A delay-differential equation model of HIV infection of CD4+ T-cells

Journal of the Korean Mathematical Society

Volumn 42, Issue 5, 2005, Pages 1071-1086

  Song, Xinyu ^a   Cheng, Shuhan ^b  

^a XINYANG NORMAL UNIVERSITY   (China)

^b SHANDONG AGRICULTURAL UNIVERSITY   (China)

Author keywords

HCV; HIV; Hopf bifurcation; Periodic solution; Stability

Indexed keywords

EID: 25444491230     PISSN: 03049914     EISSN: None     Source Type: Journal    
DOI: 10.4134/JKMS.2005.42.5.1071     Document Type: Article

References (21)

1. + lymphocytes in HIV-1 infection, Nature 373 (1995), 123-126.
2. X. Wei, S. Ghosh, M. Taylor, V. Johnson, E. Emini, P. Deutsch, J. Lifson, S. Bonhoeffer, M. Nowak, B. Hahn, S. Saag, and G. Shaw, Viral dynamics in human immunodeficiency virus type 1 infection, Nature 373 (1995), 117.
3. A. Perelson, A. Neumann, M. Markowitz, J. Leonard, and D. Ho, HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time, Science 271 (1996), 1582.
4. A. Perelson, P. Essunger, Y. Cao, M. Vesanen, A. Hurley, K. Saksela, M. Markowitz, and D. Ho, Decay characteristics of HIV-1-infected compartments during combination therapy, Nature 387 (1997), 188.
5. A. Neumann, N. Lam, H. Dahari, D. Gretch, T. Wiley, T. Layden, and A. Perelson, Hepatitis C viral dynamics in vivo and antiviral efficacy of the interferon-α therapy, Science 282 (1998), 103-107.
6. A. Perelson and P. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev. 41 (1999), no. 1, 3-44.
7. V. Herz, S. Bonhoeffer, R. Anderson, R. May, and M. Nowak, Viral dynamics in vivo: limitations on estimations on intracellular delay and virus decay, Proc. Natl. Acad. Sci. USA 93 (1996), 7247-7251.
8. Z. Grossman, M. Feinberg, V. Kuznetsov, D. Dimitrov, and W. Paul, HIV infection: how effective is drug combination treatment, Immunol. Today 19 (1998), 528.
9. Z. Grossman, M. Polis, M. Feinberg, I. Levi, S. Jankelevich, R. Yarchoan, J. Boon, F. de Wolf, J. Lange, J. Goudsmit, D. Dimitrov, and W. Paul, Ongoing HIV dissemination during HAART, Nat. Med. 5 (1999), 1099.
10. J. Mittler, B. Sulzer, A. Neumann, and A. Perelson, Influence of delayed virus production on viral dynamics in HIV-1 infected patients, Math. Biosci. 152 (1998), 143.
11. J. Tam, Delay effect in a model for virus replication, IMA J. Math. Appl. Med. Biol. 16 (1999), 29.
12. P. Nelson, J. Murray, and A. Perelson, A model of HIV-1 pathogenesis that includes an intracellular delay, Math. Biosci. 163 (2000), 201.
13. J. Mittler, M. Markowitz, D. Ho, and A. Perelson, Refined estimates for HIV-1 clearance rate and intracellular delay, AIDS, 13 (1999), 1415.
14. P. Nelson and A. Perelson, Mathematical analysis of delay differential equation models of HIV-1 infection, Math. Biosci. 179 (2002), 73-94.
15. H. I. Freedman and V. Sree Hari Rao, The trade-off between mutual interference and time lags in predator-prey systems, Bull. Math. Biol. 45 (1983), 991-1003.
16. J. K. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977.
17. J. K. Hale and P. Waltman, Persistence in infinite-dimensional systems, SIAM J. Math. Anal. 20 (1989), 388-396.
18. H. Smith, Monotone semiflows generated by functional differential equations, J. Differential Equations 66 (1987), 420-442.
19. K. Gopalsamy, Stability and oscillations in delay differential equations of population dynamics, Kluwer Academic, Dordrecht/Norwell, MA
20. Hsiu-Rong Zhu and H. Smith, Stable periodic orbits for a class three dimentional competitive systems, J. Differential Equations 110 (1994), 143-156.
21. E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal. 33 (2002), 1144-1165.