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Global analysis of age-structured within-host virus model
1. | Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, United States |
References:
[1] |
R. Adams and J. Fournier, "Sobolev Spaces,'' Second edition, Pure Appl. Math., 140, Elsevier/Academic Press, Amsterdam, 2003. |
[2] |
C. L. Althaus, A. S. De Vos and R. J. De Boer, Reassessing the human immunodeficiency virus type 1 life cycle through age-structured modeling: life span of infected cells, viral generation time, and basic reproductive number, $R_0$, J. Virol., 83 (2009), 7659-7667. |
[3] |
P. De Leenheer and S. S. Pilyugin, Multistrain virus dynamics with mutations: A global analysis, Math. Med. Biol., 25 (2008), 285-322. |
[4] |
M. A. Gilchrist, D. Coombs and A. S. Perelson, Optimizing within-host viral fitness: Infected cell lifespan and virion production rate, J. Theor. Biol., 229 (2004), 281-288.
doi: 10.1016/j.jtbi.2004.04.015. |
[5] |
J. K. Hale, "Asymptotic Behavior of Dissipative Systems,'' Math. Surv. Monogr., 25, Am. Math. Soc., Providence, RI, 1988. |
[6] |
J. K. Hale and P. Waltman, Persistence in infinite-dimensional systems, SIAM J. Math. Anal., 20 (1989), 388-395.
doi: 10.1137/0520025. |
[7] |
G. Huang, X. Liu and Y. Takeuchi, Lyapunov functions and global stability for age-structured HIV infection model, SIAM J. Appl. Math., 72 (2012), 25-38.
doi: 10.1137/110826588. |
[8] |
P. Magal, C. C. McCluskey and G. F. Webb, Lyapunov functional and global asymptotic stability for an infection-age model, Appl. Anal., 89 (2010), 1109-1140.
doi: 10.1080/00036810903208122. |
[9] |
P. Magal and X.-Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37 (2005), 251-275.
doi: 10.1137/S0036141003439173. |
[10] |
P. W. Nelson, M. A. Gilchrist, D. Coombs, J. Hyman and A. S. Perelson, An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells, Math. Biosci. Eng., 1 (2004), 267-288.
doi: 10.3934/mbe.2004.1.267. |
[11] |
P. W. Nelson and A. S. Perelson, Mathematical analysis of delay differential equation models of HIV-1 infection, Math. Biosci., 179 (2002), 73-94.
doi: 10.1016/S0025-5564(02)00099-8. |
[12] |
A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41 (1999), 3-44.
doi: 10.1137/S0036144598335107. |
[13] |
L. B. Rong, Z. Feng and A. S. Perelson, Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy, SIAM J. Appl. Math., 67 (2007), 731-756.
doi: 10.1137/060663945. |
[14] |
H. R. Thieme, Semiflows generated by Lipschitz perturbations of non-densely defined operators, Differential Integral Equations, 3 (1990), 1035-1066. |
[15] |
G. F. Webb, "Theory of Nonlinear Age-Dependent Population Dynamics,'' Monographs and Textbooks in Pure and Applied Mathematics, 89, Marcel Dekker, Inc., New York, 1985. |
show all references
References:
[1] |
R. Adams and J. Fournier, "Sobolev Spaces,'' Second edition, Pure Appl. Math., 140, Elsevier/Academic Press, Amsterdam, 2003. |
[2] |
C. L. Althaus, A. S. De Vos and R. J. De Boer, Reassessing the human immunodeficiency virus type 1 life cycle through age-structured modeling: life span of infected cells, viral generation time, and basic reproductive number, $R_0$, J. Virol., 83 (2009), 7659-7667. |
[3] |
P. De Leenheer and S. S. Pilyugin, Multistrain virus dynamics with mutations: A global analysis, Math. Med. Biol., 25 (2008), 285-322. |
[4] |
M. A. Gilchrist, D. Coombs and A. S. Perelson, Optimizing within-host viral fitness: Infected cell lifespan and virion production rate, J. Theor. Biol., 229 (2004), 281-288.
doi: 10.1016/j.jtbi.2004.04.015. |
[5] |
J. K. Hale, "Asymptotic Behavior of Dissipative Systems,'' Math. Surv. Monogr., 25, Am. Math. Soc., Providence, RI, 1988. |
[6] |
J. K. Hale and P. Waltman, Persistence in infinite-dimensional systems, SIAM J. Math. Anal., 20 (1989), 388-395.
doi: 10.1137/0520025. |
[7] |
G. Huang, X. Liu and Y. Takeuchi, Lyapunov functions and global stability for age-structured HIV infection model, SIAM J. Appl. Math., 72 (2012), 25-38.
doi: 10.1137/110826588. |
[8] |
P. Magal, C. C. McCluskey and G. F. Webb, Lyapunov functional and global asymptotic stability for an infection-age model, Appl. Anal., 89 (2010), 1109-1140.
doi: 10.1080/00036810903208122. |
[9] |
P. Magal and X.-Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37 (2005), 251-275.
doi: 10.1137/S0036141003439173. |
[10] |
P. W. Nelson, M. A. Gilchrist, D. Coombs, J. Hyman and A. S. Perelson, An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells, Math. Biosci. Eng., 1 (2004), 267-288.
doi: 10.3934/mbe.2004.1.267. |
[11] |
P. W. Nelson and A. S. Perelson, Mathematical analysis of delay differential equation models of HIV-1 infection, Math. Biosci., 179 (2002), 73-94.
doi: 10.1016/S0025-5564(02)00099-8. |
[12] |
A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41 (1999), 3-44.
doi: 10.1137/S0036144598335107. |
[13] |
L. B. Rong, Z. Feng and A. S. Perelson, Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy, SIAM J. Appl. Math., 67 (2007), 731-756.
doi: 10.1137/060663945. |
[14] |
H. R. Thieme, Semiflows generated by Lipschitz perturbations of non-densely defined operators, Differential Integral Equations, 3 (1990), 1035-1066. |
[15] |
G. F. Webb, "Theory of Nonlinear Age-Dependent Population Dynamics,'' Monographs and Textbooks in Pure and Applied Mathematics, 89, Marcel Dekker, Inc., New York, 1985. |
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