Department of Mathematics, College of Science and Arts, King Abdulaziz University, P.O. Box 344, 21911, Rabigh, Saudi Arabia.
Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat, KPK, 28420, Pakistan.
Sci Rep. 2024 Oct 18;14(1):24506. doi: 10.1038/s41598-024-73580-9.
It is important to examine and comprehend how HIV interacts with the immune system in order to manage the infection, enhance patient outcomes, advance medical research, and support global health and socioeconomic stability. In this study, we formulate the dynamics of HIV infection to investigate the intricate interactions between HIV and [Formula: see text] T-cells. The Atangana-Baleanu and Caputo-Fabrizio derivative frameworks are applied to comprehensively examine the phenomenon of HIV viral transmission. The basic concepts and results of fractional calculus are presented for the analysis of the model. In our work, we focus on the dynamical behavior of HIV and immune system. We introduce numerical schemes to elucidate the solution pathways of the recommended system of HIV. We have shown the influence of various input factors on the solution pathways of the recommended fractional system and highlighted the oscillatory behavior and chaotic nature of the dynamics. Our findings demonstrate the complexity of the system under study by revealing the existence of the chaotic and oscillatory nature in the dynamics of HIV. In order to quantitatively characterize HIV dynamics, a number of simulations are carried out, providing a visual representation of the effects of different input variables. It has been observed that the chaos and the oscillatory behaviour is strongly related to the nonlinearity of the system. The present study provides a basis for further initiatives that try to enhance interventions and policies to lessen the worldwide burden of infection.
为了管理感染、改善患者预后、推进医学研究以及支持全球健康和社会经济稳定，了解 HIV 如何与免疫系统相互作用至关重要。在这项研究中，我们构建了 HIV 感染的动力学模型，以研究 HIV 与 [Formula: see text] T 细胞之间的复杂相互作用。我们应用了 Atangana-Baleanu 和 Caputo-Fabrizio 导数框架，全面考察了 HIV 病毒传播的现象。我们为模型分析介绍了分数微积分的基本概念和结果。在我们的工作中，我们专注于 HIV 和免疫系统的动态行为。我们引入数值方案来阐明推荐的 HIV 系统的解路径。我们展示了各种输入因素对推荐分数系统解路径的影响，并强调了动力学的振荡和混沌性质。我们的研究结果通过揭示 HIV 动力学中混沌和振荡性质的存在，展示了所研究系统的复杂性。为了定量描述 HIV 动力学，我们进行了多次模拟，以可视化不同输入变量的影响。我们观察到，混沌和振荡行为与系统的非线性密切相关。本研究为进一步的举措提供了基础，旨在加强干预和政策，以减轻全球感染负担。
