Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay

Discrete and Continuous Dynamical Systems - Series B

Volumn 12, Issue 2, 2009, Pages 511-524

  Zhu, Huiyan ^a   Zou, Xingfu ^b  

^a UNIVERSITY OF SOUTH CHINA   (China)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

HIV 1 infection; Immune response; Intracellular delay; Stability

Indexed keywords

EID: 70349915787     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2009.12.511     Document Type: Conference Paper

References (23)

1. Ft. Arnaout, M. Nowak and D. Wodarz, HIV-1 dynamics revisited: Biphasic decay by cytotoxic lymphocyte killing? Proc. Roy. Soc. Lond. B, 265 (2000), 1347-1354.
2. S. Bonhoeffer, J. Coffin and M. Nowak, Human immunodeficiency virus drug therapy and virus load, Journal of Virology, 71 (1997), 3275-3278.
3. S. Busenberg and K. L. Cooke, "Vertically Transmitted Diseases, " Models and Dynamics (Biomathematics. 23), Springer, New York, 1993.
4. 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.
5. N. Burić, M. Mudrinic and N. Vasović, Time delay in a basic model of the immune response, Chaos, Solitons and Fractals, 12 (2001), 483-489.
6. A. A. Canabarro, I. M. Gléria and M. L. Lyra, Periodic solutions and chaos in a non-linear model for the delayed celluar immune response, Physica A, 342 (2004), 234-241.
7. R. Culshaw, S. Ruan and R. Spiteri, Optimal HIV treatment by maximising immune response, J. Math. Biol., 48 (2004), 545-562.
8. B. Fuchs and B. Levin, "Functions of a Complex Variable and Some of Their Applications, " Pergamon Press, 1961.
9. F. Gantmacher, "The Theory of Matrices, " Vol. 2, Chelsea, New York, 1959.
10. J. Hale and S. M. Verduyn Lunel, "Introduction to Functional Differential Equations, Applied Mathematical Science, " Vol. 99, Springer-Verlag, New York, 1993.
11. T. Kajiwara and T. Sasaki, A note on the stability analysis of pathogen-immune interaction dynamics, Discrete and Continuous Dynamical Systems - Series B, 4 (2004), 615-622.
12. Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics, " Academic Press, San Diego, 1993.
13. W. Liu, Nonlinear oscillation in models of immune response to persistent viruses, Theor. Popul. Biol., 52 (1997), 224-230.
14. M. Nowak and R. May, "Virus Dynamics, " Oxford University Press, 2000.
15. M. Nowak and C. Bangham, Population dynamics of immune response to persistent viruses, Science, 272 (1996), 74-79.
16. P. Nelson, J. Murray and A. Perelson, A model of HIV-1 pathogenesis that includes an intracellular delay, Math. Biosci., 163 (2000), 201-215.
17. P. Nelson and A. Perelson, Mathematical analysis of delay differential equation models of HIV-1 infection, Math. Bioscien., 179 (2002), 73-94.
18. A. Perelson and P. Nelson, Mathematical models of HIV dynamics in vivo, SIAM Rev., 41 (1999), 3-4.
19. 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), 1582-1586.
20. G. Stépán, "Retarded Dynamical Systems: Stability and Characteristic Functions, " Longman Science and Technical, New York, 1989.
21. K. Wang, W. Wang and X. Liu, Global Stability in a viral infection model with lytic and nonlytic immune response, Computers and Mathematics with Applications, 51 (2006), 1593-1610.
22. K. Wang, W. Wang, H. Pang and X. Liu, Complex dynamic behavior in a viral model with delayed immune response, Physica D, 226 (2007), 197-208.
23. H. Zhu and X. Zou, Impact of delays in cell infection and virus production on HIV-1 dynamics, Math. Medic. Bio., 25 (2008), 99-112.