The Global Dynamics of HIV Latency Model Including Cell-to-Cell Viral Transmission

Wajahat Ali; Zhipeng Qiu

doi:doi:10.11648/j.acm.20211004.12

| Peer-Reviewed

The Global Dynamics of HIV Latency Model Including Cell-to-Cell Viral Transmission

Wajahat Ali, Zhipeng Qiu

Published in Applied and Computational Mathematics (Volume 10, Issue 4)

Received: 29 May 2021 Accepted: 21 June 2021 Published: 9 July 2021

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

HIV spreads by cell-to-cell transfer and the release of cell-free particles. A slightly more effective method of retroviral transmission is the direct cell-to-cell transfer of HIV, according to recent reports. Intracellular interaction between unhealthy and healthy cells, in combination with cytokine discharged by the cells included, may affect the susceptibility of a target resting CD4+T cell to HIV infection and the formation of latent infection. We suggest a class of HIV latency mathematical model, integrating both cell-free virus transmission and direct cell-to-cell diffusion to improve the understanding of the dynamics of the latent reservoirs. We incorporate four components in our model: the uninfected T cells, the latently infected T cells, the active-infected T cells and the HIV viruses. We examine the latency model by introducing the basic reproduction number. We first establish the non-negativity and boundedness of the solutions of the system, and then we investigate the global stability of the steady states. The diseased-free equilibrium is globally stable when the basic reproduction number is less than 1 and if the basic reproduction number is greater than 1, the diseased equilibrium exists and is globally stable. Numerical simulations are executed to interpret the theoretical outcomes and evaluate the relative contribution of latency fractions in the virus production and the HIV latent reservoir by providing estimates.

Published in	Applied and Computational Mathematics (Volume 10, Issue 4)
DOI	10.11648/j.acm.20211004.12
Page(s)	91-99
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

HIV, Infected Latent Cells, Virus Intracellular Transmission, Global Stability

References

[1]	Agosto, L. M., Zhong, P., Munro, J., and Mothes. Highly active antiretroviral therapies are effective against HIV-1 cell-to-cell transmission. PLoS Pathog. 10 (2014), e1003982.
[2]	Agosto, L. M., Herring, M. B., Mothes, W., and Henderson, A. J. HIV-1-infected CD4+ T cells facilitate latent infection of resting CD4+ T cells through cell-cell contact. Cell Rep. 24 (2018), 2088-2100.
[3]	Sattentau, Q. Avoiding the void: cell-to-cell spread of human viruses. Nat. Rev. Microbiol. 6 (2008), 815-826.
[4]	Sigal, A., Kim, J. T., Balazs, A. B., Dekel, E., Mayo, A., Milo, R., and Baltimore, D. Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy. Nature. 477 (2011), 95-98.
[5]	Brimacombe, C. L., Grove, J., Meredith, L. W., Hu, K., Syder, A. J., Flores, M. V., Timpe, J. M., Krieger, S. E., Baumert, T. F., Tellinghuisen, T. L., and Wong-Staal F. Neutralizing antibody-resistant hepatitis C virus cell-to-cell transmission. J. Virol. 85 (2011), 596-605.
[6]	Chen, P., Hubner, W., Spinelli, M. A., and Chen, B. K. Predominant mode of human immunodeficiency virus transfer between T cells is mediated by sustained Env-dependent neutralization-resistant virological synapses. J. Virol. 81 (2007), 12582-12595.
[7]	Sato, H., Orensteint, J., Dimitrov, D., and Martin, M. Cell-to-cell spread of HIV-1 occurs within minutes and may not involve the participation of virus particles. Virology. 186 (1992), 712-724.
[8]	Johnson, D. C., and Huber, M. T. Directed egress of animal viruses promotes cell-to-cell spread. J. Virol. 76 (2002), 1-8.
[9]	Jolly, C., Kashe_, K., Hollinshead, M., and Sattentau, Q. J. HIV-1 cell to cell transfer across an Env-induced, actin-dependent synapse. J. Exp. Med. 199 (2004), 283-293.
[10]	Phillips, D. M. The role of cell-to-cell transmission in HIV infection. AIDS. 8 (1994), 719-732.
[11]	Del Portillo, A., Tripodi, J., Najfeld, V., Wodarz, D., Levy, D. N., and Chen, B. K. Multiploid inheritance of HIV-1 during cell-to-cell infection. J. Virol. 85 (2011), 7169-7176.
[12]	Iwami, S., Takeuchi, J. S., Nakaoka, S., Mammano, F., Clavel, F., Inaba, H., Kobayashi, T., Misawa, N., Aihara, K., Koyanagi, Y., and Sato, K. Cell-to-cell infection by HIV contributes over half of virus infection. Elife. 4 (2015), e08150.
[13]	Komarova, N. L., Anghelina, D., Voznesensky, I., Trinitie, B., Levy, D. N., and Wodarz, D. Relative contribution of free-virus and synaptic transmission to the spread of HIV-1 through target cell populations. Biol. Lett. 9 (2012), DOI: 10.1098/rsbl.2012.1049.
[14]	Komarova, N. L., Levy, D. N., and Wodarz, D. Synaptic transmission and the susceptibility of HIV infection to anti-viral drugs. Sci. Rep. 3 (2013), DOI: 10.1038/srep02103.
[15]	Komarova, N. L., Levy, D. N., and Wodarz, D. Effect of synaptic transmission on viral fitness in HIV infection. PloS one. 7 (2012), e48361.
[16]	Komarova, N. L., and Wodarz, D. Virus dynamics in the presence of synaptic transmission. Math. Biosci. 242 (2013), 161-171.
[17]	Pourbashash, H., Pilyugin, S. S., De Leenheer, P., and McCluskey, C. Global analysis of within host virus models with cell-to-cell viral transmission. Discrete Contin. Dyn. Syst. Ser. B 19 (2014), 3341-3357.
[18]	Yang, Y., Zou, L., and Ruan, S. Global dynamics of a delayed within-host viral infection model with both virus-to-cell and cell-to-cell transmissions. Math. Biosci. 270 (2015), 183-191.
[19]	Guo, T., Qiu, Z., and Rong, L. Analysis of an HIV model with immune responses and cell-to-cell transmission. Bull. Malaysian Math. Sci. Society. 43 (2020), 581-607.
[20]	Lai, X., and Zou, X. Modeling HIV-1 virus dynamics with both virus-to-cell infection and cell-to-cell transmission. SIAM J. Appl. Math. 74 (2014), 898-917.
[21]	Lai, X., and Zou, X. Modeling cell-to-cell spread of HIV-1 with logistic target cell growth. J. Math. Anal. Appl. 426 (2015), 563-584.
[22]	Finzi, D., Hermankova, M., Pierson, T., Carruth, L. M., Buck, C., Chaisson, R. E., Gallant, J., et al. Identification of a reservoir for HIV-1 in patients on highly active antiretroviral therapy. Science. 278 (1997), 1295-1300.
[23]	Ruelas, D. S., and Greene, W. C. An integrated overview of HIV-1 latency. Cell. 155 (2013), 519-529.
[24]	Strain, M. C., Gunthard, H. F., Havlir, D. V., Ignacio, C. C., Smith, D. M., Leigh-Brown, A. J., Opravil, M., et. al. Heterogeneous clearance rates of long-lived lymphocytes infected with HIV: intrinsic stability predicts lifelong persistence. Proc. Natl. Acad. Sci. 100 (2003), 4819-4824.
[25]	Chun, T. W., Carruth, L., Finzi, D., Shen, X., DiGiuseppe, J. A., Taylor, H., Kuo, Y. H., et al. Quantification of latent tissue reservoirs and total body viral load in HIV-1 infection. Nature. 387 (1997), 183-188.
[26]	Douek, D. C., Brenchley, J. M., Betts, M. R., Ambrozak, D. R., Hill, B. J., Okamoto, Y., Grossman, Z., et. al. HIV preferentially infects HIV-specific CD4+ T cells. Nature. 417 (2002), 95-98.
[27]	Maldarelli, F., Wu, X., Su, L., Simonetti, F. R., Shao, W., Hill, S., Coffin, J. M., et. al. Specific HIV integration sites are linked to clonal expansion and persistence of infected cells. Science. 345 (2014), 179-183.
[28]	Alshorman, A., Wang, X., Joseph Meyer, M., and Rong, L. Analysis of HIV models with two time delays. J. Biol. Dyn. 11 (2017), 40-64.
[29]	Diekmann, O., Heesterbeek, J. A. P., and Metz, J. A. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28 (1990), 365-382.
[30]	Van den Driessche, P., and Watmough, J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002), 29-48.
[31]	Perelson, A. S., Essunger, P., Cao, Y., Vesanen, M., Hurley, A., Saksela, K., Ho, D. D., et. al. Decay characteristics of HIV-1 infected compartments during combination therapy. Nature. 387 (1997), 188-191.
[32]	Perelson, A. S., and Nelson, P. W. Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41 (1999), 3-44.
[33]	Perelson, A. S., Neumann, A. U., Markowitz, M., Leonard, J. M., and Ho, D. D. HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time. Science. 271 (1996), 1582-1586.
[34]	James D. Murray. Mathematical Biology. Springer, New York, (1989).
[35]	Martin Nowak, Robert May Baron. Virus Dynamics. Oxford University Press, New York, (2000).
[36]	Pankavich, S. The effects of latent infection on the dynamics of HIV. Diff. Eq. Dyn. Sys. 24 (2016), 281-303.
[37]	Sattentau, Q. J. Cell-to-cell spread of retroviruses. Viruses. 2 (2010), 1306-1321.
[38]	Sattentau, Q. J. The direct passage of animal viruses between cells. Curr. Opin. Virol. 1 (2011), 396-402.
[39]	Rong, L., Feng, Z., and Perelson, A. S. Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy. SIAM J. Appl. Math. 67 (2007), 731-756.
[40]	Rong, L., Feng, Z., and Perelson, A. S. Emergence of HIV-1 drug resistance during antiretroviral treatment. Bull. Math. Biol. 69 (2007), 2027-2060.
[41]	Rong, L., and Perelson, A. S. Modeling HIV persistence, the latent reservoir, and viral blips. J. Theoret. Biol. 260 (2009), 308-331.
[42]	Rong, L., and Perelson, A. S. 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), e1000533.
[43]	Rong, L., and Perelson, A. S. 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.
[44]	La Salle, J. P. The stability of dynamical systems. SIAM. (1976).
[45]	Zhong, P., Agosto, L. M., Munro, J. B., and Mothes, W. Cell-to-cell transmission of viruses. Curr. Opin Virol. 3 (2013), 44-50.
[46]	Wen, Q., and Lou, J. The global dynamics of a model about HIV-1 infection in vivo. Ricerche di matematica. 58 (2009), 77-90.
[47]	Callaway, S., and Perelson, A. S. HIV-1 infection and low steady state viral loads. Bull. Math. Biol. 64 (2002), 29-64.
[48]	Mojaver, A. and Kheiri, H. Mathematical analysis of a class of HIV infection models of CD4+ T-cells with combined antiretroviral therapy. Appl. Math. Comp. 259 (2015), 258-270.
[49]	Jones, E. and Perelson, A. S. Transient viremia, plasma viral load, and reservoir replenishment in HIV-infected patients on antiretroviral therapy. Def. Synd. 45 (2007), 483-493.
[50]	Barouch, D. H., and Deeks, S. G. Immunologic strategies for HIV-1 remission and eradication. Science. 345 (2014), 169-174.

Cite This Article

Plain Text BibTeX RIS

APA Style

Wajahat Ali, Zhipeng Qiu. (2021). The Global Dynamics of HIV Latency Model Including Cell-to-Cell Viral Transmission. Applied and Computational Mathematics, 10(4), 91-99. https://doi.org/10.11648/j.acm.20211004.12

Copy | Download

ACS Style

Wajahat Ali; Zhipeng Qiu. The Global Dynamics of HIV Latency Model Including Cell-to-Cell Viral Transmission. Appl. Comput. Math. 2021, 10(4), 91-99. doi: 10.11648/j.acm.20211004.12

Copy | Download

AMA Style

Wajahat Ali, Zhipeng Qiu. The Global Dynamics of HIV Latency Model Including Cell-to-Cell Viral Transmission. Appl Comput Math. 2021;10(4):91-99. doi: 10.11648/j.acm.20211004.12

Copy | Download

@article{10.11648/j.acm.20211004.12,
  author = {Wajahat Ali and Zhipeng Qiu},
  title = {The Global Dynamics of HIV Latency Model Including Cell-to-Cell Viral Transmission},
  journal = {Applied and Computational Mathematics},
  volume = {10},
  number = {4},
  pages = {91-99},
  doi = {10.11648/j.acm.20211004.12},
  url = {https://doi.org/10.11648/j.acm.20211004.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20211004.12},
  abstract = {HIV spreads by cell-to-cell transfer and the release of cell-free particles. A slightly more effective method of retroviral transmission is the direct cell-to-cell transfer of HIV, according to recent reports. Intracellular interaction between unhealthy and healthy cells, in combination with cytokine discharged by the cells included, may affect the susceptibility of a target resting CD4+T cell to HIV infection and the formation of latent infection. We suggest a class of HIV latency mathematical model, integrating both cell-free virus transmission and direct cell-to-cell diffusion to improve the understanding of the dynamics of the latent reservoirs. We incorporate four components in our model: the uninfected T cells, the latently infected T cells, the active-infected T cells and the HIV viruses. We examine the latency model by introducing the basic reproduction number. We first establish the non-negativity and boundedness of the solutions of the system, and then we investigate the global stability of the steady states. The diseased-free equilibrium is globally stable when the basic reproduction number is less than 1 and if the basic reproduction number is greater than 1, the diseased equilibrium exists and is globally stable. Numerical simulations are executed to interpret the theoretical outcomes and evaluate the relative contribution of latency fractions in the virus production and the HIV latent reservoir by providing estimates.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - The Global Dynamics of HIV Latency Model Including Cell-to-Cell Viral Transmission
AU  - Wajahat Ali
AU  - Zhipeng Qiu
Y1  - 2021/07/09
PY  - 2021
N1  - https://doi.org/10.11648/j.acm.20211004.12
DO  - 10.11648/j.acm.20211004.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 91
EP  - 99
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20211004.12
AB  - HIV spreads by cell-to-cell transfer and the release of cell-free particles. A slightly more effective method of retroviral transmission is the direct cell-to-cell transfer of HIV, according to recent reports. Intracellular interaction between unhealthy and healthy cells, in combination with cytokine discharged by the cells included, may affect the susceptibility of a target resting CD4+T cell to HIV infection and the formation of latent infection. We suggest a class of HIV latency mathematical model, integrating both cell-free virus transmission and direct cell-to-cell diffusion to improve the understanding of the dynamics of the latent reservoirs. We incorporate four components in our model: the uninfected T cells, the latently infected T cells, the active-infected T cells and the HIV viruses. We examine the latency model by introducing the basic reproduction number. We first establish the non-negativity and boundedness of the solutions of the system, and then we investigate the global stability of the steady states. The diseased-free equilibrium is globally stable when the basic reproduction number is less than 1 and if the basic reproduction number is greater than 1, the diseased equilibrium exists and is globally stable. Numerical simulations are executed to interpret the theoretical outcomes and evaluate the relative contribution of latency fractions in the virus production and the HIV latent reservoir by providing estimates.
VL  - 10
IS  - 4
ER  -

Copy | Download

Author Information

Wajahat Ali

School of Science, Nanjing University of Science and Technology, Nanjing, China
Zhipeng Qiu

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Wajahat Ali, Zhipeng Qiu. (2021). The Global Dynamics of HIV Latency Model Including Cell-to-Cell Viral Transmission. Applied and Computational Mathematics, 10(4), 91-99. https://doi.org/10.11648/j.acm.20211004.12

Copy | Download

ACS Style

Wajahat Ali; Zhipeng Qiu. The Global Dynamics of HIV Latency Model Including Cell-to-Cell Viral Transmission. Appl. Comput. Math. 2021, 10(4), 91-99. doi: 10.11648/j.acm.20211004.12

Copy | Download

AMA Style

Wajahat Ali, Zhipeng Qiu. The Global Dynamics of HIV Latency Model Including Cell-to-Cell Viral Transmission. Appl Comput Math. 2021;10(4):91-99. doi: 10.11648/j.acm.20211004.12

Copy | Download

@article{10.11648/j.acm.20211004.12,
  author = {Wajahat Ali and Zhipeng Qiu},
  title = {The Global Dynamics of HIV Latency Model Including Cell-to-Cell Viral Transmission},
  journal = {Applied and Computational Mathematics},
  volume = {10},
  number = {4},
  pages = {91-99},
  doi = {10.11648/j.acm.20211004.12},
  url = {https://doi.org/10.11648/j.acm.20211004.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20211004.12},
  abstract = {HIV spreads by cell-to-cell transfer and the release of cell-free particles. A slightly more effective method of retroviral transmission is the direct cell-to-cell transfer of HIV, according to recent reports. Intracellular interaction between unhealthy and healthy cells, in combination with cytokine discharged by the cells included, may affect the susceptibility of a target resting CD4+T cell to HIV infection and the formation of latent infection. We suggest a class of HIV latency mathematical model, integrating both cell-free virus transmission and direct cell-to-cell diffusion to improve the understanding of the dynamics of the latent reservoirs. We incorporate four components in our model: the uninfected T cells, the latently infected T cells, the active-infected T cells and the HIV viruses. We examine the latency model by introducing the basic reproduction number. We first establish the non-negativity and boundedness of the solutions of the system, and then we investigate the global stability of the steady states. The diseased-free equilibrium is globally stable when the basic reproduction number is less than 1 and if the basic reproduction number is greater than 1, the diseased equilibrium exists and is globally stable. Numerical simulations are executed to interpret the theoretical outcomes and evaluate the relative contribution of latency fractions in the virus production and the HIV latent reservoir by providing estimates.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - The Global Dynamics of HIV Latency Model Including Cell-to-Cell Viral Transmission
AU  - Wajahat Ali
AU  - Zhipeng Qiu
Y1  - 2021/07/09
PY  - 2021
N1  - https://doi.org/10.11648/j.acm.20211004.12
DO  - 10.11648/j.acm.20211004.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 91
EP  - 99
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20211004.12
AB  - HIV spreads by cell-to-cell transfer and the release of cell-free particles. A slightly more effective method of retroviral transmission is the direct cell-to-cell transfer of HIV, according to recent reports. Intracellular interaction between unhealthy and healthy cells, in combination with cytokine discharged by the cells included, may affect the susceptibility of a target resting CD4+T cell to HIV infection and the formation of latent infection. We suggest a class of HIV latency mathematical model, integrating both cell-free virus transmission and direct cell-to-cell diffusion to improve the understanding of the dynamics of the latent reservoirs. We incorporate four components in our model: the uninfected T cells, the latently infected T cells, the active-infected T cells and the HIV viruses. We examine the latency model by introducing the basic reproduction number. We first establish the non-negativity and boundedness of the solutions of the system, and then we investigate the global stability of the steady states. The diseased-free equilibrium is globally stable when the basic reproduction number is less than 1 and if the basic reproduction number is greater than 1, the diseased equilibrium exists and is globally stable. Numerical simulations are executed to interpret the theoretical outcomes and evaluate the relative contribution of latency fractions in the virus production and the HIV latent reservoir by providing estimates.
VL  - 10
IS  - 4
ER  -

Copy | Download