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Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function
1. | School of Science and Technology, Zhejiang International Studies University, Hangzhou 310012, China |
2. | Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250 |
3. | Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China |
References:
[1] |
C. L. Althaus and R. J. De Boer, Dynamics of immune escape during HIV/SIV infection, PLoS Comput. Biol., 4 (2008), e1000103, 9pp.
doi: 10.1371/journal.pcbi.1000103. |
[2] |
F. Brauer, Z. Shuai and P. van den Driessche, Dynamics of an age-of-infection cholera model, Math. Biosci. Eng., 10 (2013), 1335-1349.
doi: 10.3934/mbe.2013.10.1335. |
[3] |
C. J. Browne and S. S. Pilyugin, Global analysis of age-structured within-host virus model, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1999-2017.
doi: 10.3934/dcdsb.2013.18.1999. |
[4] |
R. V. Culshaw and S. Ruan, A delay-differential equation model of HIV infection of CD4$^+$ T-cells, Math. Biosci., 165 (2000), 27-39.
doi: 10.1016/S0025-5564(00)00006-7. |
[5] |
C. Cosner, D.L. DeAngelis, J. S. Ault and D. B. Olson, Effects of spatial grouping on the functional response of predators, Theoret. Pop. Biol., 56 (1999), 65-75.
doi: 10.1006/tpbi.1999.1414. |
[6] |
R. J. De Boer and A. S. Perelson, Target cell limited and immune control models of HIV infection: A comparison, J. Theoret. Biol., 190 (1998), 201-214. |
[7] |
R. D. Demasse and A. Ducrot, An age-structured within-host model for multistrain malaria infections, SIAM. J. Appl. Math., 73 (2013), 572-593.
doi: 10.1137/120890351. |
[8] |
P. De Leenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math., 63 (2003), 1313-1327.
doi: 10.1137/S0036139902406905. |
[9] |
J. K. Hale, Asymptotic Behavior of Dissipative Systems, Mathematical Surveys and Monographs Vol 25, American Mathematical Society, Providence, RI, 1988. |
[10] |
J. K. Hale and P. Waltman, Persistence in infinite dimensional systems, SIAM J. Math. Anal., 20 (1989), 388-395.
doi: 10.1137/0520025. |
[11] |
G. Huang, W. Ma and Y. Takeuchi, Global properties for virus dynamics model with Beddington-DeAngelis functional response, Appl. Math. Lett., 22 (2009), 1690-1693.
doi: 10.1016/j.aml.2009.06.004. |
[12] |
G. Huang, W. Ma and Y. Takeuchi, Global analysis for delay virus dynamics model with Beddington-DeAngelis functional response, Appl. Math. Lett., 24 (2011), 1199-1203.
doi: 10.1016/j.aml.2011.02.007. |
[13] |
G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals for delay differential equations model of viral infections, SIAM J. Appl. Math., 70 (2010), 2693-2708.
doi: 10.1137/090780821. |
[14] |
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. |
[15] |
G. Huisman and R. J. De Boer, A formal derivation of the "Beddington" functional response, J. Theoret. Biol., 185 (1997), 389-400.
doi: 10.1006/jtbi.1996.0318. |
[16] |
D. Kirschner and G. F. Webb, A model for treatment strategy in the chemotherapy of AIDS, Bull. Math. Biol., 58 (1996), 367-390.
doi: 10.1016/0092-8240(95)00345-2. |
[17] |
M. Y. Li and H. Shu, Global dynamics of an in-host viral model with intracellular delay, Bull. Math. Biol., 72 (2010), 1492-1505.
doi: 10.1007/s11538-010-9503-x. |
[18] |
M. Y. Li and H. Shu, Impact of intracellular delays and target-cell dynamics on in vivo viral infections, SIAM J. Appl. Math., 70 (2010), 2434-2448.
doi: 10.1137/090779322. |
[19] |
P. Magal, Compact attractors for time-periodic age-structured population models, Electron. J. Differential Equations, 65 (2001), 1-35. |
[20] |
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. |
[21] |
P. Magal and C. C. McCluskey, Two-group infection age model including an application to nosocomial infection, SIAM J. Appl. Math., 73 (2013), 1058-1095.
doi: 10.1137/120882056. |
[22] |
P. Magal and H. R. Thieme, Eventual compactness for semiflows generated by nonlinear age-structured models, Commun. Pure Appl. Anal., 3 (2004), 695-727.
doi: 10.3934/cpaa.2004.3.695. |
[23] |
C. C. McCluskey, Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes, Math. Biosci. Eng., 9 (2012), 819-841.
doi: 10.3934/mbe.2012.9.819. |
[24] |
P. W. Nelson, M. A. Gilchrist, D. Coombs, J. M. 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. |
[25] |
A. Nowak and C. R. M. Bangham, Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74-79.
doi: 10.1126/science.272.5258.74. |
[26] |
M. A. Nowak and R. M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, Oxford, 2000. |
[27] |
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. |
[28] |
L. 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. |
[29] |
H. R. Thieme, Semiflows generated by Lipschitz perturbations of non-densely defined operators, Differential Integral Equations, 3 (1990), 1035-1066. |
show all references
References:
[1] |
C. L. Althaus and R. J. De Boer, Dynamics of immune escape during HIV/SIV infection, PLoS Comput. Biol., 4 (2008), e1000103, 9pp.
doi: 10.1371/journal.pcbi.1000103. |
[2] |
F. Brauer, Z. Shuai and P. van den Driessche, Dynamics of an age-of-infection cholera model, Math. Biosci. Eng., 10 (2013), 1335-1349.
doi: 10.3934/mbe.2013.10.1335. |
[3] |
C. J. Browne and S. S. Pilyugin, Global analysis of age-structured within-host virus model, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1999-2017.
doi: 10.3934/dcdsb.2013.18.1999. |
[4] |
R. V. Culshaw and S. Ruan, A delay-differential equation model of HIV infection of CD4$^+$ T-cells, Math. Biosci., 165 (2000), 27-39.
doi: 10.1016/S0025-5564(00)00006-7. |
[5] |
C. Cosner, D.L. DeAngelis, J. S. Ault and D. B. Olson, Effects of spatial grouping on the functional response of predators, Theoret. Pop. Biol., 56 (1999), 65-75.
doi: 10.1006/tpbi.1999.1414. |
[6] |
R. J. De Boer and A. S. Perelson, Target cell limited and immune control models of HIV infection: A comparison, J. Theoret. Biol., 190 (1998), 201-214. |
[7] |
R. D. Demasse and A. Ducrot, An age-structured within-host model for multistrain malaria infections, SIAM. J. Appl. Math., 73 (2013), 572-593.
doi: 10.1137/120890351. |
[8] |
P. De Leenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math., 63 (2003), 1313-1327.
doi: 10.1137/S0036139902406905. |
[9] |
J. K. Hale, Asymptotic Behavior of Dissipative Systems, Mathematical Surveys and Monographs Vol 25, American Mathematical Society, Providence, RI, 1988. |
[10] |
J. K. Hale and P. Waltman, Persistence in infinite dimensional systems, SIAM J. Math. Anal., 20 (1989), 388-395.
doi: 10.1137/0520025. |
[11] |
G. Huang, W. Ma and Y. Takeuchi, Global properties for virus dynamics model with Beddington-DeAngelis functional response, Appl. Math. Lett., 22 (2009), 1690-1693.
doi: 10.1016/j.aml.2009.06.004. |
[12] |
G. Huang, W. Ma and Y. Takeuchi, Global analysis for delay virus dynamics model with Beddington-DeAngelis functional response, Appl. Math. Lett., 24 (2011), 1199-1203.
doi: 10.1016/j.aml.2011.02.007. |
[13] |
G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals for delay differential equations model of viral infections, SIAM J. Appl. Math., 70 (2010), 2693-2708.
doi: 10.1137/090780821. |
[14] |
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. |
[15] |
G. Huisman and R. J. De Boer, A formal derivation of the "Beddington" functional response, J. Theoret. Biol., 185 (1997), 389-400.
doi: 10.1006/jtbi.1996.0318. |
[16] |
D. Kirschner and G. F. Webb, A model for treatment strategy in the chemotherapy of AIDS, Bull. Math. Biol., 58 (1996), 367-390.
doi: 10.1016/0092-8240(95)00345-2. |
[17] |
M. Y. Li and H. Shu, Global dynamics of an in-host viral model with intracellular delay, Bull. Math. Biol., 72 (2010), 1492-1505.
doi: 10.1007/s11538-010-9503-x. |
[18] |
M. Y. Li and H. Shu, Impact of intracellular delays and target-cell dynamics on in vivo viral infections, SIAM J. Appl. Math., 70 (2010), 2434-2448.
doi: 10.1137/090779322. |
[19] |
P. Magal, Compact attractors for time-periodic age-structured population models, Electron. J. Differential Equations, 65 (2001), 1-35. |
[20] |
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. |
[21] |
P. Magal and C. C. McCluskey, Two-group infection age model including an application to nosocomial infection, SIAM J. Appl. Math., 73 (2013), 1058-1095.
doi: 10.1137/120882056. |
[22] |
P. Magal and H. R. Thieme, Eventual compactness for semiflows generated by nonlinear age-structured models, Commun. Pure Appl. Anal., 3 (2004), 695-727.
doi: 10.3934/cpaa.2004.3.695. |
[23] |
C. C. McCluskey, Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes, Math. Biosci. Eng., 9 (2012), 819-841.
doi: 10.3934/mbe.2012.9.819. |
[24] |
P. W. Nelson, M. A. Gilchrist, D. Coombs, J. M. 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. |
[25] |
A. Nowak and C. R. M. Bangham, Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74-79.
doi: 10.1126/science.272.5258.74. |
[26] |
M. A. Nowak and R. M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, Oxford, 2000. |
[27] |
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. |
[28] |
L. 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. |
[29] |
H. R. Thieme, Semiflows generated by Lipschitz perturbations of non-densely defined operators, Differential Integral Equations, 3 (1990), 1035-1066. |
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