https://doi.org/10.1140/epjs/s11734-024-01192-5
Regular Article
Fractional-calculus analysis of the dynamics of 
T cells and human immunodeficiency viruses
1
Department of Mathematics, College of Science, Jouf University, 72388, Sakaka, Saudi Arabia
2
Institute of Informatics and Computing in Energy (IICE), Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, 43000, Kajang, Selangor, Malaysia
3
Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, 43000, Kajang, Selangor, Malaysia
4
Faculty of Engineering, Department of Industrial Engineering, King Khalid University, Abha, Saudi Arabia
b
imtiazkakakhil@gmail.com
c
rashid.jan@uniten.edu.my
Received:
5
April
2024
Accepted:
2
June
2024
Published online:
4
July
2024
Combination antiretroviral Therapy (cART) is the standard treatment approach for human immunodeficiency virus (HIV), involving the use of various antiretroviral drugs to effectively suppress the virus’s replication in the body. The objective of cART is to decrease the viral load in the blood to undetectable levels, enhance the immune system’s function, and ultimately prolong the patient’s life by preventing the progression to AIDS and associated opportunistic infections. In this work, we formulated the dynamics of HIV infection, including the effects of cART, within a fractional framework. This paper presents a numerical study that investigates the complex dynamics of HIV infection in T cells. The proposed HIV model incorporates the impact of antiretroviral medication via the Caputo–Fabrizio derivative. To comprehend the dynamics of the proposed HIV infection model, a numerical approach is employed. The dynamic behavior of the system is illustrated by examining the influence of various input parameters, aiming to capture the system’s sensitivity to these factors. Furthermore, this modeling approach highlights the interaction between the immune system and the virus. Through numerical simulations utilizing specific input values, we explore the chaotic and periodic behavior of HIV infection and provide insights into its intricate dynamics.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
