Skip to main content
Have a personal or library account? Click to login
A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation Cover

A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation

International Journal of Applied Mathematics and Computer Science
Volume 20 (2010): Issue 3 (September 2010)
By:  and    
Open Access
|Sep 2010
References

References

  1. Callaway, D. S. and Perelson, A. S. (1998). HIV-1 infection and low steady state viral loads,(5): 29-64.
    Open DOISearch in Google Scholar
  2. Culshaw, R. and Ruan, S. (2000). A delay-differential equation model of hiv infection of CD4T-cells,(1): 27-39.
    Open DOISearch in Google Scholar
  3. Culshaw, R., Ruan, S. and Webb, G. (2003). A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay,(5): 425-444.
    Open DOISearch in Google Scholar
  4. De Boer, R. J. and Perelson, A. S. (1995). Towards a general function describing T-cell proliferation,(4): 567-576.
    Open DOISearch in Google Scholar
  5. De Leenheer, P. and Smith, H. L. (2003). Virus dynamics: A global analysis,(4): 1313-1327.
    Open DOISearch in Google Scholar
  6. Diekmann, O., Heesterbeek, J. A. P. and Metz, J. (1990). On the definition and the computation of the basic reproduction ratioin models for infectious diseases in heterogeneous populations,(4): 365-382.
    Open DOISearch in Google Scholar
  7. Dimitrov, D. S., Willey, R. L., Sato, H., Chang, L. J., Blumenthal, R. and Martin, M. A. (1993). Quantitation of human immunodeficiency virus type 1 infection kinetics,(4): 2182-2190.
    Open DOISearch in Google Scholar
  8. Esteva-Peralta, L. and Velasco-Hernandez, J. X. (2002). M-matrices and local stability in epidemic models,(4-5): 491-501.
    Open DOISearch in Google Scholar
  9. Grossman, Z., Feinberg, M. B. and Paul, W. (1998). Multiple modes of cellular activation and virus transmission in HIV infection: A role for chronically and latently infected cells in sustaining viral replication,(11): 6314-6319.
    Open DOISearch in Google Scholar
  10. Hassard, B. D., Kazarinoff, N. D. and Wan, Y. H. (1981)., Cambridge University Press, Cambridge.
    Search in Google Scholar
  11. Herz, A. V. M., Bonhoeffer, S., Anderson, R. M., May, R. M. and Nowak, M. A. (1996). Viral dynamics in vivo: Limitations on estimates of intracellular delay and virus decay,(14): 7247-7251.
    Open DOISearch in Google Scholar
  12. Kirschner, D. E. (1996). Using mathematics to understand HIV immune system,(2): 191.
    Search in Google Scholar
  13. Kirschner, D. E. and Webb, G. (1996). A model for treatment strategy in the chemotherapy of AIDS,(2): 167-190.
    Open DOISearch in Google Scholar
  14. MacDonald, N. (1978)., Springer-Verlag, New York, NY.
    Open DOISearch in Google Scholar
  15. Mittler, J. E., Sulzer, B., Neumann, A. U. and Perelson, A. S. (1998). Influence of delayed viral production on viral dynamics in HIV-1 infected patients,(2): 143-163.
    Open DOISearch in Google Scholar
  16. Nelson, P. W., Murray, J. D. and Perelson, A. S. (2000). A model of HIV-1 pathogenesis that includes an intracellular delay,(2): 201-215.
    Open DOISearch in Google Scholar
  17. Nelson, P. W. and Perelson, A. S. (2002). Mathematical analysis of delay differential equation models of HIV-1 infection,(1): 73-94.
    Open DOISearch in Google Scholar
  18. Nowak, M. A. and Bangham, R. M. (1996). Population dynamics of immune responses to persistent viruses,(5258): 74-79.
    Open DOISearch in Google Scholar
  19. Nowak, M. A. and May, R. M. (2000)., Oxford University Press, New York, NY.
    Search in Google Scholar
  20. Perelson, A. S. (1989). Modelling the interaction of the immune system with HIV,C. Castillo-Chavez (Ed.),, Springer-Verlag, New York, NY, pp. 350-370.
    Open DOISearch in Google Scholar
  21. Perelson, A. S., Kirschner, D. E. and Boer, R. D. (1993). Dynamics of HIV infection of CD4T-cells,(1): 81-125.
    Open DOISearch in Google Scholar
  22. Perelson, A. S. and Nelson, P. W. (1999). Mathematical analysis of HIV-1 dynamics in vivo,(1): 3-44.
    Open DOISearch in Google Scholar
  23. Philips, D. M. (1994). The role of cell-to-cell transmission in HIV infection,(6): 719-731.
    Open DOISearch in Google Scholar
  24. Smith, H. L. (1995)., American Mathematical Society, Providence, RI.
    Search in Google Scholar
  25. Spouge, J. L., Shrager, R. I. and Dimitrov, D. S. (1996). HIV-1 infection kinetics in tissue cultures,(1): 1-22.
    Open DOISearch in Google Scholar
  26. Tam, J. (1999). Delay effect in a model for virus replication,(1): 29-37.
    Open DOISearch in Google Scholar
  27. Thieme, H. R. (1993). Persistence under relaxed point-dissipativity (with application to an endemic model),(2): 407.
    Open DOISearch in Google Scholar
  28. van den Driessche, P. and Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,(1-2): 29-48.
    Open DOISearch in Google Scholar
  29. Wang, L. and Li, M. Y. (2006). Mathematical analysis of the global dynamics of a model for HIV infection of CD4T-cells,(1): 4-57.
    Open DOISearch in Google Scholar
  30. Zhu, H. and Smith, H. L. (1994). Stable periodic orbits for a class of three dimensional competitive systems,(1): 143-156.
    Open DOISearch in Google Scholar
DOI: https://doi.org/10.2478/v10006-010-0045-z | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Journal RSS Feed
Language: English
Page range: 601 - 612
Published on: Sep 27, 2010
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
HIV,
periodic oscillations,
persistence,
stability,
tissue culture
Related subjects:
Mathematics,
Applied mathematics

© 2010 Mahiéddine Kouche, Bedr'Eddine Ainseba, published by University of Zielona Góra
This work is licensed under the Creative Commons License.

Volume 20 (2010): Issue 3 (September 2010)
Previous article