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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 169427, 12 pages
Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response
Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 Heping West Road, Shijiazhuang, Hebei 050003, China
Received 29 May 2013; Accepted 14 December 2013
Academic Editor: Juan J. Nieto
Copyright © 2013 Haibin Wang and Rui Xu. 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. A. Nowak and C. R. M. Bangham, “Population dynamics of immune responses to persistent viruses,” Science, vol. 272, no. 5258, pp. 74–79, 1996.
- 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.
- A. Korobeinikov, “Global properties of basic virus dynamics models,” Bulletin of Mathematical Biology, vol. 66, no. 4, pp. 879–883, 2004.
- 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.
- X. Wang and X. Song, “Global stability and periodic solution of a model for HIV infection of CD4+ T cells,” Applied Mathematics and Computation, vol. 189, no. 2, pp. 1331–1340, 2007.
- K. Wang, W. Wang, H. Pang, and X. Liu, “Complex dynamic behavior in a viral model with delayed immune response,” Physica D, vol. 226, no. 2, pp. 197–208, 2007.
- A. A. Canabarro, I. M. Gléria, and M. L. Lyra, “Periodic solutions and chaos in a non-linear model for the delayed cellular immune response,” Physica A, vol. 342, no. 1-2, pp. 234–241, 2004.
- H. Zhu, Y. Luo, and M. Chen, “Stability and Hopf bifurcation of a HIV infection model with CTL-response delay,” Computers and Mathematics with Applications, vol. 62, no. 8, pp. 3091–3102, 2011.
- Z. Wang and R. Xu, “Stability and Hopf bifurcation in a viral infection model with nonlinear incidence rate and delayed immune response,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 2, pp. 964–978, 2012.
- D. C. Douek, J. M. Brenchley, M. R. Betts et al., “HIV preferentially infects HIV-specific CD4+ T cells,” Nature, vol. 417, no. 6884, pp. 95–98, 2002.
- O. Bagasra and R. J. Pomerantz, “Human immunodeficiency virus type I provirus is demonstrated in peripheral blood monocytes in vivo: a study utilizing an in situ polymerase chain reaction,” AIDS Research and Human Retroviruses, vol. 9, no. 1, pp. 69–76, 1993.
- M. J. Pace, L. Agosto, E. H. Graf, and U. O'Doherty, “HIV reservoirs and latency models,” Virology, vol. 411, no. 2, pp. 344–354, 2011.
- D. C. Krakauer and M. Nowak, “T cell induced pathogenesis in HIV: bystander effects and latent infection,” Proceedings of the Royal Society B, vol. 266, no. 1423, pp. 1069–1075, 1999.
- M. A. Capistrán, “A study of latency, reactivation and apoptosis throughout HIV pathogenesis,” Mathematical and Computer Modelling, vol. 52, no. 7-8, pp. 1011–1015, 2010.
- J. K. Hale and S. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, New York, NY, USA, 1993.
- J. P. LaSalle, The Stability of Dynamical System, Regional Conference Series in Applied Mathematics, SIAM, Philadephia, Pa, USA, 1976.