Global dynamics of a mathematical model for HTLV-I infection of CD4 + T cells with delayed CTL response

Nonlinear Analysis: Real World Applications

Volumn 13, Issue 3, 2012, Pages 1080-1092

  Li, Michael Y ^a,b   Shu, Hongying ^a,b  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

CTL response; HAM TSP; Hopf bifurcation; HTLV I infection; In host models; Lyapunov functional; Time delays

Indexed keywords

BASIC REPRODUCTION NUMBER; CTL RESPONSE; CYTOTOXIC; GLOBAL DYNAMICS; GLOBALLY ASYMPTOTICALLY STABLE; HAM/TSP; HTLV-I INFECTION; HUMAN T CELLS; IMMUNE RESPONSE; IN-VIVO; LYAPUNOV FUNCTIONALS; MATHEMATICAL ANALYSIS; MYELOPATHY; PERIODIC OSCILLATION; T CELLS; THRESHOLD PARAMETERS; VIRAL INFECTIONS;

CELLS; CYTOTOXICITY; DYNAMICS; HOPF BIFURCATION; LYAPUNOV FUNCTIONS; TIME DELAY; VIRUSES;

MATHEMATICAL MODELS;

EID: 84655160894     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2011.02.026     Document Type: Article

References (34)

1. F.W. Robbins A mathematical model of HIV infection: simulating T4, T8, macrophages, antibody, and virus via specific anti-HIV response in the presence of adaptation and tropism Bull. Math. Biol. 72 2010 1208 1253
2. K. Wang, and A. Fan Global properties of an improved hepatitis B virus model Nonlinear Anal. RWA 11 2010 3131 3138
3. A.M. Elaiw Global properties of a class of HIV models Nonlinear Anal. RWA 11 2010 2253 2263
4. I.T. Vieira, and R.C.H. Cheng Small world network models of the dynamics of HIV infection Ann. Oper. Res. 178 2010 173 200
5. Y. Yu, and J.J. Nieto A viral infection model with a nonlinear infection rate Bound. Value Probl. 2009 2009 Article ID 958016, 19 pages
6. C.R.M. Bangham The immune response to HTLV-I Curr. Opin. Immunol. 12 2000 397 402 (Pubitemid 30410343)
7. C.R.M. Bangham The immune control and cell-to-cell spread of human T-lymphotropic virus type 1 J. Gen. Virol. 84 2003 3177 3189 (Pubitemid 37540747)
8. S. Jacobson Immunopathogenesis of human T cell lymphotropic virus type I-associated neurologic disease J. Infect. Dis. 186 S2 2002 S187 S192
9. N. Eshima, and M. Tabata Population dynamics of HTLV-I infection: a discrete-time mathematical epidemic model approach Math. Med. Biol. 20 2003 29 45
10. H. Gomez-Acevedo, M.Y. Li, and S. Jacobson Multi-stability in a model for CTL response to HTLV-I infection and its consequences in HAM/TSP development and prevention Bull. Math. Biol. 72 2010 681 696
11. O. Gout, and M. Baulac Medical intelligence: rapid development of myelopathy after HTVL-I Infections acquired by transfusion during cardiac transplantation N. Engl. J. Med. 322 1990 383 388 (Pubitemid 20042744)
12. M. Osame, and R. Janssen Nationwide survey of HTLV-I-associated myelopathy in Japan: association with blood transfusion Ann. Neurol. 28 1990 50 56 (Pubitemid 20222151)
13. R. Kubota, M. Osame, and S. Jacobson Retrovirus: human T-cell lymphotropic virus type I-associated diseases and immune dysfunction M.W. Cunningham, R.S. Fujinami, Effects of Microbes on the Immune System 2000 Lippincott Williams & Wilkins 349 371
14. R.C. Gallo History of the discoveries of the first human retroviruses: HTLV-1 and HTLV-2 Oncogene 24 2005 5926 5930 (Pubitemid 43086110)
15. J.M. Coffin, S.H. Hughes, and H.E. Varmus Retroviruses 1997 Cold Spring Harbor Laboratory Press New York
16. D. Wodarz, M.A. Nowak, and C.R.M. Bangham The dynamics of HTLV-I and the CTL response Immunol. Today 20 1999 220 227 (Pubitemid 29217078)
17. M.A. Nowak, and R.M. May Virus Dynamics: Mathematical Principles of Immunology and Virology 2000 Oxford University Press
18. D. Wodarz, and C.R.M. Bangham Evolutionary dynamics of HTLV-I J. Mol. Evol. 50 2000 448 455 (Pubitemid 30429959)
19. A.S. Perelson, and P.W. Nelson Mathematical analysis of HIV-I dynamics in vivo SIAM Rev. 41 1999 3 44 (Pubitemid 129723746)
20. R.J. De Boer, and A.S. Perelson Towards a general function describing T cell proliferation J. Theoret. Biol. 175 1995 567 576
21. 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 (Pubitemid 28132653)
22. M.A. Nowak, and C.R.M. Bangham Population dynamics of immune responses to persistent viruses Science 272 1996 74 79 (Pubitemid 26110757)
23. N. Buri, M. Mudrinic, and N. Vasovi Time delay in a basic model of the immune response Chaos Solitons Fractals 12 2001 483 489 (Pubitemid 32034079)
24. K. Wang, and W. Wang Complex dynamic behavior in a viral model with delayed immune response Physica D 226 2007 197 208 (Pubitemid 46185615)
25. 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
26. C.C. McCluskey Global stability for an SEIR epidemiological model with varying infectivity and infinite delay Math. Biosci. Eng. 6 2009 603 610
27. J. LaSalle, and S. Lefschetz Stability by Lyapunov's Direct Method 1961 Academic Press New York
28. J.K. Hale, and S.V. Lunel Introduction to Functional Differential Equations 1993 Springer-Verlag New York
29. J.K. Hale Theory of Functional Differential Equations 1977 Springer-Verlag Berlin
30. B.D. Hassard, N.D. Kazarinoff, and Y.H. Wan Theory and Applications of Hopf Bifurcation 1981 Cambridge University Press Cambridge
31. K. Engelborghs, T. Luzyanina, and D. Roose Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL ACM Trans. Math. Software 28 2002 1 21 (Pubitemid 135686769)
32. K. Engelborghs, T. Luzyanina, G. Samaey, DDE-BIFTOOL v. 2.00: A Matlab package for bifurcation analysis of delay differential equations, Technical Report TW-330, Department of Computer Science, K. U. Leuven, Leuven, Belgium, 2001.
33. H. Kato, and Y. Koya Oral administration of human T-cell leukemia virus type 1 induces immune unresponsiveness with persistent infection in adult rats J. Virol. 72 1998 7289 7293 (Pubitemid 28377859)
34. J. Lang, and M.Y. Li Stable and transient periodic oscillations in a mathematical model for CTL response to HTLV-I infection J. Math. Biol. 2011 10.1007/s00285-011-0455-z