<abstract xmlns="http://www.w3.org/1999/xhtml">

Over the past decade, Human Immunodeficiency Virus infection and Acquired Immunodeficiency Syndrome (HIV/AIDS) have become deadly infectious diseases, particularly in developing countries. This challenge has led to the development of some important HIV/AIDS treatment strategies, such as antiretroviral therapy (ART), among many others. This study presents a mathematical model to investigate the dynamics of HIV/AIDS transmission. Employing mathematical analysis, non-negativity, boundedness, the basic reproduction number <italic>ℛ</italic>0, and the stability of both the disease-free and endemic equilibrium of the proposed model were derived. Normalized forward sensitivity techniques are used to determine the significance and importance of sensitive parameters associated with <italic>ℛ</italic>0. To gain insights into the dynamical behavior of each compartment, an effective numerical scheme was utilized, and the results obtained suggest that there is a need, even if individuals are infected with the virus, to use non-pharmaceutical interventions as control strategies.
</abstract>

Over the past decade, Human Immunodeficiency Virus infection and Acquired Immunodeficiency Syndrome (HIV/AIDS) have become deadly infectious diseases, particularly in developing countries. This challenge has led to the development of some important HIV/AIDS treatment strategies, such as antiretroviral therapy (ART), among many others. This study presents a mathematical model to investigate the dynamics of HIV/AIDS transmission. Employing mathematical analysis, non-negativity, boundedness, the basic reproduction number ℛ0, and the stability of both the disease-free and endemic equilibrium of the proposed model were derived. Normalized forward sensitivity techniques are used to determine the significance and importance of sensitive parameters associated with ℛ0. To gain insights into the dynamical behavior of each compartment, an effective numerical scheme was utilized, and the results obtained suggest that there is a need, even if individuals are infected with the virus, to use non-pharmaceutical interventions as control strategies.

A mathematical and sensitivity analysis of an HIV/AIDS infection model

Department of Mathematics, Faculty of Natural and Applied Sciences

Department of Mathematics, Faculty of Science

King Mongkut's University of Technology North Bangkok

International Journal of Mathematics and Computer in Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"A mathematical and sensitivity analysis of an HIV/AIDS infection model"}

Over the past decade, Human Immunodeficiency Virus infection and Acquired Immunodeficiency Syndrome (HIV/AIDS) have become deadly infectious diseases,...

Compartment	Description

𝒮	Susceptible individuals
𝒮_P	HIV/AIDS Protected individuals
ℐ	Individuals infected with HIV/AIDS
𝒯	Individuals treated with HIV/AIDS

Parameters	Indices

β	+1
α	+0.12603
π	−1.1703
μ	−0.085673
d	−0.38525
γ	−0.20492

Parameters	Parameters value	Source

Δ	3.2millions humans/day	[34]
π	0.5813/day	Assume
α	0.039/day	Assume
μ	0.5/day	[34]
d	0.47/day	[34]
γ	0.25/day	[35]
β	0.4325/day	[36]

A mathematical and sensitivity analysis of an HIV/AIDS infection model

Article Category: Original Study

Pubblicato online: 02 giu 2024

Pagine: -

Ricevuto: 25 lug 2023

Accettato: 01 gen 2024

DOI: https://doi.org/10.2478/ijmce-2025-0004

Parole chiave
HIV/AIDS, mathematical model, sensitivity analysis, numerical simulations

© 2025 Idris Ahmed et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Interpretation of state variables and parameters for the HIV/AIDS model (2).

Forward normalized sensitivity indices.

Numerical values for parameters of model (2).

A mathematical and sensitivity analysis of an HIV/AIDS infection model

Article Category: Original Study

Pubblicato online: 02 giu 2024

Pagine: -

Ricevuto: 25 lug 2023

Accettato: 01 gen 2024

DOI: https://doi.org/10.2478/ijmce-2025-0004

Parole chiaveHIV/AIDS, mathematical model, sensitivity analysis, numerical simulations

© 2025 Idris Ahmed et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Interpretation of state variables and parameters for the HIV/AIDS model (2).

Forward normalized sensitivity indices.

Numerical values for parameters of model (2).

Parole chiave
HIV/AIDS, mathematical model, sensitivity analysis, numerical simulations