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Global dynamics for viral infection model with Beddington-DeAngelis functional response and an eclipse stage of infected cells
1. | School of Mathematics and Statistics, Southwest University, Chongqing 400715, China, China |
2. | School of Mathematical Science, Heilongjiang University, Harbin 150080, China |
References:
[1] |
S. Bonhoeffer, J. Coffin and M. Nowak, Human immunodeficiency virus drug therapy and virus load, J. Virol., 71 (1997), 3275-3278. |
[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] |
J. R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, J. Animal Ecol., 44 (1975), 331-340.
doi: 10.2307/3866. |
[4] |
D. L. DeAngelis, R. A. Goldstein and R. V. O'Neill, A model for trophic interaction, Ecology, 56 (1975), 881-892. |
[5] |
P. Essunger and A. S. Perelson, Modeling HIV infection of CD4$^+$ T-cell subpopulations, J. Theoret. Biol., 170 (1994), 367-391.
doi: 10.1006/jtbi.1994.1199. |
[6] |
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. |
[7] |
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. Nat. Acad. Sci., 93 (1996), 7247-7251.
doi: 10.1073/pnas.93.14.7247. |
[8] |
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. |
[9] |
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. |
[10] |
Z. Hu, W. Pang, F. Liao and W. Ma, Analysis of a CD$4^{+}$ T Cell viral infection model with a class of saturated infection rate, Disc. Cont. Dyn. Sys. B, 19 (2014), 735-745.
doi: 10.3934/dcdsb.2014.19.735. |
[11] |
A. Korobeinikov, Global asymptotic properties of virus dynamics models with dose-dependent parasite reproduction and virulence and non-linear incidence rate, Math. Med. Bio., 26 (2009), 225-239. |
[12] |
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879-883.
doi: 10.1016/j.bulm.2004.02.001. |
[13] |
A. Korobeinikov, Global properties of infectious disease model with nonlinear incidence, Bull. Math. Biol., 69 (2007), 1871-1886.
doi: 10.1007/s11538-007-9196-y. |
[14] |
T. Kajiwara, T. Sasaki and Y. Takeuchi, Construction of Lyapunov functionals for delay differential equations in virology and epidemiology, Nonlinear Anal.: Real World Appl., 13 (2012), 1802-1826.
doi: 10.1016/j.nonrwa.2011.12.011. |
[15] |
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, 1993. |
[16] |
X. Liu, H. Wang, Z. Hu and W. Ma, Global stability of an HIV pathogenesis model with cure rate, Nonlinear Anal.: Real World Appl., 12 (2011), 2947-2961.
doi: 10.1016/j.nonrwa.2011.04.016. |
[17] |
S. Lewin, T. Walters and S. Locarnini, Hepatitis B treatment: Rational combination chemotherapy based on viral kinetic and animal model studies, Antiviral Research, 55 (2002), 381-396.
doi: 10.1016/S0166-3542(02)00071-2. |
[18] |
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. |
[19] |
M. Y. Li and H. Shu, Impact of intracellular delay and target-cell dynamics on in vivo viral infections, SIAM J. Appl. Math., 70 (2010), 2434-2448.
doi: 10.1137/090779322. |
[20] |
D. Li and W. Ma, Asymptotic properties of an HIV-1 infection model with time delay, J. Math. Anal. Appl., 335 (2007), 683-691.
doi: 10.1016/j.jmaa.2007.02.006. |
[21] |
C. C. McCluskey, Global stability of an SIR epidemic model with delay and general non linear incidence, Math. Biosci. Eng., 7 (2010), 837-850.
doi: 10.3934/mbe.2010.7.837. |
[22] |
C. C. McCluskey, Complete global stability for an SIR epidemic model with delay-distributed or discrete, Nonlinear Anal.: Real World Appl., 11 (2010), 55-59.
doi: 10.1016/j.nonrwa.2008.10.014. |
[23] |
J. Mittler, B. Sulzer, A. Neumann and A. Perelson, Influence of delayed viral production on viral dynamics in HIV-1 infected patients, Math. Biosci., 152 (1998), 143-163.
doi: 10.1016/S0025-5564(98)10027-5. |
[24] |
M. Nowak and R. M. May, Virus Dynamics, Cambridge University Press, Cambridge, 2000. |
[25] |
M. Nowak, S. Bonhoeffer, A. Hill, R. Boehme, H. Thomas and H. Mcdade, Viral dynamics in hepatitis B virus infection, Proc. Natl. Acad. Sci. USA, 93 (1996), 4398-4402.
doi: 10.1073/pnas.93.9.4398. |
[26] |
Y. Nakata, Global dynamics of a cell mediated immunity in viral infection models with distributed delays, J. Math. Anal. Appl., 375 (2011), 14-27.
doi: 10.1016/j.jmaa.2010.08.025. |
[27] |
A. S. Perelson, D. E. 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. |
[28] |
A. S. 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. |
[29] |
A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-I dynamics in vivo, SIAM Rev., 41 (1999), 3-44.
doi: 10.1137/S0036144598335107. |
[30] |
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. |
[31] |
R. R. Regoes, D. Ebert and S. Bonhoeffer, Dose-dependent infection rates of parasites produce the Allee effect in epidemiology, Proc. R. Soc. Lond. Ser., 269 (2002), 271-279.
doi: 10.1098/rspb.2001.1816. |
[32] |
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. |
[33] |
P. K. Srivastava and P. Chandra, Modeling the dynamics of HIV and CD4+ T cells during primary infection, Nonlinear Anal.: Real World Appl., 11 (2010), 612-618.
doi: 10.1016/j.nonrwa.2008.10.037. |
[34] |
Y. Tian and X. Liu, Global dynamics of a virus dynamical model with general incidence rate and cure rate, Nonlinear Anal.: Real World Appl., 16 (2014), 17-26.
doi: 10.1016/j.nonrwa.2013.09.002. |
[35] |
J. Wang, G. Huang and Y. Takeuchi, Global asymptotic stability for HIV-1 dynamics with two distributed delays, Math. Med. Biol., 29 (2012), 283-300.
doi: 10.1093/imammb/dqr009. |
[36] |
J. Wang and L. Guan, Global stability for a HIV-1 infection model with cell-mediated immune response and intracellular delay, Disc. Cont. Dyn. Sys. B, 17 (2012), 297-302.
doi: 10.3934/dcdsb.2012.17.297. |
[37] |
J. Wang, J. Pang and T. Kuniya, A note on global stability for malaria infections model with latencies, Math. Biosci. Eng., 11 (2014), 995-1001.
doi: 10.3934/mbe.2014.11.995. |
[38] |
J. Wang, J. Pang, T. Kuniya and Y. Enatsu, Global threshold dynamics in a five-dimensional virus model with cell-mediated, humoral immune responses and distributed delays, Appl. Math. Comput., 241 (2014), 298-316.
doi: 10.1016/j.amc.2014.05.015. |
[39] |
J. Wang and S. Liu, The stability analysis of a general viral infection model with distributed delays and multi-staged infected progression, Commun. Nonlinear Sci. Numer. Simulat., 20 (2015), 263-272.
doi: 10.1016/j.cnsns.2014.04.027. |
[40] |
R. Xu, Global stability ofan HIV-1 infection model with saturation infection and intracellular delay, J. Math. Anal. Appl., 375 (2011), 75-81.
doi: 10.1016/j.jmaa.2010.08.055. |
[41] |
Z. Yuan and X. Zou, Global threshold dynamics in an HIV virus model with nonlinear infection rate and distributed invasion and production delays, Math. Biosci. Eng., 10 (2013), 483-498.
doi: 10.3934/mbe.2013.10.483. |
[42] |
C. Lv, L. Huang and Z. Yuan, Global stability for an HIV-1 infection model with Beddington-DeAngelis incidence rate and CTL immune response, Commun. Nonlinear Sci. Numer. Simulat., 19 (2014), 121-127.
doi: 10.1016/j.cnsns.2013.06.025. |
[43] |
H. Zhu and X. Zou, Impact of delays in cell infection and virus production on HIV-1 dynamics, Math. Med. Biol., 25 (2008), 99-112.
doi: 10.1093/imammb/dqm010. |
[44] |
J. A. Zack, S. J. Arrigo, S. R. Weitsman, A. S. Go, A. Haislip and I. S. Chen, HIV-1 entry into quiescent primary lymphocytes: Molecular analysis reveals a labile latent viral structure, Cell, 61 (1990), 213-222.
doi: 10.1016/0092-8674(90)90802-L. |
[45] |
J. A. Zack, A. M. Haislip, P. Krogstad and I. S. Chen, Incompletely reverse-transcribed human immunodeficiency virus type 1 genomes in quiescent cells can function as intermediates in the retroviral cycle, J. Virol., 66 (1992), 1717-1725. |
[46] |
X. Y. Zhou, X. Y. Song and X. Y. Shi, A differential equation model of HIV infection of CD4$^+$ T-cells with cure rate, J. Math. Anal. Appl., 342 (2008), 1342-1355.
doi: 10.1016/j.jmaa.2008.01.008. |
show all references
References:
[1] |
S. Bonhoeffer, J. Coffin and M. Nowak, Human immunodeficiency virus drug therapy and virus load, J. Virol., 71 (1997), 3275-3278. |
[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] |
J. R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, J. Animal Ecol., 44 (1975), 331-340.
doi: 10.2307/3866. |
[4] |
D. L. DeAngelis, R. A. Goldstein and R. V. O'Neill, A model for trophic interaction, Ecology, 56 (1975), 881-892. |
[5] |
P. Essunger and A. S. Perelson, Modeling HIV infection of CD4$^+$ T-cell subpopulations, J. Theoret. Biol., 170 (1994), 367-391.
doi: 10.1006/jtbi.1994.1199. |
[6] |
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. |
[7] |
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. Nat. Acad. Sci., 93 (1996), 7247-7251.
doi: 10.1073/pnas.93.14.7247. |
[8] |
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. |
[9] |
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. |
[10] |
Z. Hu, W. Pang, F. Liao and W. Ma, Analysis of a CD$4^{+}$ T Cell viral infection model with a class of saturated infection rate, Disc. Cont. Dyn. Sys. B, 19 (2014), 735-745.
doi: 10.3934/dcdsb.2014.19.735. |
[11] |
A. Korobeinikov, Global asymptotic properties of virus dynamics models with dose-dependent parasite reproduction and virulence and non-linear incidence rate, Math. Med. Bio., 26 (2009), 225-239. |
[12] |
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879-883.
doi: 10.1016/j.bulm.2004.02.001. |
[13] |
A. Korobeinikov, Global properties of infectious disease model with nonlinear incidence, Bull. Math. Biol., 69 (2007), 1871-1886.
doi: 10.1007/s11538-007-9196-y. |
[14] |
T. Kajiwara, T. Sasaki and Y. Takeuchi, Construction of Lyapunov functionals for delay differential equations in virology and epidemiology, Nonlinear Anal.: Real World Appl., 13 (2012), 1802-1826.
doi: 10.1016/j.nonrwa.2011.12.011. |
[15] |
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, 1993. |
[16] |
X. Liu, H. Wang, Z. Hu and W. Ma, Global stability of an HIV pathogenesis model with cure rate, Nonlinear Anal.: Real World Appl., 12 (2011), 2947-2961.
doi: 10.1016/j.nonrwa.2011.04.016. |
[17] |
S. Lewin, T. Walters and S. Locarnini, Hepatitis B treatment: Rational combination chemotherapy based on viral kinetic and animal model studies, Antiviral Research, 55 (2002), 381-396.
doi: 10.1016/S0166-3542(02)00071-2. |
[18] |
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. |
[19] |
M. Y. Li and H. Shu, Impact of intracellular delay and target-cell dynamics on in vivo viral infections, SIAM J. Appl. Math., 70 (2010), 2434-2448.
doi: 10.1137/090779322. |
[20] |
D. Li and W. Ma, Asymptotic properties of an HIV-1 infection model with time delay, J. Math. Anal. Appl., 335 (2007), 683-691.
doi: 10.1016/j.jmaa.2007.02.006. |
[21] |
C. C. McCluskey, Global stability of an SIR epidemic model with delay and general non linear incidence, Math. Biosci. Eng., 7 (2010), 837-850.
doi: 10.3934/mbe.2010.7.837. |
[22] |
C. C. McCluskey, Complete global stability for an SIR epidemic model with delay-distributed or discrete, Nonlinear Anal.: Real World Appl., 11 (2010), 55-59.
doi: 10.1016/j.nonrwa.2008.10.014. |
[23] |
J. Mittler, B. Sulzer, A. Neumann and A. Perelson, Influence of delayed viral production on viral dynamics in HIV-1 infected patients, Math. Biosci., 152 (1998), 143-163.
doi: 10.1016/S0025-5564(98)10027-5. |
[24] |
M. Nowak and R. M. May, Virus Dynamics, Cambridge University Press, Cambridge, 2000. |
[25] |
M. Nowak, S. Bonhoeffer, A. Hill, R. Boehme, H. Thomas and H. Mcdade, Viral dynamics in hepatitis B virus infection, Proc. Natl. Acad. Sci. USA, 93 (1996), 4398-4402.
doi: 10.1073/pnas.93.9.4398. |
[26] |
Y. Nakata, Global dynamics of a cell mediated immunity in viral infection models with distributed delays, J. Math. Anal. Appl., 375 (2011), 14-27.
doi: 10.1016/j.jmaa.2010.08.025. |
[27] |
A. S. Perelson, D. E. 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. |
[28] |
A. S. 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. |
[29] |
A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-I dynamics in vivo, SIAM Rev., 41 (1999), 3-44.
doi: 10.1137/S0036144598335107. |
[30] |
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. |
[31] |
R. R. Regoes, D. Ebert and S. Bonhoeffer, Dose-dependent infection rates of parasites produce the Allee effect in epidemiology, Proc. R. Soc. Lond. Ser., 269 (2002), 271-279.
doi: 10.1098/rspb.2001.1816. |
[32] |
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. |
[33] |
P. K. Srivastava and P. Chandra, Modeling the dynamics of HIV and CD4+ T cells during primary infection, Nonlinear Anal.: Real World Appl., 11 (2010), 612-618.
doi: 10.1016/j.nonrwa.2008.10.037. |
[34] |
Y. Tian and X. Liu, Global dynamics of a virus dynamical model with general incidence rate and cure rate, Nonlinear Anal.: Real World Appl., 16 (2014), 17-26.
doi: 10.1016/j.nonrwa.2013.09.002. |
[35] |
J. Wang, G. Huang and Y. Takeuchi, Global asymptotic stability for HIV-1 dynamics with two distributed delays, Math. Med. Biol., 29 (2012), 283-300.
doi: 10.1093/imammb/dqr009. |
[36] |
J. Wang and L. Guan, Global stability for a HIV-1 infection model with cell-mediated immune response and intracellular delay, Disc. Cont. Dyn. Sys. B, 17 (2012), 297-302.
doi: 10.3934/dcdsb.2012.17.297. |
[37] |
J. Wang, J. Pang and T. Kuniya, A note on global stability for malaria infections model with latencies, Math. Biosci. Eng., 11 (2014), 995-1001.
doi: 10.3934/mbe.2014.11.995. |
[38] |
J. Wang, J. Pang, T. Kuniya and Y. Enatsu, Global threshold dynamics in a five-dimensional virus model with cell-mediated, humoral immune responses and distributed delays, Appl. Math. Comput., 241 (2014), 298-316.
doi: 10.1016/j.amc.2014.05.015. |
[39] |
J. Wang and S. Liu, The stability analysis of a general viral infection model with distributed delays and multi-staged infected progression, Commun. Nonlinear Sci. Numer. Simulat., 20 (2015), 263-272.
doi: 10.1016/j.cnsns.2014.04.027. |
[40] |
R. Xu, Global stability ofan HIV-1 infection model with saturation infection and intracellular delay, J. Math. Anal. Appl., 375 (2011), 75-81.
doi: 10.1016/j.jmaa.2010.08.055. |
[41] |
Z. Yuan and X. Zou, Global threshold dynamics in an HIV virus model with nonlinear infection rate and distributed invasion and production delays, Math. Biosci. Eng., 10 (2013), 483-498.
doi: 10.3934/mbe.2013.10.483. |
[42] |
C. Lv, L. Huang and Z. Yuan, Global stability for an HIV-1 infection model with Beddington-DeAngelis incidence rate and CTL immune response, Commun. Nonlinear Sci. Numer. Simulat., 19 (2014), 121-127.
doi: 10.1016/j.cnsns.2013.06.025. |
[43] |
H. Zhu and X. Zou, Impact of delays in cell infection and virus production on HIV-1 dynamics, Math. Med. Biol., 25 (2008), 99-112.
doi: 10.1093/imammb/dqm010. |
[44] |
J. A. Zack, S. J. Arrigo, S. R. Weitsman, A. S. Go, A. Haislip and I. S. Chen, HIV-1 entry into quiescent primary lymphocytes: Molecular analysis reveals a labile latent viral structure, Cell, 61 (1990), 213-222.
doi: 10.1016/0092-8674(90)90802-L. |
[45] |
J. A. Zack, A. M. Haislip, P. Krogstad and I. S. Chen, Incompletely reverse-transcribed human immunodeficiency virus type 1 genomes in quiescent cells can function as intermediates in the retroviral cycle, J. Virol., 66 (1992), 1717-1725. |
[46] |
X. Y. Zhou, X. Y. Song and X. Y. Shi, A differential equation model of HIV infection of CD4$^+$ T-cells with cure rate, J. Math. Anal. Appl., 342 (2008), 1342-1355.
doi: 10.1016/j.jmaa.2008.01.008. |
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2020 Impact Factor: 1.327
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