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Impact of delay on HIV-1 dynamics of fighting a virus with another virus
1. | Department of Applied Mathematics, Western University, London, Ontario N6A 5B7, Canada, Canada, Canada |
References:
[1] |
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.
doi: 10.1137/S0036141000376086. |
[2] |
S. Busenberg and K. Cooke, Vertically Transmitted Diseases: Models and Dynamics, Springer, New York, 1993.
doi: 10.1007/978-3-642-75301-5. |
[3] | |
[4] |
J. Hale and S. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-4342-7. |
[5] |
B. D. Hassard, N. D. Kazarinoff and Y.-H. Wan, Theory and Applications of Hopf Bifurcation, Cambridge University Press, Cambridge, 1981. |
[6] |
X. Jiang, P. Yu, Z. Yuan and X. Zou, Dynamics of an HIV-1 therapy model of fighting a virus with another virus, Journal of Biological Dynamics, 3 (2009), 387-409.
doi: 10.1080/17513750802485007. |
[7] |
T. Kajiwara, T. Saraki and Y. Takeuchi, Construction of lyapunov functionals for delay differential equations in virology and epidemiology, Nonlinear Analysis: Real World Applications, 13 (2012), 1802-1826.
doi: 10.1016/j.nonrwa.2011.12.011. |
[8] |
J. LaSalle, The Stability of Dynamical Systems, SIAM, Philadelphia, 1976. |
[9] |
C. Michie, A. McLean, C. Alcock and P. Beverly, Lifespan of human lymphocyte subsets defined by cd45 isoforms, Nature, 360 (1992), 264-265.
doi: 10.1038/360264a0. |
[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), 143-163. |
[11] |
P. W. Nelson, J. D. Murray and A. S. Perelson, A model of HIV-1 pathogenesis that includes an intracellular delay, Mathematical Biosciences, 163 (2000), 201-215.
doi: 10.1016/S0025-5564(99)00055-3. |
[12] |
G. Nolan, Harnessing viral devices as pharmaceuticals: Fighting HIV-1s fire with fire, Cell, 90 (1997), 821-824. |
[13] |
T. Revilla and G. García-Ramos, Fighting a virus with a virus: A dynamic model for HIV-1 therapy, Math. Biosci., 185 (2003), 191-203.
doi: 10.1016/S0025-5564(03)00091-9. |
[14] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, Vol. 41, American Mathematical Socienty, Providence, RI, 1995. |
[15] |
E. Wagner and M. Hewlett, Basic Virology, Blackwell, New York, 1999. |
[16] |
P. Yu, Y. Ding and W. Jiang, Equivalence of MTS method and CMR method for delay differential equations associated with semisimple singularity, Int. J. Bifurcation and Chaos, 24 (2014), 1450003, 49 pp.
doi: 10.1142/S0218127414500035. |
[17] |
P. Yu and X. Zou, Bifurcation analysis on an HIV-1 Model with constant injection of recombinant, Int. J. Bifurcation and Chaos, 22 (2012), 1250062, 21 pp.
doi: 10.1142/S0218127412500629. |
[18] |
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.
doi: 10.1093/imammb/dqm010. |
[19] |
H. Zhu and X. Zou, Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay, Disc. Cont. Dyan. Syst. B., 12 (2009), 511-524.
doi: 10.3934/dcdsb.2009.12.511. |
show all references
References:
[1] |
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.
doi: 10.1137/S0036141000376086. |
[2] |
S. Busenberg and K. Cooke, Vertically Transmitted Diseases: Models and Dynamics, Springer, New York, 1993.
doi: 10.1007/978-3-642-75301-5. |
[3] | |
[4] |
J. Hale and S. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-4342-7. |
[5] |
B. D. Hassard, N. D. Kazarinoff and Y.-H. Wan, Theory and Applications of Hopf Bifurcation, Cambridge University Press, Cambridge, 1981. |
[6] |
X. Jiang, P. Yu, Z. Yuan and X. Zou, Dynamics of an HIV-1 therapy model of fighting a virus with another virus, Journal of Biological Dynamics, 3 (2009), 387-409.
doi: 10.1080/17513750802485007. |
[7] |
T. Kajiwara, T. Saraki and Y. Takeuchi, Construction of lyapunov functionals for delay differential equations in virology and epidemiology, Nonlinear Analysis: Real World Applications, 13 (2012), 1802-1826.
doi: 10.1016/j.nonrwa.2011.12.011. |
[8] |
J. LaSalle, The Stability of Dynamical Systems, SIAM, Philadelphia, 1976. |
[9] |
C. Michie, A. McLean, C. Alcock and P. Beverly, Lifespan of human lymphocyte subsets defined by cd45 isoforms, Nature, 360 (1992), 264-265.
doi: 10.1038/360264a0. |
[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), 143-163. |
[11] |
P. W. Nelson, J. D. Murray and A. S. Perelson, A model of HIV-1 pathogenesis that includes an intracellular delay, Mathematical Biosciences, 163 (2000), 201-215.
doi: 10.1016/S0025-5564(99)00055-3. |
[12] |
G. Nolan, Harnessing viral devices as pharmaceuticals: Fighting HIV-1s fire with fire, Cell, 90 (1997), 821-824. |
[13] |
T. Revilla and G. García-Ramos, Fighting a virus with a virus: A dynamic model for HIV-1 therapy, Math. Biosci., 185 (2003), 191-203.
doi: 10.1016/S0025-5564(03)00091-9. |
[14] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, Vol. 41, American Mathematical Socienty, Providence, RI, 1995. |
[15] |
E. Wagner and M. Hewlett, Basic Virology, Blackwell, New York, 1999. |
[16] |
P. Yu, Y. Ding and W. Jiang, Equivalence of MTS method and CMR method for delay differential equations associated with semisimple singularity, Int. J. Bifurcation and Chaos, 24 (2014), 1450003, 49 pp.
doi: 10.1142/S0218127414500035. |
[17] |
P. Yu and X. Zou, Bifurcation analysis on an HIV-1 Model with constant injection of recombinant, Int. J. Bifurcation and Chaos, 22 (2012), 1250062, 21 pp.
doi: 10.1142/S0218127412500629. |
[18] |
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.
doi: 10.1093/imammb/dqm010. |
[19] |
H. Zhu and X. Zou, Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay, Disc. Cont. Dyan. Syst. B., 12 (2009), 511-524.
doi: 10.3934/dcdsb.2009.12.511. |
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