,” Electronic Journal of Qualitative Theory of Differential Equations, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  8. X. Zhou and J. Cui, “Global stability of the viral dynamics with Crowley-Martin functional response,” Bulletin of the Korean Mathematical Society, vol. 48, no. 3, pp. 555–574, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  9. A. Korobeinikov, “Global asymptotic properties of virus dynamics models with dose-dependent parasite reproduction and virulence, and non-linear incidence rate,” Mathematical Medicine and Biology, vol. 26, pp. 225–239, 2009.
  10. R. V. Culshaw and S. Ruan, “A delay-differential equation model of HIV infection of CD4+ T-cells,” Mathematical Biosciences, vol. 165, no. 1, pp. 27–39, 2000. View at Publisher · View at Google Scholar · View at Scopus
  11. P. W. Nelson, J. D. Murray, and A. S. Perelson, “A model of HIV-1 pathogenesis that includes an intracellular delay,” Mathematical Biosciences, vol. 163, no. 2, pp. 201–215, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. N. M. Dixit and A. S. Perelson, “Complex patterns of viral load decay under antiretroviral therapy: influence of pharmacokinetics and intracellular delay,” Journal of Theoretical Biology, vol. 226, no. 1, pp. 95–109, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  13. S. Liu and L. Wang, “Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy,” Mathematical Biosciences and Engineering, vol. 7, no. 3, pp. 675–685, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. G. Huang, W. Ma, and Y. Takeuchi, “Global analysis for delay virus dynamics model with Beddington-DeAngelis functional response,” Applied Mathematics Letters, vol. 24, no. 7, pp. 1199–1203, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. P. W. Nelson and A. S. Perelson, “Mathematical analysis of delay differential equation models of HIV-1 infection,” Mathematical Biosciences, vol. 179, no. 1, pp. 73–94, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. R. Xu, “Global dynamics of an HIV-1 infection model with distributed intracellular delays,” Computers & Mathematics with Applications, vol. 61, no. 9, pp. 2799–2805, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. G. Huang, Y. Takeuchi, and W. Ma, “Lyapunov functionals for delay differential equations model of viral infections,” SIAM Journal on Applied Mathematics, vol. 70, no. 7, pp. 2693–2708, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. M. Y. Li and H. Shu, “Impact of intracellular delays and target-cell dynamics on in vivo viral infections,” SIAM Journal on Applied Mathematics, vol. 70, no. 7, pp. 2434–2448, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. 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 Scopus
  20. D. S. Callaway and A. S. Perelson, “HIV-1 infection and low steady state viral loads,” Bulletin of Mathematical Biology, vol. 64, no. 1, pp. 29–64, 2002. View at Publisher · View at Google Scholar · View at Scopus
  21. A. S. Perelson and P. W. Nelson, “Mathematical analysis of HIV-1 dynamics in vivo,” SIAM Review, vol. 41, no. 1, pp. 3–44, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. A. M. Elaiw and X. Xia, “HIV dynamics: analysis and robust multirate MPC-based treatment schedules,” Journal of Mathematical Analysis and Applications, vol. 359, no. 1, pp. 285–301, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  23. A. M. Elaiw and A. M. Shehata, “Stability and feedback stabilization of HIV infection model with two classes of target cells,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 963864, 20 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. A. M. Elaiw, “Global properties of a class of HIV models,” Nonlinear Analysis, vol. 11, no. 4, pp. 2253–2263, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. A. M. Elaiw and S. A. Azoz, “Global properties of a class of HIV infection models with Beddington-DeAngelis functional response,” Mathematical Methods in the Applied Sciences, vol. 36, no. 4, pp. 383–394, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  26. A. Elaiw, I. Hassanien, and S. Azoz, “Global stability of HIV infection models with intracellular delays,” Journal of the Korean Mathematical Society, vol. 49, no. 4, pp. 779–794, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. A. M. Elaiw, “Global dynamics of an HIV infection model with two classes of target cells and distributed delays,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 253703, 13 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. A. M. Elaiw, “Global properties of a class of virus infection models with multitarget cells,” Nonlinear Dynamics, vol. 69, no. 1-2, pp. 423–435, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. A. M. Elaiw and M. A. Alghamdi, “Global properties of virus dynamics models with multitarget cells and discrete-time delays,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 201274, 19 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. A. A. Bakr, A. M. Elaiw, and Z. A. S. Raizah, “Mathematical analysis of virus dynamics model with multitarget cells in vivo,” Mathematical Sciences Letters, vol. 2, no. 3, 2013.
  31. M. A. Obaid, “Global analysis of a virus infection model with multitarget cells and distrib- uted intracellular delays,” Life Science Journal, vol. 9, no. 4, pp. 1500–1508, 2012.
  32. J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, vol. 99 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1993. View at MathSciNet
  33. C. C. McCluskey, “Complete global stability for an SIR epidemic model with delay—distributed or discrete,” Nonlinear Analysis, vol. 11, no. 1, pp. 55–59, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. T. Kajiwara, T. Sasaki, and Y. Takeuchi, “Construction of Lyapunov functionals for delay differential equations in virology and epidemiology,” Nonlinear Analysis, vol. 13, no. 4, pp. 1802–1826, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet