Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics

Bassey Echeng Bassey; Adagba Odey Henry

doi:doi:10.11648/j.pamj.20211001.12

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Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics

Bassey Echeng Bassey, Adagba Odey Henry

Published in Pure and Applied Mathematics Journal (Volume 10, Issue 1)

Received: 24 December 2020 Accepted: 20 February 2021 Published: 4 March 2021

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Abstract

Devastatingly, in spite of the long standing research works on HIV/AIDS infection and treatment dynamics, reviews of existing models clearly shown that the behavioral attitude to treatment consistency by those screened to become aware and those receiving treatment have not been given the desired attention. Moreso, the inconsistency following avoidable treatment truncation and later resumption of treatment by these classes of infectives, which could lead to colossal drug abuse is also not accorded the much expected consideration. Therefore, in this present study, we sought and formulated a nonlinear 6-Dimensional deterministic mathematical HIV/AIDS dynamic model that accounted for the global stability analysis of the role of antiretroviral therapy abuse for the treatment of HIV/AIDS epidemic. The model is structured upon dynamical interactions between 6-subpopulations and HI-virus under bilinear control functions with constant screening of the susceptible. It is assumed that the rate of resumption of ART upon truncation is less than initial ART truncation following the incorporation of HIV aware infectives not ready to receive ART treatment and HIV aware infectives with truncated treatment protocol The system mathematical well-posedness was investigated and model reproduction number determined for both off- treatment (with value ) and for onset-treatment (with value ). We considered the model for off-treatment and thereafter by incorporating LaSalle’s invariant principle into classical Lyapunov function method, we presented an approach for the global stability analysis of the role of ART abuse in HIV/AIDS treatment. Furthermore, the analysis and results of this paper presented a dynamic methodological application of bilinear control functions and an impeccable understanding of the fundamental mechanism in HIV/AIDS treatment in the presence of ART abuse. Using in-built Runge-Kutta of order of precision 4 in a Mathcad surface, numerical validity of model is conducted to investigate the study theoretical and analytical predictions. Results shows that application of onset-treatment functions with trend of ART abuse yield tremendous reduction in HIV/AIDS infection epidemic following the recovery rate of the susceptible population with value increasing from 0.5 cells/mm³ to 1.203 cells/mm³ within the first months and attained stability of 0.62 cells/mm³ through the time interval of 20- 30 months.

Published in	Pure and Applied Mathematics Journal (Volume 10, Issue 1)
DOI	10.11648/j.pamj.20211001.12
Page(s)	9-31
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

Antiretroviral-Therapy-abuse, Global-Stability-Conditions, Lyapunov-Function, Bilinear-Control-Functions, Upper-Triangular-Matrix, Mass-Action, Theoretical Predictions, Analytical Results

References

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APA Style

Bassey Echeng Bassey, Adagba Odey Henry. (2021). Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics. Pure and Applied Mathematics Journal, 10(1), 9-31. https://doi.org/10.11648/j.pamj.20211001.12

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ACS Style

Bassey Echeng Bassey; Adagba Odey Henry. Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics. Pure Appl. Math. J. 2021, 10(1), 9-31. doi: 10.11648/j.pamj.20211001.12

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AMA Style

Bassey Echeng Bassey, Adagba Odey Henry. Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics. Pure Appl Math J. 2021;10(1):9-31. doi: 10.11648/j.pamj.20211001.12

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@article{10.11648/j.pamj.20211001.12,
  author = {Bassey Echeng Bassey and Adagba Odey Henry},
  title = {Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics},
  journal = {Pure and Applied Mathematics Journal},
  volume = {10},
  number = {1},
  pages = {9-31},
  doi = {10.11648/j.pamj.20211001.12},
  url = {https://doi.org/10.11648/j.pamj.20211001.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20211001.12},
  abstract = {Devastatingly, in spite of the long standing research works on HIV/AIDS infection and treatment dynamics, reviews of existing models clearly shown that the behavioral attitude to treatment consistency by those screened to become aware and those receiving treatment have not been given the desired attention. Moreso, the inconsistency following avoidable treatment truncation and later resumption of treatment by these classes of infectives, which could lead to colossal drug abuse is also not accorded the much expected consideration. Therefore, in this present study, we sought and formulated a nonlinear 6-Dimensional deterministic mathematical HIV/AIDS dynamic model that accounted for the global stability analysis of the role of antiretroviral therapy abuse for the treatment of HIV/AIDS epidemic. The model is structured upon dynamical interactions between 6-subpopulations and HI-virus under bilinear control functions with constant screening of the susceptible. It is assumed that the rate of resumption of ART upon truncation is less than initial ART truncation following the incorporation of HIV aware infectives not ready to receive ART treatment and HIV aware infectives with truncated treatment protocol The system mathematical well-posedness was investigated and model reproduction number determined for both off- treatment (with value ) and for onset-treatment (with value ). We considered the model for off-treatment and thereafter by incorporating LaSalle’s invariant principle into classical Lyapunov function method, we presented an approach for the global stability analysis of the role of ART abuse in HIV/AIDS treatment. Furthermore, the analysis and results of this paper presented a dynamic methodological application of bilinear control functions and an impeccable understanding of the fundamental mechanism in HIV/AIDS treatment in the presence of ART abuse. Using in-built Runge-Kutta of order of precision 4 in a Mathcad surface, numerical validity of model is conducted to investigate the study theoretical and analytical predictions. Results shows that application of onset-treatment functions with trend of ART abuse yield tremendous reduction in HIV/AIDS infection epidemic following the recovery rate of the susceptible population with value increasing from 0.5 cells/mm3 to 1.203 cells/mm3 within the first  months and attained stability of 0.62 cells/mm3 through the time interval of 20- 30 months.},
 year = {2021}
}

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TY  - JOUR
T1  - Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics
AU  - Bassey Echeng Bassey
AU  - Adagba Odey Henry
Y1  - 2021/03/04
PY  - 2021
N1  - https://doi.org/10.11648/j.pamj.20211001.12
DO  - 10.11648/j.pamj.20211001.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 9
EP  - 31
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20211001.12
AB  - Devastatingly, in spite of the long standing research works on HIV/AIDS infection and treatment dynamics, reviews of existing models clearly shown that the behavioral attitude to treatment consistency by those screened to become aware and those receiving treatment have not been given the desired attention. Moreso, the inconsistency following avoidable treatment truncation and later resumption of treatment by these classes of infectives, which could lead to colossal drug abuse is also not accorded the much expected consideration. Therefore, in this present study, we sought and formulated a nonlinear 6-Dimensional deterministic mathematical HIV/AIDS dynamic model that accounted for the global stability analysis of the role of antiretroviral therapy abuse for the treatment of HIV/AIDS epidemic. The model is structured upon dynamical interactions between 6-subpopulations and HI-virus under bilinear control functions with constant screening of the susceptible. It is assumed that the rate of resumption of ART upon truncation is less than initial ART truncation following the incorporation of HIV aware infectives not ready to receive ART treatment and HIV aware infectives with truncated treatment protocol The system mathematical well-posedness was investigated and model reproduction number determined for both off- treatment (with value ) and for onset-treatment (with value ). We considered the model for off-treatment and thereafter by incorporating LaSalle’s invariant principle into classical Lyapunov function method, we presented an approach for the global stability analysis of the role of ART abuse in HIV/AIDS treatment. Furthermore, the analysis and results of this paper presented a dynamic methodological application of bilinear control functions and an impeccable understanding of the fundamental mechanism in HIV/AIDS treatment in the presence of ART abuse. Using in-built Runge-Kutta of order of precision 4 in a Mathcad surface, numerical validity of model is conducted to investigate the study theoretical and analytical predictions. Results shows that application of onset-treatment functions with trend of ART abuse yield tremendous reduction in HIV/AIDS infection epidemic following the recovery rate of the susceptible population with value increasing from 0.5 cells/mm3 to 1.203 cells/mm3 within the first  months and attained stability of 0.62 cells/mm3 through the time interval of 20- 30 months.
VL  - 10
IS  - 1
ER  -

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Author Information

Bassey Echeng Bassey

Department of Industrial Mathematics and Applied Statistics, Ebonyi State University, Abakaliki, Nigeria
Adagba Odey Henry

Department of Industrial Mathematics and Applied Statistics, Ebonyi State University, Abakaliki, Nigeria

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Bassey Echeng Bassey, Adagba Odey Henry. (2021). Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics. Pure and Applied Mathematics Journal, 10(1), 9-31. https://doi.org/10.11648/j.pamj.20211001.12

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ACS Style

Bassey Echeng Bassey; Adagba Odey Henry. Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics. Pure Appl. Math. J. 2021, 10(1), 9-31. doi: 10.11648/j.pamj.20211001.12

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AMA Style

Bassey Echeng Bassey, Adagba Odey Henry. Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics. Pure Appl Math J. 2021;10(1):9-31. doi: 10.11648/j.pamj.20211001.12

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@article{10.11648/j.pamj.20211001.12,
  author = {Bassey Echeng Bassey and Adagba Odey Henry},
  title = {Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics},
  journal = {Pure and Applied Mathematics Journal},
  volume = {10},
  number = {1},
  pages = {9-31},
  doi = {10.11648/j.pamj.20211001.12},
  url = {https://doi.org/10.11648/j.pamj.20211001.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20211001.12},
  abstract = {Devastatingly, in spite of the long standing research works on HIV/AIDS infection and treatment dynamics, reviews of existing models clearly shown that the behavioral attitude to treatment consistency by those screened to become aware and those receiving treatment have not been given the desired attention. Moreso, the inconsistency following avoidable treatment truncation and later resumption of treatment by these classes of infectives, which could lead to colossal drug abuse is also not accorded the much expected consideration. Therefore, in this present study, we sought and formulated a nonlinear 6-Dimensional deterministic mathematical HIV/AIDS dynamic model that accounted for the global stability analysis of the role of antiretroviral therapy abuse for the treatment of HIV/AIDS epidemic. The model is structured upon dynamical interactions between 6-subpopulations and HI-virus under bilinear control functions with constant screening of the susceptible. It is assumed that the rate of resumption of ART upon truncation is less than initial ART truncation following the incorporation of HIV aware infectives not ready to receive ART treatment and HIV aware infectives with truncated treatment protocol The system mathematical well-posedness was investigated and model reproduction number determined for both off- treatment (with value ) and for onset-treatment (with value ). We considered the model for off-treatment and thereafter by incorporating LaSalle’s invariant principle into classical Lyapunov function method, we presented an approach for the global stability analysis of the role of ART abuse in HIV/AIDS treatment. Furthermore, the analysis and results of this paper presented a dynamic methodological application of bilinear control functions and an impeccable understanding of the fundamental mechanism in HIV/AIDS treatment in the presence of ART abuse. Using in-built Runge-Kutta of order of precision 4 in a Mathcad surface, numerical validity of model is conducted to investigate the study theoretical and analytical predictions. Results shows that application of onset-treatment functions with trend of ART abuse yield tremendous reduction in HIV/AIDS infection epidemic following the recovery rate of the susceptible population with value increasing from 0.5 cells/mm3 to 1.203 cells/mm3 within the first  months and attained stability of 0.62 cells/mm3 through the time interval of 20- 30 months.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics
AU  - Bassey Echeng Bassey
AU  - Adagba Odey Henry
Y1  - 2021/03/04
PY  - 2021
N1  - https://doi.org/10.11648/j.pamj.20211001.12
DO  - 10.11648/j.pamj.20211001.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 9
EP  - 31
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20211001.12
AB  - Devastatingly, in spite of the long standing research works on HIV/AIDS infection and treatment dynamics, reviews of existing models clearly shown that the behavioral attitude to treatment consistency by those screened to become aware and those receiving treatment have not been given the desired attention. Moreso, the inconsistency following avoidable treatment truncation and later resumption of treatment by these classes of infectives, which could lead to colossal drug abuse is also not accorded the much expected consideration. Therefore, in this present study, we sought and formulated a nonlinear 6-Dimensional deterministic mathematical HIV/AIDS dynamic model that accounted for the global stability analysis of the role of antiretroviral therapy abuse for the treatment of HIV/AIDS epidemic. The model is structured upon dynamical interactions between 6-subpopulations and HI-virus under bilinear control functions with constant screening of the susceptible. It is assumed that the rate of resumption of ART upon truncation is less than initial ART truncation following the incorporation of HIV aware infectives not ready to receive ART treatment and HIV aware infectives with truncated treatment protocol The system mathematical well-posedness was investigated and model reproduction number determined for both off- treatment (with value ) and for onset-treatment (with value ). We considered the model for off-treatment and thereafter by incorporating LaSalle’s invariant principle into classical Lyapunov function method, we presented an approach for the global stability analysis of the role of ART abuse in HIV/AIDS treatment. Furthermore, the analysis and results of this paper presented a dynamic methodological application of bilinear control functions and an impeccable understanding of the fundamental mechanism in HIV/AIDS treatment in the presence of ART abuse. Using in-built Runge-Kutta of order of precision 4 in a Mathcad surface, numerical validity of model is conducted to investigate the study theoretical and analytical predictions. Results shows that application of onset-treatment functions with trend of ART abuse yield tremendous reduction in HIV/AIDS infection epidemic following the recovery rate of the susceptible population with value increasing from 0.5 cells/mm3 to 1.203 cells/mm3 within the first  months and attained stability of 0.62 cells/mm3 through the time interval of 20- 30 months.
VL  - 10
IS  - 1
ER  -

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