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The effects of CTL immune response on HIV infection model with potent therapy, latently infected cells and cell-to-cell viral transmission

  • Received: 20 January 2018 Accepted: 07 June 2019 Published: 26 July 2019
  • In this paper, a mathematical model is formulated to investigate the effect of cytotoxic T lymphocyte (CTL) immune response on human immunodeficiency virus (HIV) infection dynamics. The model includes latently infected cells, antiretroviral therapy, cell-free virus infection and cell-to-cell viral transmission. By constructing Lyapunov functionals, the global stability of three equilibria is obtained. More specifically, the infection-free equilibrium Ef is globally asymptotically stable when the basic reproductive numbers R0<1, implying that the virus can be eventually cleared; the infected equilibrium without immune response Ew is globally asymptotically stable when the CTL immune response reproduction number R1 is less than one and R0 is greater than one, implying that the infection becomes chronic, but CTL immune response has not been established; the infected equilibrium with immune response Ec is globally asymptotically stable when R1>1, implying that the infection becomes chronic with persistent CTL immune response. Numerical simulations confirm the above theoretical results. Moreover, the inclusion of CTL immune response can generate a higher level of uninfected CD4+ T cells, and significantly reduce infected cells and viral load. These results may help to improve the understanding of HIV infection dynamics.

    Citation: Ting Guo, Zhipeng Qiu. The effects of CTL immune response on HIV infection model with potent therapy, latently infected cells and cell-to-cell viral transmission[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 6822-6841. doi: 10.3934/mbe.2019341

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  • In this paper, a mathematical model is formulated to investigate the effect of cytotoxic T lymphocyte (CTL) immune response on human immunodeficiency virus (HIV) infection dynamics. The model includes latently infected cells, antiretroviral therapy, cell-free virus infection and cell-to-cell viral transmission. By constructing Lyapunov functionals, the global stability of three equilibria is obtained. More specifically, the infection-free equilibrium Ef is globally asymptotically stable when the basic reproductive numbers R0<1, implying that the virus can be eventually cleared; the infected equilibrium without immune response Ew is globally asymptotically stable when the CTL immune response reproduction number R1 is less than one and R0 is greater than one, implying that the infection becomes chronic, but CTL immune response has not been established; the infected equilibrium with immune response Ec is globally asymptotically stable when R1>1, implying that the infection becomes chronic with persistent CTL immune response. Numerical simulations confirm the above theoretical results. Moreover, the inclusion of CTL immune response can generate a higher level of uninfected CD4+ T cells, and significantly reduce infected cells and viral load. These results may help to improve the understanding of HIV infection dynamics.




    [1] A. S. Perelson, D. E. Kirschner and R. D. Boer, Dynamics of HIV infection of CD4+ T cells, Math. Biosci., 114 (1993), 81–125.
    [2] Y. Wang, J. Liu and L. Liu, Viral dynamics of an HIV model with latent infection incorporating antiretroviral therapy, Adv. Differ. Equations, 225 (2016).
    [3] WHO, 10 facts on HIV/AIDS, 2017. Available from: http://www.who.int/features/factfiles/hiv/zh/.
    [4] WHO, HIV/AIDS: Fact sheet, 2017. Available from: http://www.who.int/mediacentre/factsheets/fs360/en/.
    [5] A. Mojaver and H. Kheiri, Mathematical analysis of a class of HIV infection models of CD4+ T-cells with combined antiretroviral therapy, Appl. Math. Comput., 259 (2015), 258–270.
    [6] X. Wang, X. Song, S. Tang, et al., Dynamics of an HIV Model with Multiple Infection Stages and Treatment with Different Drug Classes, Bull. Math. Biol., 78 (2016), 322–349.
    [7] L. Rong and A. S. Perelson, Modeling HIV persistence, the latent reservoir, and viral blips, J. Theor. Biol., 260 (2009), 308–331.
    [8] J. M. Kitayimbwa, J. T. Mugisha and R. A. Saenz, The role of backward mutations on the within-host dynamics of HIV-1, J. Math. Biol., 67 (2013), 1111–1139.
    [9] S. Palmer, L. Josefsson and J. M. Coffin, HIV reservoirs and the possibility of a cure for HIV infection, J. Intern. Med., 270 (2011), 550–560.
    [10] L. Rong and A. S. Perelson, Modeling Latently Infected Cell Activation: Viral and Latent Reservoir Persistence, and Viral Blips in HIV-infected Patients on Potent Therapy, Plos Comput. Biol., 5 (2009).
    [11] F. Maldarelli, S. Palmer, M. S. King, et al., ART suppresses plasma HIV-1 RNA to a stable set point predicted by pretherapy viremia, Plos Pathog., 3 (2007).
    [12] H. S. Ariel, C. L. Lu, K. Florian, et al., Broadly Neutralizing Antibodies and Viral Inducers Decrease Rebound from HIV-1 Latent Reservoirs in Humanized Mice, Cell, 158 (2014), 989–999.
    [13] X. Wang, G. Mink, D. Lin, et al., Influence of raltegravir intensification on viral load and 2-LTR dynamics in HIV patients on suppressive antiretroviral therapy, J. Theor. Biol., 416 (2017), 16–27.
    [14] A. Bosque, K. A. Nilson, A. B. Macedo, et al., Benzotriazoles Reactivate Latent HIV-1 through Inactivation of STAT5 SUMOylation, Cell Rep., 18 (2017), 1324–1334.
    [15] S. Pankavich, The Effects of Latent Infection on the Dynamics of HIV, Differ. Equ. Dyn. Syst., 24 (2016), 281–303.
    [16] C. M. Pinto, Persistence of low levels of plasma viremia and of the latent reservoir in patients under ART: A fractional-order approach, Commun. Nonlinear Sci. Numer. Simulat., 43 (2017), 251–260.
    [17] D. C. Johnson and M. T. Huber, Directed egress of animal viruses promotes cell-to-cell spread, J. Virol., 76 (2002), 1–8.
    [18] D. Mazurov, A. Ilinskaya, G. Heidecker, et al., Quantitative comparison of HTLV-1 and HIV-1 cell-to-cell infection with new replication dependent vectors, Plos Path., 6 (2010).
    [19] H. Sato, J. Orenstein, D. Dimitrov, et al., Cell-to-cell spread of HIV-1 occurs within minutes and may not involve the participation of virus particles, Virology, 186 (1992), 712–724.
    [20] C. J. Duncan, R. A. Russell and Q. J. Sattentau, High multiplicity HIV-1 cell-to-cell transmission from macrophages to CD4+ T cells limits antiretroviral efficacy, AIDS, 27 (2013), 2201–2206.
    [21] J. Wang, J. Pang, T. Kuniya, et al., Global threshold dynamics in a five-dimensional virus model with cell-mediated, humoral immune responses and distributed delays, Appl. Math. Comput., 241 (2014), 298–316.
    [22] Y. Nakata, Global dynamics of a cell mediated immunity in viral infection models with distributed delays, J. Math. Anal. Appl., 375 (2010), 14-27.
    [23] Z. Yuan, Z. Ma and X. Tang, Global stability of a delayed HIV infection model with nonlinear incidence rate, Nonlinear Dynam., 68 (2012), 207–214.
    [24] Z. Yuan and X. Zou, Global threshold dynamics in an HIV virus model with nonlinear infection rate and distributed invasion and production delays, Math. Biosci. Eng., 10 (2013), 483–498.
    [25] R. Arnaout, M. Nowak and D. Wodarz, HIV-1 dynamics revisited: biphasic decay by cytotoxic lymphocyte killing?, Proc. R. Soc. London, 265 (2000), 1347–1354.
    [26] J. M. Conway and A. S. Perelson, Post-treatment control of HIV infection, Proc. Natl. Acad. Sci. B, 112 (2015), 5467–5472.
    [27] Y. Wang, Y. Zhou, F.Brauer, et al., Viraldynamics model with CTL immuneresponse incorporating antiretroviral therapy, J. Math. Biol., 67 (2013), 901-934.
    [28] H. Pourbashash, S. S. Pilyugin, C. McCluskey, et al., Global analysis of within host virus models with cell-to-cell viral transmission, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 3341–3357.
    [29] B. Song, J. Lou and Q. Wen, Modelling two different therapy strategies for drug T-20 on HIV-1 patients, J. Appl. Math. Mech., 32 (2011), 419–436.
    [30] D. S. Callaway and A. S. Perelson, HIV-1 infection and low steady state viral loads, Bull. Math. Biol., 64 (2002), 29–64.
    [31] K. Allali, J. Danane and Y. Kuang, Global analysis for an HIV infection model with CTL immune response and infected cells in eclipse phase, Appl. Sci., 7 (2017), 861.
    [32] L. Rong, Z. Feng and A. S. Perelson, Emergence of HIV-1 Drug Resistance During Antiretroviral Treatment, Bull. Math. Biol., 69 (2007), 2027–2060.
    [33] H. Zhu, Y. Luo and M. Chen, Stability and Hopf bifurcation of a HIV infection model with CTL- response delay, Comput. Math. Appl., 62 (2011), 3091–3102.
    [34] X. Wang, A. M. Elaiw and X. Song, Global properties of a delayed HIV infection model with CTL immune response, Appl. Math. Comput., 218 (2012), 9405–9414.
    [35] B. M. Adams, H. T. Banks, M. Davidian, et al., HIV dynamics: Modeling, data analysis, and optimal treatment protocols, J. Comput. Appl. Math., 184 (2005), 10–49.
    [36] L. Rong and A. S. Perelson, Asymmetric division of activated latently infected cells may explain the decay kinetics of the HIV-1 latent reservoir and intermittent viral blips, Math. Biosci., 217 (2009), 77–87.
    [37] P. Driessche and P. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.
    [38] J. P. LaSalle, The stability of dynamical systems, Philadelphia, 1976.
    [39] X. Tian and R. Xu, Global stability and Hopf bifurcation of an HIV-1 infection model with saturation incidence and delayed CTL immune response, Appl. Math. Comput., 237 (2014), 146–154.
    [40] M. Louie, C. Hogan, M. D. Mascio, et al., Determining the relative efficacy of highly active antiretroviral therapy, J. Infect. Dis., 187 (2003), 896–900.
    [41] M. A. Nowak and C. R. Bangham, Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74–79.
    [42] A. S. Perelson, P. Essunger, Y. Cao, et al., Decay characteristics of HIV-1-infected compartments during combination therapy, Nature, 387 (1997), 188–191.
    [43] J. Wang, M. Guo, X. Liu, et al., Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay, Appl. Math. Comput., 291 (2016), 149–161.
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