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The global dynamics of a model about HIV-1 infection in vivo

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Abstract

A four dimension ODE model is built to study the infection of human immunodeficiency virus (HIV) in vivo. We include in this model four components: the healthy T cells, the latent-infected T cells, the active-infected T cells and the HIV virus. Two types of HIV transmissions in vivo are also included in the model: the virus-to-cell transmission, and the cell-to-cell HIV transmission. There are two possible equilibriums: the healthy equilibrium, and the infected steady state. The basic reproduction number R 0 is introduced. When R 0 < 1, the healthy equilibrium is globally stable and when R 0 > 1, the infected equilibrium exists and is globally stable. Through simulations, we find that, the cell-to-cell HIV transmission is very important for the final outcome of the HIV attacking. Some important clinical observations about the HIV infection situation in lymph node are also verified.

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References

  1. Perelson A.S., Kirschner D.E., Boer R.D.: Dynamics of HIV infection of CD4+ T cells. Math. Biosci. 114, 81–125 (1992)

    Article  Google Scholar 

  2. Perelson A.S.: Modeling the Interaction of the Immue System with HIV, Mathematical and Statistical Approaches to AIDS Epidemiology, pp. 350. Springer, Berlin (1989)

    Google Scholar 

  3. Kirschner D.E.: Using mathematics to understand HIV immue dynamics. Notices Am. Math. Soc. 43, 191 (1996)

    MATH  MathSciNet  Google Scholar 

  4. Perelson A.S., Nelson P.W.: Mathematical analysis of HIV −1 dynamics in vivio. SIAM Rev. 41, 3 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  5. Rebecca V.C., Ruan S.: A delay-differential equation model of HIV infection of CD4+ T cells. Math. Biosci. 165, 27–39 (2000)

    Article  MATH  Google Scholar 

  6. Lifson J.D. et al.: Induction of CD4-dependent cell fusion by the HTLV-III/LAV envelope glycoprotein. Nature 323, 725–728 (1986)

    Article  Google Scholar 

  7. Sodroski J., Goh W.C., Rosen C., Campbell K., Haseltine W.A.: Role of the HTLV-III/LAV envelope in syncytium formation and cytopathicity. Nature 322, 470–474 (1986)

    Article  Google Scholar 

  8. Budka H.: Multinucleated giant cells in brain: a hallmark of the acquired immune deficiency syndrome (AIDS). Acta Neuropathol. 69, 253–258 (1986)

    Article  Google Scholar 

  9. Frankel S.S. et al.: Replication of HIV-1 in dendritic cell-derived syncytia at the mucosal surface of the adenoid. Science 272, 115–117 (1996)

    Article  Google Scholar 

  10. Koenig S. et al.: Detection of AIDS virus in macrophages in brain tissue from AIDS patients with encephalopathy. Science 233, 1089–1093 (1986)

    Article  Google Scholar 

  11. Castedo M. et al.: Sequential involvement of Cdk1, mTOR and p53 in apoptosis induced by the HIV-1 envelope. EMBO J. 21, 4070–4080 (2002)

    Article  Google Scholar 

  12. Ferri K.F. et al.: Apoptosis control in syncytia induced by the HIV type 1-envelope glycoprotein complex: role of mitochondria and caspases. J. Exp. Med. 192, 1081–1092 (2000)

    Article  Google Scholar 

  13. Laurent-Crawford A.G. et al.: The cytopathic effect of HIV is associated with apoptosis. Virology 185, 829–839 (1991)

    Article  Google Scholar 

  14. Amendola A. et al.: Induction of tissue transglutaminase in HIV patogenesis: evidence for high rate apoptosis of CD4+ T lymphocytes and accessory cells in lymphoid tissues. Proc. Natl. Acad. Sci. USA 93, 11057–11062 (1996)

    Article  Google Scholar 

  15. Gupta P., Balachandran R., Ho M., Enrico A., Rinaldo C.: Cell-to-cell transmission of human immunodeficiency virus type 1 in the presence of azidothymidine and neutralizing antibody. J. Virol. 63, 2361–2365 (1989)

    Google Scholar 

  16. Phillips D.M.: The role of cell-to-cell transmission in HIV infection. AIDS 8, 719–731 (1994)

    Article  Google Scholar 

  17. Sato H., Orenstein J., Dimitrov D., Martin M.: Cell-to-cell spread of HIV-1 occurs within minutes and may not involve the participation of virus particles. Virology 186, 712–724 (1992)

    Article  Google Scholar 

  18. Gummurulu S., Kinsey M.C., Emerman M.: An in vitro rapid-turnover assay for human immunodeficiency virus type 1 replication selects for cell-to-cell spread of virus. J. Virol. 74, 10882–10891 (2000)

    Article  Google Scholar 

  19. Levy, J.: HIV and the Pathogenesis of AIDS, ISBN 7-03-007902-7 (1998)

  20. Frost S.D., Mclean A.R.: Quasispecies dynamics and the emergence of drug resistance during zidovudine therapy of HIV infection. AIDS 8, 323–332 (1994)

    Article  Google Scholar 

  21. Nowak M.A., Bonhoeffer S., Shaw G.M., May R.M.: Anti-viral drug treatment: Dynamics of resistance in free virus and infected cell population. J. Theor. Biol. 184, 203–221 (1997)

    Article  Google Scholar 

  22. Arnaout R.A., Nowak M.A.: Competivie coexistence in antiviral immunity. J. Theor. Biol. 204, 431–440 (2000)

    Article  Google Scholar 

  23. Wodarz D., Lloyd A.L.: Innmune responses and the emergence of drug-resistant virus strains in vivo. Proc. R. Soc. Lond. B. 271, 1101–1109 (2004)

    Article  Google Scholar 

  24. Culshaw R.V., Ruan S.: A delay-differential equation model of HIV infection of CD4+ T cells. Math. Biosci. 165, 27–39 (2000)

    Article  MATH  Google Scholar 

  25. Lou J., Ruggeri T., Tebaldi C.: Modelling cancer in HIV-1 infected individuals: Equilibria, cycles and chaotic behavior. Math. Biosci. Eng. 3(2), 313–324 (2006)

    MATH  MathSciNet  Google Scholar 

  26. Lou J., Ruggeri T., Ma Z.: Cycles and chaotic behavior in an AIDS-related cancer dynamic model in vivo. J. Biol. Syst. 15(2), 149–168 (2007)

    Article  Google Scholar 

  27. Lou J., Ma Z., Shao Y.M., Han L.T.: Modelling the interaction of T Cells, antigen presenting cells and HIV-1 in vivo. Comput. Math. Appl. 48, 9–33 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  28. LaSalle J.P.: The Stability of Dynamical System. SIAM, Philadelphia (1976)

    Google Scholar 

  29. Smith R.J.: Adherence to antiretroviral HIV drugs: how many doses can you miss before resistance emerges?. Proc. R. Soc. B. 273, 617–624 (2006)

    Article  Google Scholar 

  30. Haase A.T. et al.: Quantitative image analysis of HIV-1 infection in lymphoid tissue. Science 274, 985 (1996)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, 99 Shangda Road, 200444, Shanghai, People’s Republic of China

    Qingzhi Wen & Jie Lou

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  1. Qingzhi Wen
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  2. Jie Lou
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Correspondence to Jie Lou.

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Communicated by T. Ruggeri.

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Wen, Q., Lou, J. The global dynamics of a model about HIV-1 infection in vivo. Ricerche mat. 58, 77–90 (2009). https://doi.org/10.1007/s11587-009-0048-y

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  • DOI: https://doi.org/10.1007/s11587-009-0048-y

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