Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

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

School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

Special Issues: Advanced Big Data Analysis for Precision Medicine

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 $E_{f}$ is globally asymptotically stable when the basic reproductive numbers $\mathcal{R}_{0}<1$, implying that the virus can be eventually cleared; the infected equilibrium without immune response $E_{w}$ is globally asymptotically stable when the CTL immune response reproduction number $\mathcal{R}_{1}$ is less than one and $\mathcal{R}_{0}$ is greater than one, implying that the infection becomes chronic, but CTL immune response has not been established; the infected equilibrium with immune response $E_{c}$ is globally asymptotically stable when $\mathcal{R}_{1}>1$, 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.
  Figure/Table
  Supplementary
  Article Metrics

Keywords HIV; CTL immune response; antiretroviral therapy; latently infected cells; cell-to-cell viral transmission; global stability

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. Mathematical Biosciences and Engineering, 2019, 16(6): 6822-6841. doi: 10.3934/mbe.2019341

References

  • 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.

 

Reader Comments

your name: *   your email: *  

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved