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Mathematical Biosciences and Engineering

2016, Volume 13, Issue 2: 343-367. doi: 10.3934/mbe.2015006
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Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay

  • 1.
    School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049
  • Received: 01 April 2015 Accepted: 29 June 2018 Published: 25 November 2015

  • MSC : Primary: 34K20, 92D30; Secondary: 34C23, 34K60.

  • A within-host viral infection model with both virus-to-cell and cell-to-cell transmissions and time delay in immune response is investigated. Mathematical analysis shows that delay may destabilize the infected steady state and lead to Hopf bifurcation. Moreover, the direction of the Hopf bifurcation and the stability of the periodic solutions are investigated by normal form and center manifold theory.Numerical simulations are done to explore the rich dynamics,including stability switches, Hopf bifurcations, and chaotic oscillations.

    Citation: Jinhu Xu, Yicang Zhou. Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay[J]. Mathematical Biosciences and Engineering, 2016, 13(2): 343-367. doi: 10.3934/mbe.2015006

    Related Papers:

  • A within-host viral infection model with both virus-to-cell and cell-to-cell transmissions and time delay in immune response is investigated. Mathematical analysis shows that delay may destabilize the infected steady state and lead to Hopf bifurcation. Moreover, the direction of the Hopf bifurcation and the stability of the periodic solutions are investigated by normal form and center manifold theory.Numerical simulations are done to explore the rich dynamics,including stability switches, Hopf bifurcations, and chaotic oscillations.


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    [1] SIAM Rev., 41 (1999), 3-44.
    [2] SIAM J. Appl. Math., 63 (2003), 1313-1327.
    [3] Math. Biosci., 200 (2006), 1-27.
    [4] Proc. Natl. Acad. Sci. USA, 93 (1996), 7247-7251.
    [5] Math. Biosci., 235 (2012), 98-109.
    [6] Math. Biosci., 165 (2000), 27-39.
    [7] Math. Biosci., 152 (1998), 143-163.
    [8] Math. Biosci., 163 (2000), 201-215.
    [9] Bull. Math. Biol., 72 (2010), 1492-1505.
    [10] Math. Biosci. Eng., 7 (2010), 675-685.
    [11] J. Math. Biol., 46 (2003), 425-444.
    [12] Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 513-526.
    [13] Comput. Math. Appl., 62 (2011), 3091-3102.
    [14] Math. Biosci., 219 (2009), 104-112.
    [15] Bull. Math. Biol., 73 (2011), 1774-1793.
    [16] Math. Biosci. Eng.,12 (2015), 185-208.
    [17] J. Virol., 81 (2007), 1000-1012.
    [18] J. Virol., 67 (1993), 2182-2190.
    [19] Virology, 186 (1992), 712-724.
    [20] J. Virol., 74 (2000), 10882-10891.
    [21] J. Gen. Virol., 90 (2009), 48-58.
    [22] Nat. Med., 17 (2011), 589-595.
    [23] PloS one., 8 (2013), e64221.
    [24] J. Virol., 72 (1998), 4371-4378.
    [25] Current opinion in virology, 1 (2011), 396-402.
    [26] Virology., 244 (1998), 294-301.
    [27] Nat Immunol., 1 (2000), 23-29.
    [28] Curr Opin HIV AIDS., 4 (2009), 143-149.
    [29] Nat Rev Microbiol, 6 (2008), 815-826.
    [30] Current molecular medicine., 12 (2012), 83-95.
    [31] SIAM J. Appl. Math., 74 (2014), 898-917.
    [32] J. Math. Anal. Appl., 426 (2015), 563-584.
    [33] Science., 272 (1996), 74-79.
    [34] Comput. Math. Appl., 51 (2006), 1593-1610.
    [35] Springer-Verlag, 1993.
    [36] Commun. Pure. Appl. Math., 38 (1985), 733-753.
    [37] J. Math. Anal. Appl., 178 (1993), 344-362.
    [38] vol. 23. Biomathematics. New York: Springer, 1993.
    [39] Chaos Solitions Fractals., 26 (2005), 519-526.
    [40] Springer, Heidelberg, 1977.
    [41] London math society lecture note series, vol. 41. Cambridge University Press, 1981.
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  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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