Global stability and Hopf bifurcation of an HIV-1 infection model with saturation incidence and delayed CTL immune response

Applied Mathematics and Computation

Volumn 237, Issue , 2014, Pages 146-154

  Tian, Xiaohong ^a   Xu, Rui ^a  

^a INSTITUTE OF APPLIED MATHEMATICS   (China)

Author keywords

CTL immune response; Global stability; HIV 1 infection model; Hopf bifurcation; LaSalle's invariance principle

Indexed keywords

IMMUNE SYSTEM;

BASIC REPRODUCTION RATIOS; BASIC REPRODUCTIVE RATIO; CTL IMMUNE RESPONSE; GLOBAL STABILITY; GLOBALLY ASYMPTOTICALLY STABLE; HIV-1 INFECTIONS; INFECTION FREE EQUILIBRIUM; LASALLE'S INVARIANCE PRINCIPLE;

HOPF BIFURCATION;

EID: 84898930647     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2014.03.091     Document Type: Review

References (17)

1. D. Burg, L. Rong, and A.U. Neumann et al. Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection J. Theor. Biol. 259 2009 751 759
2. 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
3. + T cells in primary HIV-1 infection J. Virol. 77 2003 6867 6878
4. 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
5. J.R. Haddock, and J. Terjéki Liapunov-Razumikhin functions and an invariance principle for functional-differential equations J. Differ. Equ. 48 1983 95 122
6. J.K. Hale, and S.V. Lunel Introduction to Functional Differential Equations 1993 Springer New York
7. T. Kajiwara, and T. Sasaki Global stability of pathogen-immune dynamics with absorption J. Math. Biol. 4 2009 258 269
8. M. Nowak, and C.R.M. Bangham Population dynamics of immune responses to persistent viruses Science 272 1996 74 79
9. A.S. Perelson, and P.W. Nelson Mathematical analysis of HIV-1 dynamics in vivo SIAM Rev. 41 1999 3 44
10. R.R. Regoes, D. Ebert, and S. Bonhoeffer Dose-dependent infection rates of parasites produce the Allee effect in epidemiology Proc. R. Soc. London B 269 2002 271 279
11. P.K. Roy, and A.N. Chatterjee T-cell proliferation in a mathematical model of CTL activity through HIV-1 infection Proc. World Congr. Eng. 1 2010 1 6
12. X. Shi, X. Zhou, and X. Song Dynamical behavior of a delay virus dynamics model with CTL immune response Nonlinear Anal. RWA 11 2010 1795 1809
13. X. Song, and A.U. Neumann Global stability and periodic solution of the viral dynamics J. Math. Anal. Appl. 329 2007 281 297
14. Q. Xie, D. Huang, and S. Zhang et al. Analysis of a viral infection model with delayed immune response Appl. Math. Model. 34 2010 2388 2395
15. K. Wang, W. Wang, and H. Pang et al. Complex dynamic behavior in a viral model with delayed immune response Physica D 226 2007 197 208
16. X. Yan, and W. Li Stability and bifurcation in a simplified four-neuron BAM neural network with multiple delays Discrete Dyn. Nat. Soc. 2006 1 29 10.1155/DDNS/2006/32529 (Article ID 32529)
17. H. Zhu, and X. Zou Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay Discrete Contin. Dyn. Syst. Ser. B 12 2009 511 524