A Mathematical Model Analysis for the Transmission Dynamics of HIV/AIDS with Control Strategy

Bogale Assefa Belayneh; Purnachandra Rao Koya

doi:doi:10.11648/j.mma.20210603.11

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A Mathematical Model Analysis for the Transmission Dynamics of HIV/AIDS with Control Strategy

Bogale Assefa Belayneh, Purnachandra Rao Koya

Published in Mathematical Modelling and Applications (Volume 6, Issue 3)

Received: 30 July 2021 Accepted: 13 August 2021 Published: 23 August 2021

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Abstract

This paper examines the transmission dynamics of HIV infection with public health intervention strategies treatment and awareness on the proper procedure of ART treatment. For the problem, a deterministic mathematical model is proposed and analysed qualitatively using the concept of stability of differential equations. The effective reproduction number is computed in terms of model parameters. The existence and stability of disease free and endemic steady states are recognized. The disease free and endemic equilibria are indicated to be locally and globally asymptotically stable whenever the effective reproduction number is less than unity and greater than unity respectively. This means that, HIV infection will die out in the community when the effective reproduction number is less than the threshold value and persist otherwise. Based on the sensitivity analysis of the effective reproduction number, we found that the rate of ART treatment and the rate of awareness on the proper procedure of ART are influential in reducing the magnitude of the reproduction number and thus they are important in decreasing the number of infected population. Numerical simulations support our analytical results that implementing ART treatment at every stage of HIV/AIDS had high impact in reducing the infected population than implementing on a single stage for those who follow the proper procedure of ART treatment. It also verifies the positive impact of awareness on the proper procedure of ART treatment in reducing infected individuals by reducing treatment waning rate. Therefore, our result suggests that ART treatment should be implemented together with awareness on the proper procedure of ART treatment to control the spread of HIV in the community.

Published in	Mathematical Modelling and Applications (Volume 6, Issue 3)
DOI	10.11648/j.mma.20210603.11
Page(s)	56-69
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

Antiretroviral Treatment, HIV/AIDS Dynamics, Horizontal Transmission, Reproduction Number, Stability

References

[1]	Alexander Kramer et al. Modern Infectious Disease Epidemiology. Springer Science+Business Media, LLC 2010.
[2]	FMoH, November 2018. Guideline for HIV CARE/ART clinical mentoring in Ethiopia. (http://www.afro.who).
[3]	Kathleen M. MacQueen Division of HIV/AIDS, National Center. (1994). The epidemiology of HIV Transmission: Trends, Structure and Dynamics. Annual Review of Anthropology, Vol. 23, pp. 509-526.
[4]	Maimunah, Dipo Aldila. (2018). Mathematical model for HIV spreads control program with ART treatment. Journal of Physics: Conf. Series 974 (2018) 012035.
[5]	S. Mushayabasa, C. P. BhunuIs. (2012). HIV infection associated with an increased risk for cholera? Insights from a mathematical model. BioSystems 109 (2012) 203–213AL.
[6]	A Cristiana J. Silva and Delfim F. M. Torres. (2015). A TB-HIV/AIDS Coinfection model and optimal control treatment. Department of Mathematics, University of Aveiro, 3810- 193 Aveiro, Portugal.
[7]	AAM Arafa, SZ Rida and Khalil. (2012). Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection. Nonlinear Biomedical Physics 2012, 6: 1.
[8]	Ofosuhene O. Apenteng; Noor Azina Ismail. (2019). Modelling the impact of migration on HIV persistency in Ghana. Statistics, Optimization and Information Computing, 7 (1), 55-65.
[9]	Rebecca V. Culshaw, Ph.D. Mathematical Modeling of AIDS Progression: Limitations, Expectations, and Future Directions. Journal of American Physicians and Surgeons. Volume 11 Number 4 Winter 2006.
[10]	Susan Cassels, PhD et al. (2008). Mathematical Models for HIV Transmission Dynamics: Tools for Social and Behavioral Science Research. J Acquir Immune Defic Syndr. 2008 March 1; 47 (Suppl 1): S34–S39.
[11]	Abdallah S. Waziri, Estomih S. Massawe, Oluwole Daniel Makinde. (2012). Mathematical Modelling of HIV/AIDS Dynamics with Treatment and Vertical Transmission. Applied Mathematics 2012. 2 (3): 77-89.
[12]	Epidemiology of HIV/AIDS. (En.wikipedia.org/wiki/Epidemiolog _of HIV/AIDS).
[13]	Epidemiology of HIV/AIDS. (En.wikipedia.org/wiki/HIV/AIDS in Africa).
[14]	Timothy L. Mah, Daniel T. Halperin. (2008). Concurrent Sexual Partnerships and the HIV Epidemics in Africa: Evidence to Move Forward. AIDS Behav (2010) 14: 11–16.
[15]	UNAIDS. 2017, Joint United Nations Programme on HIV/AIDS.
[16]	WANG Jun-jie Kathleen Heather Reilly, LUO Jing, WANG Ning. (2010). Dynamic mathematical models of HIV/AIDS transmission in China. Chin Med J (Engl). 123 (15): 2120-21272.
[17]	FMOH. November, 2018. HIV prevention in Ethiopia National Road Map 2018-2020.
[18]	FMOH. August, 2018, National Consolidated guidelines for comprehensive HIV prevention, care and treatment.
[19]	Fatmawati and Hengki Tasman. (2016). An Optimal Treatment Control of TB-HIV Coinfection. International Journal of Mathematics and Mathematical Sciences Volume 2016, Article ID 8261208, 11 pages.
[20]	K. O. Okosun, O. D. Makinde, I. Takaidza. (2012). Impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives. Applied Mathematical Modelling 37 (2013) 3802–3820.
[21]	Oluwaseun Sharomi, Chandra N. Podder, Abba B. Gumel. (2008). Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment. Mathematical biosciences and engineering, Volume 5, pp. 145–174 D (9).
[22]	Zohragul Osman, Xamxinur Abdurahman. (2015). Stability Analysis of a Delayed HIV/AIDS Epidemic Model with Treatment and Vertical Transmission.
[23]	Carlos Castillo-Chavez Zhilan Feng and Wenzhang Huang. (2001). On the computation of Ro and its role on global stability. N-1553 (607) 255-8103.

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APA Style

Bogale Assefa Belayneh, Purnachandra Rao Koya. (2021). A Mathematical Model Analysis for the Transmission Dynamics of HIV/AIDS with Control Strategy. Mathematical Modelling and Applications, 6(3), 56-69. https://doi.org/10.11648/j.mma.20210603.11

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ACS Style

Bogale Assefa Belayneh; Purnachandra Rao Koya. A Mathematical Model Analysis for the Transmission Dynamics of HIV/AIDS with Control Strategy. Math. Model. Appl. 2021, 6(3), 56-69. doi: 10.11648/j.mma.20210603.11

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AMA Style

Bogale Assefa Belayneh, Purnachandra Rao Koya. A Mathematical Model Analysis for the Transmission Dynamics of HIV/AIDS with Control Strategy. Math Model Appl. 2021;6(3):56-69. doi: 10.11648/j.mma.20210603.11

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@article{10.11648/j.mma.20210603.11,
  author = {Bogale Assefa Belayneh and Purnachandra Rao Koya},
  title = {A Mathematical Model Analysis for the Transmission Dynamics of HIV/AIDS with Control Strategy},
  journal = {Mathematical Modelling and Applications},
  volume = {6},
  number = {3},
  pages = {56-69},
  doi = {10.11648/j.mma.20210603.11},
  url = {https://doi.org/10.11648/j.mma.20210603.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20210603.11},
  abstract = {This paper examines the transmission dynamics of HIV infection with public health intervention strategies treatment and awareness on the proper procedure of ART treatment. For the problem, a deterministic mathematical model is proposed and analysed qualitatively using the concept of stability of differential equations. The effective reproduction number is computed in terms of model parameters. The existence and stability of disease free and endemic steady states are recognized.  The disease free and endemic equilibria are indicated to be locally and globally asymptotically stable whenever the effective reproduction number is less than unity and greater than unity respectively. This means that, HIV infection will die out in the community when the effective reproduction number is less than the threshold value and persist otherwise. Based on the sensitivity analysis of the effective reproduction number, we found that the rate of ART treatment and the rate of awareness on the proper procedure of ART are influential in reducing the magnitude of the reproduction number and thus they are important in decreasing the number of infected population. Numerical simulations support our analytical results that implementing ART treatment at every stage of HIV/AIDS had high impact in reducing the infected population than implementing on a single stage for those who follow the proper procedure of ART treatment. It also verifies the positive impact of awareness on the proper procedure of ART treatment in reducing infected individuals by reducing treatment waning rate. Therefore, our result suggests that ART treatment should be implemented together with awareness on the proper procedure of ART treatment to control the spread of HIV in the community.},
 year = {2021}
}

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TY  - JOUR
T1  - A Mathematical Model Analysis for the Transmission Dynamics of HIV/AIDS with Control Strategy
AU  - Bogale Assefa Belayneh
AU  - Purnachandra Rao Koya
Y1  - 2021/08/23
PY  - 2021
N1  - https://doi.org/10.11648/j.mma.20210603.11
DO  - 10.11648/j.mma.20210603.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 56
EP  - 69
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20210603.11
AB  - This paper examines the transmission dynamics of HIV infection with public health intervention strategies treatment and awareness on the proper procedure of ART treatment. For the problem, a deterministic mathematical model is proposed and analysed qualitatively using the concept of stability of differential equations. The effective reproduction number is computed in terms of model parameters. The existence and stability of disease free and endemic steady states are recognized.  The disease free and endemic equilibria are indicated to be locally and globally asymptotically stable whenever the effective reproduction number is less than unity and greater than unity respectively. This means that, HIV infection will die out in the community when the effective reproduction number is less than the threshold value and persist otherwise. Based on the sensitivity analysis of the effective reproduction number, we found that the rate of ART treatment and the rate of awareness on the proper procedure of ART are influential in reducing the magnitude of the reproduction number and thus they are important in decreasing the number of infected population. Numerical simulations support our analytical results that implementing ART treatment at every stage of HIV/AIDS had high impact in reducing the infected population than implementing on a single stage for those who follow the proper procedure of ART treatment. It also verifies the positive impact of awareness on the proper procedure of ART treatment in reducing infected individuals by reducing treatment waning rate. Therefore, our result suggests that ART treatment should be implemented together with awareness on the proper procedure of ART treatment to control the spread of HIV in the community.
VL  - 6
IS  - 3
ER  -

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Author Information

Bogale Assefa Belayneh

Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia
Purnachandra Rao Koya

Department of Mathematics, Wollega University, Nekemte, Ethiopia

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APA Style

Bogale Assefa Belayneh, Purnachandra Rao Koya. (2021). A Mathematical Model Analysis for the Transmission Dynamics of HIV/AIDS with Control Strategy. Mathematical Modelling and Applications, 6(3), 56-69. https://doi.org/10.11648/j.mma.20210603.11

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ACS Style

Bogale Assefa Belayneh; Purnachandra Rao Koya. A Mathematical Model Analysis for the Transmission Dynamics of HIV/AIDS with Control Strategy. Math. Model. Appl. 2021, 6(3), 56-69. doi: 10.11648/j.mma.20210603.11

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AMA Style

Bogale Assefa Belayneh, Purnachandra Rao Koya. A Mathematical Model Analysis for the Transmission Dynamics of HIV/AIDS with Control Strategy. Math Model Appl. 2021;6(3):56-69. doi: 10.11648/j.mma.20210603.11

Copy | Download

@article{10.11648/j.mma.20210603.11,
  author = {Bogale Assefa Belayneh and Purnachandra Rao Koya},
  title = {A Mathematical Model Analysis for the Transmission Dynamics of HIV/AIDS with Control Strategy},
  journal = {Mathematical Modelling and Applications},
  volume = {6},
  number = {3},
  pages = {56-69},
  doi = {10.11648/j.mma.20210603.11},
  url = {https://doi.org/10.11648/j.mma.20210603.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20210603.11},
  abstract = {This paper examines the transmission dynamics of HIV infection with public health intervention strategies treatment and awareness on the proper procedure of ART treatment. For the problem, a deterministic mathematical model is proposed and analysed qualitatively using the concept of stability of differential equations. The effective reproduction number is computed in terms of model parameters. The existence and stability of disease free and endemic steady states are recognized.  The disease free and endemic equilibria are indicated to be locally and globally asymptotically stable whenever the effective reproduction number is less than unity and greater than unity respectively. This means that, HIV infection will die out in the community when the effective reproduction number is less than the threshold value and persist otherwise. Based on the sensitivity analysis of the effective reproduction number, we found that the rate of ART treatment and the rate of awareness on the proper procedure of ART are influential in reducing the magnitude of the reproduction number and thus they are important in decreasing the number of infected population. Numerical simulations support our analytical results that implementing ART treatment at every stage of HIV/AIDS had high impact in reducing the infected population than implementing on a single stage for those who follow the proper procedure of ART treatment. It also verifies the positive impact of awareness on the proper procedure of ART treatment in reducing infected individuals by reducing treatment waning rate. Therefore, our result suggests that ART treatment should be implemented together with awareness on the proper procedure of ART treatment to control the spread of HIV in the community.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - A Mathematical Model Analysis for the Transmission Dynamics of HIV/AIDS with Control Strategy
AU  - Bogale Assefa Belayneh
AU  - Purnachandra Rao Koya
Y1  - 2021/08/23
PY  - 2021
N1  - https://doi.org/10.11648/j.mma.20210603.11
DO  - 10.11648/j.mma.20210603.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 56
EP  - 69
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20210603.11
AB  - This paper examines the transmission dynamics of HIV infection with public health intervention strategies treatment and awareness on the proper procedure of ART treatment. For the problem, a deterministic mathematical model is proposed and analysed qualitatively using the concept of stability of differential equations. The effective reproduction number is computed in terms of model parameters. The existence and stability of disease free and endemic steady states are recognized.  The disease free and endemic equilibria are indicated to be locally and globally asymptotically stable whenever the effective reproduction number is less than unity and greater than unity respectively. This means that, HIV infection will die out in the community when the effective reproduction number is less than the threshold value and persist otherwise. Based on the sensitivity analysis of the effective reproduction number, we found that the rate of ART treatment and the rate of awareness on the proper procedure of ART are influential in reducing the magnitude of the reproduction number and thus they are important in decreasing the number of infected population. Numerical simulations support our analytical results that implementing ART treatment at every stage of HIV/AIDS had high impact in reducing the infected population than implementing on a single stage for those who follow the proper procedure of ART treatment. It also verifies the positive impact of awareness on the proper procedure of ART treatment in reducing infected individuals by reducing treatment waning rate. Therefore, our result suggests that ART treatment should be implemented together with awareness on the proper procedure of ART treatment to control the spread of HIV in the community.
VL  - 6
IS  - 3
ER  -

Copy | Download