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Analysis of a CD4$^+$ T cell viral infection model with a class of saturated infection rate
1. | Department of Applied Mathematics, University of Science and Technology Beijing, Beijing, 100083, China, China, China |
2. | Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083 |
References:
[1] |
S. Bonhoeffer, R. M. May, G. M. Shaw and M. A. Nowak, Virus dynamics and drug therapy, Proc. Natl. Acad., Sci. USA., 94 (1997), 6971-6976. |
[2] |
B. Buonomo and C. Vargas-De-León, Global stability for an HIV-1 infection model including an eclipse stage of infected cells, J. Math. Anal. Appl., 385 (2012), 709-720.
doi: 10.1016/j.jmaa.2011.07.006. |
[3] |
D. Ebert, C. D. Zschokke-Rohringer and H. J. Carius, Dose effects and density- dependent regulation of two microparasites of Daphnia magna, Oecologia, 122 (2000), 200-209.
doi: 10.1007/PL00008847. |
[4] |
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.
doi: 10.1038/373123a0. |
[5] |
D. Kirschner, Using mathematics to understand HIV immune dynamics, Notices Amer. Math. Soc., 43 (1996), 191-202. |
[6] |
A. Korobeinikov and G. C. Wake, Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models, Appl. Math. Lett., 15 (2002), 955-960.
doi: 10.1016/S0893-9659(02)00069-1. |
[7] |
M. Y. Li, H. L. Smith and L. Wang, Global dynamics of an SEIR epidemic model with vertical transmission, SIAM J. Math. Anal., 62 (2001), 58-69.
doi: 10.1137/S0036139999359860. |
[8] |
C. C. McCluskey, Global stability for a class of mass action systems allowing for latency in tuberculosis, J. Math. Anal. Appl., 338 (2008), 518-535.
doi: 10.1016/j.jmaa.2007.05.012. |
[9] |
M. Nowak, R. Anderson, M. Boerlijst, S. Bonhoeffer, R. May and A. McMichael, HIV-1 evolution and disease progression, Science, 274 (1996), 1008-1011.
doi: 10.1126/science.274.5289.1008. |
[10] |
M. Nowak, S. Bonhoeffer, G. Shaw and R. May, Anti-viral drug treatment: Dynamics of resistance in free virus and infected cell populations, J. Theoret. Biol., 184 (1997), 203-217.
doi: 10.1006/jtbi.1996.0307. |
[11] |
M. A. Nowak and R. M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, Oxford, 2000. |
[12] |
A. S. Perelson, Modelling viral and immune system dynamics, Nat. Rev. Immunol, 2 (2002), 28-36.
doi: 10.1038/nri700. |
[13] |
A. Perelson, D. Kirschner and R. De Boer, Dynamics of HIV infection of CD4+ T cells, Math. Biosci., 114 (1993), 81-125.
doi: 10.1016/0025-5564(93)90043-A. |
[14] |
A. Perelson and P. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41 (1999), 3-44.
doi: 10.1137/S0036144598335107. |
[15] |
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.
doi: 10.1126/science.271.5255.1582. |
[16] |
R. R. Regoes, D. Ebert and S. Bonhoeffer, Dose-dependent infection rates of parasites produce the Allee effect in epidemiology, Proc. R. Soc. Lond. B., 269 (2002), 271-279.
doi: 10.1098/rspb.2001.1816. |
[17] |
L. Rong, M. A. Gilchrist, Z. Feng and A. S. Perelson, Modeling within-host HIV-1 dynamics and the evolution of drug resistance: Trade-offs between viral enzyme function and drug susceptibility, J. Theoret. Biol., 247 (2007), 804-818.
doi: 10.1016/j.jtbi.2007.04.014. |
[18] |
X. Song and A. U. Neumann, Global stability and periodic solution of the viral dynamics, J. Math. Anal. Appl., 329 (2007), 281-297.
doi: 10.1016/j.jmaa.2006.06.064. |
[19] |
J. Tumwiine, J. Y. T. Mugisha and L. S. Luboobi, A host-vector model for malaria with infective immigrants, J. Math. Anal. Appl., 361 (2010), 139-149.
doi: 10.1016/j.jmaa.2009.09.005. |
[20] |
C. Vargas De León, Constructions of Lyapunov functions for classic SIS, SIR and SIRS epidemic models with variable population size, Foro-Red-Mat: Revista Electrónica de Contenido Matemático, 26 (2009). |
[21] |
L. Wang and M. Y. Li, Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells, Math. Biosci., 200 (2006), 44-57.
doi: 10.1016/j.mbs.2005.12.026. |
show all references
References:
[1] |
S. Bonhoeffer, R. M. May, G. M. Shaw and M. A. Nowak, Virus dynamics and drug therapy, Proc. Natl. Acad., Sci. USA., 94 (1997), 6971-6976. |
[2] |
B. Buonomo and C. Vargas-De-León, Global stability for an HIV-1 infection model including an eclipse stage of infected cells, J. Math. Anal. Appl., 385 (2012), 709-720.
doi: 10.1016/j.jmaa.2011.07.006. |
[3] |
D. Ebert, C. D. Zschokke-Rohringer and H. J. Carius, Dose effects and density- dependent regulation of two microparasites of Daphnia magna, Oecologia, 122 (2000), 200-209.
doi: 10.1007/PL00008847. |
[4] |
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.
doi: 10.1038/373123a0. |
[5] |
D. Kirschner, Using mathematics to understand HIV immune dynamics, Notices Amer. Math. Soc., 43 (1996), 191-202. |
[6] |
A. Korobeinikov and G. C. Wake, Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models, Appl. Math. Lett., 15 (2002), 955-960.
doi: 10.1016/S0893-9659(02)00069-1. |
[7] |
M. Y. Li, H. L. Smith and L. Wang, Global dynamics of an SEIR epidemic model with vertical transmission, SIAM J. Math. Anal., 62 (2001), 58-69.
doi: 10.1137/S0036139999359860. |
[8] |
C. C. McCluskey, Global stability for a class of mass action systems allowing for latency in tuberculosis, J. Math. Anal. Appl., 338 (2008), 518-535.
doi: 10.1016/j.jmaa.2007.05.012. |
[9] |
M. Nowak, R. Anderson, M. Boerlijst, S. Bonhoeffer, R. May and A. McMichael, HIV-1 evolution and disease progression, Science, 274 (1996), 1008-1011.
doi: 10.1126/science.274.5289.1008. |
[10] |
M. Nowak, S. Bonhoeffer, G. Shaw and R. May, Anti-viral drug treatment: Dynamics of resistance in free virus and infected cell populations, J. Theoret. Biol., 184 (1997), 203-217.
doi: 10.1006/jtbi.1996.0307. |
[11] |
M. A. Nowak and R. M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, Oxford, 2000. |
[12] |
A. S. Perelson, Modelling viral and immune system dynamics, Nat. Rev. Immunol, 2 (2002), 28-36.
doi: 10.1038/nri700. |
[13] |
A. Perelson, D. Kirschner and R. De Boer, Dynamics of HIV infection of CD4+ T cells, Math. Biosci., 114 (1993), 81-125.
doi: 10.1016/0025-5564(93)90043-A. |
[14] |
A. Perelson and P. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41 (1999), 3-44.
doi: 10.1137/S0036144598335107. |
[15] |
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.
doi: 10.1126/science.271.5255.1582. |
[16] |
R. R. Regoes, D. Ebert and S. Bonhoeffer, Dose-dependent infection rates of parasites produce the Allee effect in epidemiology, Proc. R. Soc. Lond. B., 269 (2002), 271-279.
doi: 10.1098/rspb.2001.1816. |
[17] |
L. Rong, M. A. Gilchrist, Z. Feng and A. S. Perelson, Modeling within-host HIV-1 dynamics and the evolution of drug resistance: Trade-offs between viral enzyme function and drug susceptibility, J. Theoret. Biol., 247 (2007), 804-818.
doi: 10.1016/j.jtbi.2007.04.014. |
[18] |
X. Song and A. U. Neumann, Global stability and periodic solution of the viral dynamics, J. Math. Anal. Appl., 329 (2007), 281-297.
doi: 10.1016/j.jmaa.2006.06.064. |
[19] |
J. Tumwiine, J. Y. T. Mugisha and L. S. Luboobi, A host-vector model for malaria with infective immigrants, J. Math. Anal. Appl., 361 (2010), 139-149.
doi: 10.1016/j.jmaa.2009.09.005. |
[20] |
C. Vargas De León, Constructions of Lyapunov functions for classic SIS, SIR and SIRS epidemic models with variable population size, Foro-Red-Mat: Revista Electrónica de Contenido Matemático, 26 (2009). |
[21] |
L. Wang and M. Y. Li, Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells, Math. Biosci., 200 (2006), 44-57.
doi: 10.1016/j.mbs.2005.12.026. |
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