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Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection
1. | Department of Mathematics, Beijing Technology and Business University, Beijing, 100048, China |
References:
[1] |
A. A. Canabarro, I. M. Gleria and M. L. Lyra, Periodic solutions and chaos in a non-linear model for the delayed cellular immune response, Physica A, 342 (2004), 234-241.
doi: 10.1016/S0378-4371(04)00503-5. |
[2] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
doi: 10.1007/BF00178324. |
[3] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibra for compartmental models of disease trensmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[4] |
S. A. Gourley, Y. Kuang and J. D. Nagy, Dynamics of a delay differential model of hepatitis B virus infection, J. Biol. Dynam., 2 (2008), 140-153.
doi: 10.1080/17513750701769873. |
[5] |
K. Hattaf, N. Yousfi and A. Tridane, Mathematical analysis of a virus dynamics model with general incidence rate and cure rate, Nonlinear Anal-Real, 13 (2012), 1866-1872.
doi: 10.1016/j.nonrwa.2011.12.015. |
[6] |
Z. X. Hu, J. J. Zhang and H. Wang, et al., Dynamics analysis of a delayed viral infection model with logistic growth and immune impairment, Appl. Math. Model., 38 (2014), 524-534.
doi: 10.1016/j.apm.2013.06.041. |
[7] |
G. Huang, W. B. 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. |
[8] |
Y. Ji, L. Q. Min and Y. A. Ye, Global analysis of a viral infection model with application to HBV infection, J. Biol. Syst., 18 (2010), 325-337.
doi: 10.1142/S0218339010003299. |
[9] |
S. Lewin, T. Walters and S. Locarnini, Hepatitis B treatment: Rational combination chemotherapy based on viral kinetic and animal model studies, Antivir. Res., 55 (2002), 381-396.
doi: 10.1016/S0166-3542(02)00071-2. |
[10] |
D. Li and W. B. 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. |
[11] |
L. Q. Min, Y. M. Su and Y. Kuang, Mathematical analysis of a basic virus infection model with application to HBV infection, Rocky Mt. J. Math., 38 (2008), 1573-1585.
doi: 10.1216/RMJ-2008-38-5-1573. |
[12] |
Y. Nakata, Global dynamics of a viral infection model with a latent period and Beddington-DeAngelis response, Nonlinear Anal-Theor., 74 (2011), 2929-2940.
doi: 10.1016/j.na.2010.12.030. |
[13] |
M. A. Nowak and R. M. May, Virus Dynamics, Oxford University Press, New York, 2000. |
[14] |
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. |
[15] |
X. Y. 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. |
[16] |
X. Y. Song, X. Y. Zhou and X. Zhao, Properties of stability and Hopf bifurcaion for a HIV infection model with time delay, Appl. Math. Model., 34 (2010), 1511-1523.
doi: 10.1016/j.apm.2009.09.006. |
[17] |
Y. N. Tian and X. N. Liu, Global dynamics of a virus dynamical model with general incidence rate and cure rate, Nonlinear Anal-Real, 16 (2014), 17-26.
doi: 10.1016/j.nonrwa.2013.09.002. |
[18] |
K. F. Wang, A. J. Fan and A. Torres, Global properties of an improved hepatitis B virus model, Nonlinear Anal-Real, 11 (2010), 3131-3138.
doi: 10.1016/j.nonrwa.2009.11.008. |
[19] |
T. L. Wang, Z. X. Hu and F. C. Liao, et al., Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity, Math. Comput. Simulat., 89 (2013), 13-22.
doi: 10.1016/j.matcom.2013.03.004. |
[20] |
S. L. Wang, X. Y. Song and Z. H. Ge, Dynamics analysisi of a delayed viral infection model with immune impairment, Appl. Math. Model., 35 (2011), 4877-4885.
doi: 10.1016/j.apm.2011.03.043. |
[21] |
Z. P. Wang and R. Xu, Stability and Hopf bifurcation in a viral infection model with nonlinear incidence rate and delayed immune response, Commun. Nonlinear Sci. Numer. Simulat., 17 (2012), 964-978.
doi: 10.1016/j.cnsns.2011.06.024. |
[22] |
R. Xu, Global stability of an 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. |
show all references
References:
[1] |
A. A. Canabarro, I. M. Gleria and M. L. Lyra, Periodic solutions and chaos in a non-linear model for the delayed cellular immune response, Physica A, 342 (2004), 234-241.
doi: 10.1016/S0378-4371(04)00503-5. |
[2] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
doi: 10.1007/BF00178324. |
[3] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibra for compartmental models of disease trensmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[4] |
S. A. Gourley, Y. Kuang and J. D. Nagy, Dynamics of a delay differential model of hepatitis B virus infection, J. Biol. Dynam., 2 (2008), 140-153.
doi: 10.1080/17513750701769873. |
[5] |
K. Hattaf, N. Yousfi and A. Tridane, Mathematical analysis of a virus dynamics model with general incidence rate and cure rate, Nonlinear Anal-Real, 13 (2012), 1866-1872.
doi: 10.1016/j.nonrwa.2011.12.015. |
[6] |
Z. X. Hu, J. J. Zhang and H. Wang, et al., Dynamics analysis of a delayed viral infection model with logistic growth and immune impairment, Appl. Math. Model., 38 (2014), 524-534.
doi: 10.1016/j.apm.2013.06.041. |
[7] |
G. Huang, W. B. 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. |
[8] |
Y. Ji, L. Q. Min and Y. A. Ye, Global analysis of a viral infection model with application to HBV infection, J. Biol. Syst., 18 (2010), 325-337.
doi: 10.1142/S0218339010003299. |
[9] |
S. Lewin, T. Walters and S. Locarnini, Hepatitis B treatment: Rational combination chemotherapy based on viral kinetic and animal model studies, Antivir. Res., 55 (2002), 381-396.
doi: 10.1016/S0166-3542(02)00071-2. |
[10] |
D. Li and W. B. 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. |
[11] |
L. Q. Min, Y. M. Su and Y. Kuang, Mathematical analysis of a basic virus infection model with application to HBV infection, Rocky Mt. J. Math., 38 (2008), 1573-1585.
doi: 10.1216/RMJ-2008-38-5-1573. |
[12] |
Y. Nakata, Global dynamics of a viral infection model with a latent period and Beddington-DeAngelis response, Nonlinear Anal-Theor., 74 (2011), 2929-2940.
doi: 10.1016/j.na.2010.12.030. |
[13] |
M. A. Nowak and R. M. May, Virus Dynamics, Oxford University Press, New York, 2000. |
[14] |
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. |
[15] |
X. Y. 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. |
[16] |
X. Y. Song, X. Y. Zhou and X. Zhao, Properties of stability and Hopf bifurcaion for a HIV infection model with time delay, Appl. Math. Model., 34 (2010), 1511-1523.
doi: 10.1016/j.apm.2009.09.006. |
[17] |
Y. N. Tian and X. N. Liu, Global dynamics of a virus dynamical model with general incidence rate and cure rate, Nonlinear Anal-Real, 16 (2014), 17-26.
doi: 10.1016/j.nonrwa.2013.09.002. |
[18] |
K. F. Wang, A. J. Fan and A. Torres, Global properties of an improved hepatitis B virus model, Nonlinear Anal-Real, 11 (2010), 3131-3138.
doi: 10.1016/j.nonrwa.2009.11.008. |
[19] |
T. L. Wang, Z. X. Hu and F. C. Liao, et al., Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity, Math. Comput. Simulat., 89 (2013), 13-22.
doi: 10.1016/j.matcom.2013.03.004. |
[20] |
S. L. Wang, X. Y. Song and Z. H. Ge, Dynamics analysisi of a delayed viral infection model with immune impairment, Appl. Math. Model., 35 (2011), 4877-4885.
doi: 10.1016/j.apm.2011.03.043. |
[21] |
Z. P. Wang and R. Xu, Stability and Hopf bifurcation in a viral infection model with nonlinear incidence rate and delayed immune response, Commun. Nonlinear Sci. Numer. Simulat., 17 (2012), 964-978.
doi: 10.1016/j.cnsns.2011.06.024. |
[22] |
R. Xu, Global stability of an 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. |
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