Mathematical Biosciences and Engineering, 2015, 12(1): 1-21. doi: 10.3934/mbe.2015.12.1.

Primary: 92C50; Secondary: 34E13, 92C60.

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A singularly perturbed HIV model with treatment and antigenic variation

1. Instituto Nacional de Matemática Pura e Aplicada, Rio do Janeiro, RJ 22460-320

We study the long term dynamics and the multiscale aspects of a within-host HIV model that takes into account both mutation and treatment with enzyme inhibitors. This model generalizes a number of other models that have been extensively used to describe the HIV dynamics. Since the free virus dynamics occur on a much faster time-scale than cell dynamics, the model has two intrinsic time scales and should be viewed as a singularly perturbed system. Using Tikhonov's theorem we prove that the model can be approximated by a lower dimensional nonlinear model. Furthermore, we show that this reduced system is globally asymptotically stable by using Lyapunov's stability theory.
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Keywords immune response; Lyapunov functions.; Global stability; multiscale analysis; HIV; mutation

Citation: Nara Bobko, Jorge P. Zubelli. A singularly perturbed HIV model with treatment and antigenic variation. Mathematical Biosciences and Engineering, 2015, 12(1): 1-21. doi: 10.3934/mbe.2015.12.1

References

  • 1. Nature, 333 (1988), 514-519.
  • 2. Proceedings of the Royal Society of London. Series B: Biological Sciences, 270 (2003), 1651-1657.
  • 3. Mathematical Biosciences and Engineering, 10 (2013), 499-521.
  • 4. (2010).
  • 5. Proceedings of the National Academy of Sciences, 94 (1997), 6971-6976.
  • 6. Proceedings of the National Academy of Sciences, 83 (1986), 9159-9163.
  • 7. Ministério da Saúde, 2013.
  • 8. Journal of Differential Equations, 31 (1979), 53-98.
  • 9. JAIDS Journal of Acquired Immune Deficiency Syndromes, 7 (1994), 236-244.
  • 10. PLoS computational biology, 9 (2013), e1002971, 12 pp.
  • 11. Current HIV research, 2 (2004), 23-37.
  • 12. Nature, 373 (1995), 123-126.
  • 13. Cambridge University Press, 1998.
  • 14. vol. 114, Springer New York, 1996.
  • 15. AMS notices, 43 (1996), 191-202.
  • 16. Bulletin of Mathematical Biology, 66 (2004), 879-883.
  • 17. Proceedings of the Royal Society of London. Series B: Biological Sciences, 268 (2001), 847-854.
  • 18. Journal of Clinical Investigation, 105 (2000), R1-R8.
  • 19. Immunology and cell biology, 85 (2006), 6-15.
  • 20. Mathematical Biosciences, 179 (2002), 73-94.
  • 21. Oxford University Press, 2000.
  • 22. Science, 272 (1996), 74-79.
  • 23. (2012).
  • 24. Mac Graw Hill, 1978.
  • 25. Ph.D. thesis, IMPA, 2005.
  • 26. Mathematical biosciences, 114 (1993), 81-125.
  • 27. SIAM review, 41 (1999), 3-44.
  • 28. The Hopkins HIV Report, 8 (1996), no. 3.
  • 29. Nature Reviews Genetics, 5 (2004), 52-61.
  • 30. Journal of molecular evolution, 40 (1995), 249-259.
  • 31. no. Ed. 4, WB Saunders, 1995.
  • 32. Ph.D. thesis, AIMS, 2012.
  • 33. Nature Reviews Microbiology, 1 (2003), 181-190.
  • 34. SIAM Journal on Applied Mathematics, 63 (2003), 1313-1327.
  • 35. Science, 242 (1988), 1554-1557.
  • 36. Journal of mathematical biology, 68 (2014), 1269-1293.
  • 37. Bull. Math. Biol., 73 (2011), 609-625.
  • 38. Journal of Theoretical Biology, 203 (2000), 285-301.
  • 39. Journal of differential equations, 92 (1991), 252-281.
  • 40. Springer-Verlag Berlin, 1984.
  • 41. Moskva: Vysshaya Shkola, 1990 (Russian).
  • 42. Advances in Complex Systems, 10 (2007), 495-503.
  • 43. Dover Publications, Inc., New York, 1987.
  • 44. (2013).

 

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