Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size

Udoo Iorlumun Joseph Martins; Kimbir Richard Anande; Remilekun Mathew Odekunle

doi:doi:10.11648/j.ajam.20150306.16

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Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size

Udoo Iorlumun Joseph Martins, Kimbir Richard Anande, Remilekun Mathew Odekunle

Published in American Journal of Applied Mathematics (Volume 3, Issue 6)

Received: 6 October 2015 Accepted: 23 October 2015 Published: 24 November 2015

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Abstract

A mathematical model of the transmission dynamics of HIV/AIDS, incorporating counselling, vaccination and antiretroviral therapy (ART) in a varying population, is presented. The existence and stability of the disease-free equilibrium states of the variants of the model are investigated, from which threshold values for vaccination and ART administration rates are established. Furthermore, numerical experiments are carried out to illustrate the effects of vaccination and ART, separately and in combination, on the transmission dynamics of HIV/AIDS in such populations.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 6)
DOI	10.11648/j.ajam.20150306.16
Page(s)	271-282
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), 2015. Published by Science Publishing Group

Keywords

HIV/AIDS, Counselling, Vaccination, ART, Mathematical Model, Stability, Eradication, Threshold Values

References

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APA Style

Udoo Iorlumun Joseph Martins, Kimbir Richard Anande, Remilekun Mathew Odekunle. (2015). Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size. American Journal of Applied Mathematics, 3(6), 271-282. https://doi.org/10.11648/j.ajam.20150306.16

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ACS Style

Udoo Iorlumun Joseph Martins; Kimbir Richard Anande; Remilekun Mathew Odekunle. Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size. Am. J. Appl. Math. 2015, 3(6), 271-282. doi: 10.11648/j.ajam.20150306.16

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AMA Style

Udoo Iorlumun Joseph Martins, Kimbir Richard Anande, Remilekun Mathew Odekunle. Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size. Am J Appl Math. 2015;3(6):271-282. doi: 10.11648/j.ajam.20150306.16

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@article{10.11648/j.ajam.20150306.16,
  author = {Udoo Iorlumun Joseph Martins and Kimbir Richard Anande and Remilekun Mathew Odekunle},
  title = {Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {6},
  pages = {271-282},
  doi = {10.11648/j.ajam.20150306.16},
  url = {https://doi.org/10.11648/j.ajam.20150306.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150306.16},
  abstract = {A mathematical model of the transmission dynamics of HIV/AIDS, incorporating counselling, vaccination and antiretroviral therapy (ART) in a varying population, is presented. The existence and stability of the disease-free equilibrium states of the variants of the model are investigated, from which threshold values for vaccination and ART administration rates are established. Furthermore, numerical experiments are carried out to illustrate the effects of vaccination and ART, separately and in combination, on the transmission dynamics of HIV/AIDS in such populations.},
 year = {2015}
}

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TY  - JOUR
T1  - Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size
AU  - Udoo Iorlumun Joseph Martins
AU  - Kimbir Richard Anande
AU  - Remilekun Mathew Odekunle
Y1  - 2015/11/24
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150306.16
DO  - 10.11648/j.ajam.20150306.16
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 271
EP  - 282
PB  - Science Publishing Group
SN  - 2330-006X
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AB  - A mathematical model of the transmission dynamics of HIV/AIDS, incorporating counselling, vaccination and antiretroviral therapy (ART) in a varying population, is presented. The existence and stability of the disease-free equilibrium states of the variants of the model are investigated, from which threshold values for vaccination and ART administration rates are established. Furthermore, numerical experiments are carried out to illustrate the effects of vaccination and ART, separately and in combination, on the transmission dynamics of HIV/AIDS in such populations.
VL  - 3
IS  - 6
ER  -

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Author Information

Udoo Iorlumun Joseph Martins

Department of Mathematics, School of Sciences, College of Education, Zing, Taraba State, Nigeria
Kimbir Richard Anande

Department of Mathematics, Statistics and Computer Science, Federal University of Agriculture, Makurdi, Benue State, Nigeria
Remilekun Mathew Odekunle

Department of Mathematics, School of Pure and Applied Sciences, Modibbo Adama University of Technology, Yola, Adamawa State, Nigeria

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Plain Text BibTeX RIS

APA Style

Udoo Iorlumun Joseph Martins, Kimbir Richard Anande, Remilekun Mathew Odekunle. (2015). Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size. American Journal of Applied Mathematics, 3(6), 271-282. https://doi.org/10.11648/j.ajam.20150306.16

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ACS Style

Udoo Iorlumun Joseph Martins; Kimbir Richard Anande; Remilekun Mathew Odekunle. Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size. Am. J. Appl. Math. 2015, 3(6), 271-282. doi: 10.11648/j.ajam.20150306.16

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AMA Style

Udoo Iorlumun Joseph Martins, Kimbir Richard Anande, Remilekun Mathew Odekunle. Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size. Am J Appl Math. 2015;3(6):271-282. doi: 10.11648/j.ajam.20150306.16

Copy | Download

@article{10.11648/j.ajam.20150306.16,
  author = {Udoo Iorlumun Joseph Martins and Kimbir Richard Anande and Remilekun Mathew Odekunle},
  title = {Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {6},
  pages = {271-282},
  doi = {10.11648/j.ajam.20150306.16},
  url = {https://doi.org/10.11648/j.ajam.20150306.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150306.16},
  abstract = {A mathematical model of the transmission dynamics of HIV/AIDS, incorporating counselling, vaccination and antiretroviral therapy (ART) in a varying population, is presented. The existence and stability of the disease-free equilibrium states of the variants of the model are investigated, from which threshold values for vaccination and ART administration rates are established. Furthermore, numerical experiments are carried out to illustrate the effects of vaccination and ART, separately and in combination, on the transmission dynamics of HIV/AIDS in such populations.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Modelling HIV/AIDS Transmission Dynamics Considering Counselling, Vaccination and Antiretroviral Therapy (ART) in a Population of Varying Size
AU  - Udoo Iorlumun Joseph Martins
AU  - Kimbir Richard Anande
AU  - Remilekun Mathew Odekunle
Y1  - 2015/11/24
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150306.16
DO  - 10.11648/j.ajam.20150306.16
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 271
EP  - 282
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150306.16
AB  - A mathematical model of the transmission dynamics of HIV/AIDS, incorporating counselling, vaccination and antiretroviral therapy (ART) in a varying population, is presented. The existence and stability of the disease-free equilibrium states of the variants of the model are investigated, from which threshold values for vaccination and ART administration rates are established. Furthermore, numerical experiments are carried out to illustrate the effects of vaccination and ART, separately and in combination, on the transmission dynamics of HIV/AIDS in such populations.
VL  - 3
IS  - 6
ER  -

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