\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Global analysis of within host virus models with cell-to-cell viral transmission

Abstract Related Papers Cited by
  • Recent experimental studies have shown that HIV can be transmitted directly from cell to cell when structures called virological synapses form during interactions between T cells. In this article, we describe a new within-host model of HIV infection that incorporates two mechanisms: infection by free virions and the direct cell-to-cell transmission. We conduct the local and global stability analysis of the model. We show that if the basic reproduction number ${\mathcal R}_0\leq 1$, the virus is cleared and the disease dies out; if ${\mathcal R}_0>1$, the virus persists in the host. We also prove that the unique positive equilibrium attracts all positive solutions under additional assumptions on the parameters. Finally, a multi strain model incorporating cell-to-cell viral transmission is proposed and shown to exhibit a competitive exclusion principle.
    Mathematics Subject Classification: Primary: 37N25, 97M60; Secondary: 34A34, 34D23.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    W. A. Coppel, Stability and Asymptotic Behavior of Differential Equations, Heath and Co., Boston, 1965.

    [2]

    P. De Leenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math., 63 (2003), 1313-1327.doi: 10.1137/S0036139902406905.

    [3]

    P. De Leenheer and S. S. Pilyugin, Multistrain virus dynamics with mutations: A global analysis, Math. Med. Biol., 25 (2008), 285-322.

    [4]

    N. Dixit and A. Perelson, Multiplicity of human immunodeficiency virus infections in lymphoid tissue, J. Virol., 78 (2004), 8942-8945.doi: 10.1128/JVI.78.16.8942-8945.2004.

    [5]

    M. Fiedler, Additive compound matrices and inequality for eigenvalues of stochastic matrices, Czech. Math. J., 24 (1974), 392-402.

    [6]

    H. I. Freedman, M. X. Tang and S. G. Ruan, Uniform persistence and flows near a closed positively invariant set, J. Dynam. Differential Equations, 6 (1994), 583-600.doi: 10.1007/BF02218848.

    [7]

    H. K. Khalil, Nonlinear Systems, 3rd Edition, Prentice Hall, 2002.

    [8]

    A. Korobeinikov, Global properties of SIR and SEIR epidemic models with multiple parallel infectious stages, Bull. Math. Biol., 71 (2009), 75-83.doi: 10.1007/s11538-008-9352-z.

    [9]

    M. Y. Li, J. R. Graef, L. Wang and J. Karsai, Global dynamics of a SEIR model with varying total population size, Math. Biosci., 160 (1999), 191-213.doi: 10.1016/S0025-5564(99)00030-9.

    [10]

    M. Y. Li and J. S. Muldowney, A geometric approach to the global-stability problems, SIAM J. Math. Anal., 27 (1996), 1070-1083.doi: 10.1137/S0036141094266449.

    [11]

    M. Y. Li and J. S. Muldowney, Global stability for the SEIR model in epidemiology, Math. Biosci., 125 (1995), 155-164.doi: 10.1016/0025-5564(95)92756-5.

    [12]

    R. H. Jr. Martin, Logarithmic norms and projections applied to linear differential systems, J. Math. Anal. Appl., 45 (1974), 432-454.doi: 10.1016/0022-247X(74)90084-5.

    [13]

    D. Mazurov, A. Ilinskaya, G. Heidecker, P. Lloyd and D. Derse, Quantitative comparison of HTLV-1 and HIV-1 Cell-to- Cell infection with new replication dependent vectors, PLoS Pathogens, 6 (2010), e1000788.doi: 10.1371/journal.ppat.1000788.

    [14]

    B. Monel, E. Beaumont, D. Vendrame, O. Schwartz, D. Brand and F. Mammano, HIV cell-to-cell transmission requires the production of infectious virus particles and does not proceed through Env-mediated fusion pores, J. Virol., 86 (2012), 3924-3933.doi: 10.1128/JVI.06478-11.

    [15]

    J. S. Muldowney, Compound matrices and ordinary differential equations, Rocky Mount. J. Math., 20 (1990), 857-872.doi: 10.1216/rmjm/1181073047.

    [16]

    M. A. Nowak and R. M. May, Virus Dynamics, Oxford University press, New York, 2000.

    [17]

    A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41 (1999), 3-44.doi: 10.1137/S0036144598335107.

    [18]

    V. Piguet and Q. Sattentau, Dangerous liaisons at the virological synapse, J. Clin. Invest., 114 (2004), 605-610.doi: 10.1172/JCI200422812.

    [19]

    O. Schwartz, Immunological and virological aspects of HIV cell-to-cell transfer, Retrovirology, 6 (2009), I16.doi: 10.1186/1742-4690-6-S2-I16.

    [20]

    H. L. Smith and P. Waltman, Perturbation of a globally stable steady state, Proc. Am. Math. Soc., 127 (1999), 447-453.doi: 10.1090/S0002-9939-99-04768-1.

    [21]

    M. Sourisseau, N. Sol-Foulon, F. Porrot, F. Blanchet and O. Schwartz, Inefficient human immunodeficiency virus replication in mobile lymphocytes, J. Virol., 81 (2007), 1000-1012.doi: 10.1128/JVI.01629-06.

    [22]

    P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.doi: 10.1016/S0025-5564(02)00108-6.

    [23]

    L. Wang and S. Ellermeyer, HIV infection and $CD4^+$ T cell dynamics, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 1417-1430.doi: 10.3934/dcdsb.2006.6.1417.

    [24]

    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), 44-57.doi: 10.1016/j.mbs.2005.12.026.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(267) Cited by(0)

Access History

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return