Global dynamics of a viral infection model with a latent period and Beddington-DeAngelis response

Nonlinear Analysis, Theory, Methods and Applications

Volumn 74, Issue 9, 2011, Pages 2929-2940

  Nakata, Yukihiko ^a,b  

^a WASEDA UNIVERSITY   (Japan)

^b BCAM BASQUE CENTER FOR APPLIED MATHEMATICS   (Spain)

Author keywords

Global asymptotic stability; Nonlinear incidence rate; Uniform persistence; Virus dynamics models

Indexed keywords

BASIC REPRODUCTION NUMBER; GLOBAL ASYMPTOTIC STABILITY; GLOBAL DYNAMICS; GLOBALLY ASYMPTOTICALLY STABLE; IN-VIVO; INCIDENCE RATE; INFECTED CELLS; NONLINEAR FUNCTIONS; NONLINEAR INCIDENCE RATE; UNIFORM PERSISTENCE; VIRAL INFECTION MODEL; VIRUS DYNAMICS MODELS; VIRUS INFECTION;

ASYMPTOTIC STABILITY; DYNAMICS;

VIRUSES;

EID: 79952575805     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2010.12.030     Document Type: Article

References (19)

1. A. Herz, S. Bonhoeffer, R. Anderson, R. May, and M. Nowak Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay Proceedings of the National Academy of Sciences 93 14 1996 7247 7251 (Pubitemid 26243534)
2. P.W. Nelson, and A.S. Perelson Mathematical analysis of delay differential equation models of HIV-1 infection Mathematical Biosciences 179 1 2002 73 94 (Pubitemid 34686428)
3. M. Nowak, and C. Bangham Population dynamics of immune responses to persistent viruses Science 272 5258 1996 74
4. A. Korobeinikov Global asymptotic properties of virus dynamics models with dose-dependent parasite reproduction and virulence and non-linear incidence rate Mathematical Medicine and Biology 26 3 2009 225 239
5. G. Huang, W. Ma, and Y. Takeuchi Global properties for virus dynamics model with BeddingtonDeAngelis functional response Applied Mathematics Letters 22 11 2009 1690 1693
6. H. Zhu, and X. Zou Dynamics of a HIV-1 Infection model with cell-mediated immune response and intracellular delay Discrete and Continuous Dynamical Systems Series B 12 2 2009 511 524
7. M.Y. Li, and H. Shu Global dynamics of an in-host viral model with intracellular delay Bulletin of Mathematical Biology 72 6 2010 1492 1505
8. J.E. Mittler, B. Sulzer, A.U. Neumann, and A.S. Perelson Influence of delayed viral production on viral dynamics in HIV-1 infected patients Mathematical Biosciences 152 2 1998 143 163 (Pubitemid 28450733)
9. A. Korobeinikov Global properties of basic virus dynamics models Bulletin of Mathematical Biology 66 4 2004 879 883 (Pubitemid 38800956)
10. A. Korobeinikov Global properties of infectious disease models with nonlinear incidence Bulletin of Mathematical Biology 69 6 2007 1871 1886 (Pubitemid 47222242)
11. D. Li, and W. Ma Asymptotic properties of a HIV-1 infection model with time delay Journal of Mathematical Analysis and Applications 335 1 2007 683 691
12. A.S. Perelson, and P.W. Nelson Mathematical analysis of HIV-1 dynamics in vivo SIAM Review 41 1 1999 3 44 (Pubitemid 129723746)
13. T. Revilla, and G. Garcia-Ramos Fighting a virus with a virus: a dynamic model for HIV-1 therapy Mathematical Biosciences 185 2 2003 191 203 (Pubitemid 37108375)
14. S. Bonhoeffer, R.M. May, G.M. Shaw, and M.A. Nowak Virus dynamics and drug therapy Proceedings of the National Academy of Sciences of the United States of America 94 13 1997 6971 6976 (Pubitemid 27281975)
15. X. Song, and A.U. Neumann Global stability and periodic solution of the viral dynamics Journal of Mathematical Analysis and Applications 329 1 2007 281 297
16. H. Zhu, and X. Zou Impact of delays in cell infection and virus production on HIV-1 dynamics Mathematical Medicine and Biology 25 2 2008 99
17. C.C. McCluskey Complete global stability for an SIR epidemic model with delay distributed or discrete Nonlinear Analysis: Real World Applications 11 1 2010 55 59
18. J. Hale, and P. Waltman Persistence in infinite-dimensional systems SIAM Journal on Mathematical Analysis 20 1989 388
19. X.-Q. Zhao Dynamical systems in population biology CMS Books in Mathematics/Ouvrages de Mathmatiques de la SMC vol. 16 2003 Springer-Verlag New York