Impact of intracellular delays and target-cell dynamics on in vivo viral infections

SIAM Journal on Applied Mathematics

Volumn 70, Issue 7, 2010, Pages 2434-2448

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

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Global stability; In host models; Intracellular delays; Lyapunov functionals; Periodic oscillations; Target cell dynamics

Indexed keywords

GLOBAL STABILITY; IN-HOST MODELS; INTRACELLULAR DELAYS; LYAPUNOV FUNCTIONALS; PERIODIC OSCILLATION;

ASYMPTOTIC ANALYSIS; DISEASES; VIRUSES;

DYNAMICS;

EID: 77956234983     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/090779322     Document Type: Article

References (30)

1. A. S. Perelson, D. E. Kirschner, and R. de Boer, Dynamics of HIV infection of CD4+ T-cells, Math. Biosci., 114 (1993), pp. 81-125.
2. A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-I dynamics in vivo, SIAM Rev., 41 (1999), pp. 3-44.
3. A. S. Perelson, A. U. Neumann, M. Markowitz, J. M. Leonard, and D. D. Ho, HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span, and viral generation time, Science, 271 (1996), pp. 1582-1586.
4. M. A. Nowak, S. Bonhoeffer, A. M. Hill, R. Boehme, H. C. Thomas, and H. Mcdade, Viral dynamics in hepatitis B virus infection, Proc. Natl. Acad. Sci. USA, 93 (1996), pp. 4398-4402.
5. S. Bonhoeffer, R. M. May, G. M. Shaw, and M. A. Nowak, Virus dynamics and drug therapy, Proc. Natl. Acad. Sci. USA, 94 (1997), pp. 6971-6976.
6. L. Wang, M. Y. Li, and D. Kirschner, Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression, Math. Biosci., 179 (2002), pp. 207-217.
7. P. Katri and S. Ruan, Dynamics of human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells, C. R. Biologies, 327 (2004), pp. 1009-1016.
8. V. Herz, S. Bonhoeffer, R. Anderson, R. May, and M. Nowak, Viral dynamics in vivo: Limitations on estimates of intracellular delay and virus decay, Proc. Natl. Acad. Sci. USA, 93 (1996), pp. 7247-7251.
9. P. W. Nelson, J. D. Murray, and A. S. Perelson, A model of HIV-1 pathogenesis that includes an intracellular delay, Math. Biosci., 163 (2000), pp. 201-215.
10. R. V. Culshaw and S. Ruan, A delay-differential equation model of HIV infection of CD4+ T-cells, Math. Biosci., 165 (2000), pp. 27-39.
11. P. W. Nelson and A. S. Perelson, Mathematical analysis of delay differential equation models of HIV-1 infection, Math. Biosci., 179 (2002), pp. 73-94.
12. R. V. Culshaw, S. Ruan, and G. Webb, A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay, J. Math. Biol., 46 (2003), pp. 425-444.
13. Y. Wang, Y. C. Zhou, J. Wu, and J. Heffernan, Oscillatory viral dynamics in a delayed HIV pathogenesis model, Math. Biosci., 219 (2009), pp. 104-112.
14. L. Wang and M. Y. Li, Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells, Math. Biosci., 200 (2006), pp. 44-57.
15. P. De Leenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math., 63 (2003), pp. 1313-1327.
16. A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), pp. 879-883.
17. M. Y. Li and H. Shu, Global dynamics of an in-host viral model with intracellular delay, Bull. Math. Biol., to appear.
18. C. C. McCluskey, Complete global stability for an SIR epidemic model with delay-distributed or discrete, Nonlinear Anal., 11 (2010), pp. 55-59.
19. C. C. McCluskey, Global stability for an SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. Eng., 6 (2009), pp. 603-610.
20. A. Korobeinikov, Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission, Bull. Math. Biol., 30 (2006), pp. 615-626.
21. P. Georgescu and Y.-H. Hsieh, Global stability for a virus dynamics model with nonlinear incidence of infection and removal, SIAM J. Appl. Math., 67 (2006), pp. 337-353.
22. F. V. Atkinson and J. R. Haddock, On determining phase spaces for functional differential equations, Funkcial. Ekvac., 31 (1988), pp. 331-347.
23. J. Hale and S. Verduyn Lunel, Introduction to Functional Differential Equations, Appl. Math. Sci., Springer-Verlag, New York, 1993.
24. J. R. Haddock and J. Terjéki, Liapunov-Razumikhin functions and an invariance principle for functional-differential equations, J. Differential Equations, 48 (1983), pp. 95-122.
25. J. R. Haddock, T. Krisztin, and J. Terjéki, Invariance principles for autonomous functional-differential equations, J. Integral Equations, 10 (1985), pp. 123-136.
26. W. M. Ruess and W. H. Summers, Linearized stability for abstract differential equations with delay, J. Math. Anal. Appl., 198 (1996), pp. 310-336.
27. M. Y. Li, J. R. Graef, L. Wang, and J. Karsai, Global dynamics of an SEIR model with a varying total population size, Math. Biosci., 160 (1999), pp. 191-213.
28. N. P. Bhatia and G. P. Szegö, Dynamical Systems: Stability Theory and Applications, Lecture Notes in Math. 35, Springer, Berlin, 1967.
29. H. L. Smith and P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge University Press, Cambridge, UK, 1995.
30. M. S. Ciupe, B. L. Bivort, D. M. Bortz, and P. W. Nelson, Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models, Math. Biosci., 200 (2006), pp. 1-27.