Proceedings of the 12th International Conference on Green Technology (ICGT 2022)

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Dynamics of HIV Transmission with Saturated Incidence and Treatment Strategy

Authors
Marsudi1, *, Agus Widodo1, Darmajid1
1Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, 65145, Malang, Indonesia
*Corresponding author. Email: marsudi61@ub.ac.id
Corresponding Author
Marsudi
Available Online 29 May 2023.
DOI
10.2991/978-94-6463-148-7_22How to use a DOI?
Keywords
HIV dynamics; basic reproduction number; saturated incidence; stability; treatment
Abstract

This paper presents a mathematical model for dynamics of HIV transmission by considering a saturated incidence type interaction for the human to human sexual transmission. The equilibria of the model are discovered, and the basic reproduction number is calculated. The analysis shows that if the basic reproduction number is less than unity, the disease-free equilibrium is locally and globally asymptotically stable. It is proved using differential equation theory and a comparison theorem. The Lyapunov function and the LaSalle invariance principle show that the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity. According to the sensitivity analysis, the effective contact rate was more sensitive to the basic reproduction rate than the treatment rate. The numerical simulations show that as the saturation incidence rate increases, the force of infection decreases. The prevalence of HIV/AIDS decreases as the saturation rate increases.

Copyright
© 2023 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the 12th International Conference on Green Technology (ICGT 2022)
Series
Advances in Engineering Research
Publication Date
29 May 2023
ISBN
10.2991/978-94-6463-148-7_22
ISSN
2352-5401
DOI
10.2991/978-94-6463-148-7_22How to use a DOI?
Copyright
© 2023 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Marsudi
AU  - Agus Widodo
AU  - Darmajid
PY  - 2023
DA  - 2023/05/29
TI  - Dynamics of HIV Transmission with Saturated Incidence and Treatment Strategy
BT  - Proceedings of the 12th International Conference on Green Technology (ICGT 2022)
PB  - Atlantis Press
SP  - 207
EP  - 221
SN  - 2352-5401
UR  - https://doi.org/10.2991/978-94-6463-148-7_22
DO  - 10.2991/978-94-6463-148-7_22
ID  - 2023
ER  -