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

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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

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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), 2021. Published by Science Publishing Group

Keywords

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

References

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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

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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

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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

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@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}
}

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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  -

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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

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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

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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

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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

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@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