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Volume 2013 (2013), Article ID 103708, 11 pages
Stochastic Model for In-Host HIV Dynamics with Therapeutic Intervention
1Center for Applied Research in Mathematical Sciences, Strathmore University, P.O. Box 59857 00200, Nairobi, Kenya
2Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda
Received 22 February 2013; Accepted 27 March 2013
Academic Editors: X.-Y. Lou and J. Suehnel
Copyright © 2013 Waema R. Mbogo 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.
- M. Yan and Z. Xiang, “A delay-differential equation model of HIV infection of CD4+ T-cells with cure rate,” International Mathematical Forum, vol. 7, pp. 1475–1481, 2012.
- 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.
- D. E. Kirschner, “Using mathematics to understand HIV immune dynamics,” Mathematical Reviews, vol. 43, pp. 191–202, 1996.
- A. S. Perelson, A. U. Neumann, M. Markowitz, J. M. Leonard, and D. D. Ho, “HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time,” Science, vol. 271, no. 5255, pp. 1582–1586, 1996.
- J. W. Mellors, A. Munoz, J. V. Giorgi et al., “Plasma viral load and CD4+ lymphocytes as prognostic markers of HIV-1 infection,” Annals of Internal Medicine, vol. 126, pp. 946–954, 1997.
- M. Nijhuis, C. A. B. Boucher, P. Schipper, T. Leitner, R. Schuurman, and J. Albert, “Stochastic processes strongly influence HIV-1 evolution during suboptimal protease-inhibitor therapy,” Proceedings of the National Academy of Sciences of the United States of America, vol. 95, no. 24, pp. 14441–14446, 1998.
- W. Y. Tan and Z. Xiang, “Some state space models of HIV pathogenesis under treatment by anti-viral drugs in HIV-infected individuals,” Mathematical Biosciences, vol. 156, no. 1-2, pp. 69–94, 1999.
- D. R. Bangsberg, T. C. Porco, C. Kagay et al., “Modeling the HIV protease inhibitor adherence-resistance curve by use of empirically derived estimates,” Journal of Infectious Diseases, vol. 190, no. 1, pp. 162–165, 2004.
- S. S. Y. Venkata, M. O. L. Morire, U. Swaminathan, and M. Yeko, “A stochastic model of the dynamics of HIV under a combination therapeutic intervention,” Orion, vol. 25, pp. 17–30, 2009.
- P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29–48, 2002.
- O. Arino, M. L. Hbid, and A. E. Dads, Delay Differential Equations and Applications, Series II, Springer, Berlin, Germany, 2006.
- A. S. Perelson, D. E. Kirschner, and R. De Boer, “Dynamics of HIV infection of CD4+ T cells,” Mathematical Biosciences, vol. 144, no. 1, pp. 81–125, 1993.
- P. De Leenheer and H. L. Smith, “Virus dynamics: a global analysis,” SIAM Journal on Applied Mathematics, vol. 63, no. 4, pp. 1313–1327, 2003.
- 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.
- L. Wang and M. Y. Li, “Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells,” Mathematical Biosciences, vol. 200, no. 1, pp. 44–57, 2006.
- L. Wang and S. Ellermeyer, “HIV infection and CD4+ T cell dynamics,” Discrete and Continuous Dynamical Systems B, vol. 6, no. 6, pp. 1417–1430, 2006.
- 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.
- A. V. M. Herz, S. Bonhoeffer, R. M. Anderson, R. M. May, and M. A. Nowak, “Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay,” Proceedings of the National Academy of Sciences of the United States of America, vol. 93, no. 14, pp. 7247–7251, 1996.
- 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.
- M. Y. Li and H. Shu, “Multiple stable periodic oscillations in a mathematical model of CTL response to HTLV-I infection,” Bulletin of Mathematical Biology, vol. 73, no. 8, pp. 1774–1793, 2011.
- 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.
- 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.
- Y. Wang, Y. Zhou, J. Wu, and J. Heffernan, “Oscillatory viral dynamics in a delayed HIV pathogenesis model,” Mathematical Biosciences, vol. 219, no. 2, pp. 104–112, 2009.
- M. Y. Li and H. Shu, “Global dynamics of an in-host viral model with intracellular delay,” Bulletin of Mathematical Biology, vol. 72, no. 6, pp. 1492–1505, 2010.
- M. A. Nowak and R. M. May, Virus Dynamics, Cambridge University Press, Cambridge, UK, 2000.
- H. C. Tuckwell and F. Y. M. Wan, “On the behavior of solutions in viral dynamical models,” BioSystems, vol. 73, no. 3, pp. 157–161, 2004.