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Global stability for a HIV-1 infection model with cell-mediated immune response and intracellular delay
1. | School of Mathematical Science, Heilongjiang University, Harbin, Heilongjiang 150080, China |
2. | Department of Mathematics, Arts and Science College, Harbin Normal University, Harbin, Heilongjiang 150025, China |
References:
[1] |
R. 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.
doi: 10.1098/rspb.2000.1149. |
[2] |
R. Culshaw, S. Ruan and R. Spiteri, Optimal HIV treatment by maximising immune response, J. Math. Biol., 48 (2004), 545-562.
doi: 10.1007/s00285-003-0245-3. |
[3] |
G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals for delay differential equations model for viral infections, SIAM J. Appl. Math., 70 (2010), 2693-2708.
doi: 10.1137/090780821. |
[4] |
J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional-Differential Equations," Applied Mathematical Science, 99, Springer-Verlag, New York, 1993. |
[5] |
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879-883.
doi: 10.1016/j.bulm.2004.02.001. |
[6] |
Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics," Mathematics in Science and Engineering, 191, Academics Press, Inc., Boston, MA, 1993. |
[7] |
C. C. McCluskey, Complete global stability for an SIR epidemic model with delay-distributed or discrete, Nonlinear Anal. Real World Appl., 11 (2010), 55-59.
doi: 10.1016/j.nonrwa.2008.10.014. |
[8] |
M. Nowak and C. Bangham, Population dynamics of immune response to persistent viruses, Science, 272 (1996), 74-79.
doi: 10.1126/science.272.5258.74. |
[9] |
K. Wang, W. Wang and X. Liu, Global stability in a viral infection model with lytic and nonlytic immune response, Comput. Math. Appl., 51 (2006), 1593-1610.
doi: 10.1016/j.camwa.2005.07.020. |
[10] |
J. Wang, G. Huang, Y. Takeuchi and S. Liu, SVEIR epidemiological model with varying infectivity and distributed delays, Math. Biosci. Eng., 8 (2011), 875-888.
doi: 10.3934/mbe.2011.8.875. |
[11] |
J. Wang, G. Huang and Y. Takeuchi, Global asymptotic stability for HIV-1 dynamics with two distributed delays, Math. Medic. Bio.
doi: 10.1093/imammb/dqr009. |
[12] |
H. Zhu and X. Zou, Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay, Discrete and Continuous Dynamical Systems Series B, 12 (2009), 511-524. |
show all references
References:
[1] |
R. 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.
doi: 10.1098/rspb.2000.1149. |
[2] |
R. Culshaw, S. Ruan and R. Spiteri, Optimal HIV treatment by maximising immune response, J. Math. Biol., 48 (2004), 545-562.
doi: 10.1007/s00285-003-0245-3. |
[3] |
G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals for delay differential equations model for viral infections, SIAM J. Appl. Math., 70 (2010), 2693-2708.
doi: 10.1137/090780821. |
[4] |
J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional-Differential Equations," Applied Mathematical Science, 99, Springer-Verlag, New York, 1993. |
[5] |
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879-883.
doi: 10.1016/j.bulm.2004.02.001. |
[6] |
Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics," Mathematics in Science and Engineering, 191, Academics Press, Inc., Boston, MA, 1993. |
[7] |
C. C. McCluskey, Complete global stability for an SIR epidemic model with delay-distributed or discrete, Nonlinear Anal. Real World Appl., 11 (2010), 55-59.
doi: 10.1016/j.nonrwa.2008.10.014. |
[8] |
M. Nowak and C. Bangham, Population dynamics of immune response to persistent viruses, Science, 272 (1996), 74-79.
doi: 10.1126/science.272.5258.74. |
[9] |
K. Wang, W. Wang and X. Liu, Global stability in a viral infection model with lytic and nonlytic immune response, Comput. Math. Appl., 51 (2006), 1593-1610.
doi: 10.1016/j.camwa.2005.07.020. |
[10] |
J. Wang, G. Huang, Y. Takeuchi and S. Liu, SVEIR epidemiological model with varying infectivity and distributed delays, Math. Biosci. Eng., 8 (2011), 875-888.
doi: 10.3934/mbe.2011.8.875. |
[11] |
J. Wang, G. Huang and Y. Takeuchi, Global asymptotic stability for HIV-1 dynamics with two distributed delays, Math. Medic. Bio.
doi: 10.1093/imammb/dqr009. |
[12] |
H. Zhu and X. Zou, Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay, Discrete and Continuous Dynamical Systems Series B, 12 (2009), 511-524. |
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