References
-
D. Ho, A. Neumann, A. Perelson, W. Chen, J. Leonard, and M. Markowitz, Rapid turnover of plasma virions and
$CD4^+$ lymphocytes in HIV-1 infection,Nature 373 (1995), 123-126 https://doi.org/10.1038/373123a0 - 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 https://doi.org/10.1038/373117a0
- 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
- 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 https://doi.org/10.1038/387188a0
- A. Neumann, N. Lam, H. Dahari, D. Gretch, T. Wiley, T. Layden, and A. Perel- son, Hepatitis C viral dynamics in vivo and antiviral efficacy of the interferon-ff therapy, Science 282 (1998), 103-107
- A. Perelson and P. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev. 41 (1999), no. 1, 3-44 https://doi.org/10.1137/S0036144598335107
- 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 https://doi.org/10.1073/pnas.93.14.7247
- Z. Grossman, M. Feinberg, V. Kuznetsov, D. Dimitrov, and W. Paul, HIV infection: how effective is drug combination treatment, Immunol. Today 19 (1998), 528 https://doi.org/10.1016/S0167-5699(98)01353-X
- 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 https://doi.org/10.1038/13410
- 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 https://doi.org/10.1016/S0025-5564(98)10027-5
- J. Tam, Delay effect in a model for virus replication, IMA J. Math. Appl. Med. Biol. 16 (1999), 29 https://doi.org/10.1093/imammb/16.1.29
- P. Nelson, J. Murray, and A. Perelson,A model of HIV-1 pathogenesis that includes an intracellular delay, Math. Biosci. 163 (2000), 201 https://doi.org/10.1016/S0025-5564(99)00055-3
- J. Mittler, M. Markowitz, D. Ho, and A. Perelson,Refined estimates for HIV-1 clearance rate and intracellular delay, AIDS, 13 (1999), 1415 https://doi.org/10.1097/00002030-199907300-00023
- P. Nelson and A. Perelson, Mathematical analysis of delay differential equation models of HIV-1 infection, Math. Biosci. 179 (2002), 73-94 https://doi.org/10.1016/S0025-5564(02)00099-8
- 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 https://doi.org/10.1007/BF02458826
- J. K. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977
- J. K. Hale and P. Waltman, Persistence in infinite-dimensional systems, SIAM J. Math. Anal. 20 (1989), 388-396 https://doi.org/10.1137/0520025
- H. Smith, Monotone semiflows generated by functional differential equations, J. Differential Equations 66 (1987), 420-442 https://doi.org/10.1016/0022-0396(87)90027-1
- K. Gopalsamy, Stability and oscillations in delay differential equations of population dynamics, Kluwer Academic, Dordrecht/Norwell, MA
- Hsiu-Rong Zhu and H. Smith, Stable periodic orbits for a class three dimentional competitive systems, J. Differential Equations 110 (1994), 143-156 https://doi.org/10.1006/jdeq.1994.1063
- 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 https://doi.org/10.1137/S0036141000376086
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