Butt Azhar Iqbal Kashif, Imran Muhammad, Azeem Komal, Ismaeel Tariq, McKinney Brett Allen
Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa, Saudi.
Tandy School of Computer Science, The University of Tulsa, Tulsa, OK, United States of America.
PLoS One. 2024 Dec 31;19(12):e0315850. doi: 10.1371/journal.pone.0315850. eCollection 2024.
In this manuscript, we present a novel mathematical model for understanding the dynamics of HIV/AIDS and analyzing optimal control strategies. To capture the disease dynamics, we propose a new Caputo-Fabrizio fractional-order mathematical model denoted as SEIEUPIATR, where the exposed class is subdivided into two categories: exposed-identified EI and exposed-unidentified EU individuals. Exposed-identified individuals become aware of the disease within three days, while exposed-unidentified individuals remain unaware for more than three days. Simultaneously, we introduce a treatment compartment with post-exposure prophylaxis (PEP), represented as P, designed for individuals of the exposed identified class. These individuals initiate treatment upon identification and continue for 28 days, resulting in full recovery from HIV. Additionally, we categorize infectious individuals into two groups: under-treatment individuals, denoted as T, and those with fully developed AIDS not receiving antiretroviral therapy (ART) treatment, denoted as A. We establish that the proposed model has a unique, bounded, and positive solution, along with other fundamental characteristics. Disease-free and endemic equilibrium points and their associated properties (such as the reproduction number [Formula: see text] and stability analysis) are determined. Sensitivity analysis is performed to assess the impact of parameters on [Formula: see text] and hence on the disease dynamics. Finally, we formulate a fractional optimal control problem to examine strategies for minimizing HIV/AIDS infection while keeping costs at a minimum. We adopt the use of condoms and changes in sexual habits as optimal controls. The numerical results are presented and discussed through graphs.
在本手稿中，我们提出了一种新颖的数学模型，用于理解艾滋病毒/艾滋病的动态变化并分析最优控制策略。为了捕捉疾病动态，我们提出了一个新的Caputo-Fabrizio分数阶数学模型，记为SEIEUPIATR，其中暴露类被细分为两类：已识别暴露者EI和未识别暴露者EU个体。已识别暴露者在三天内意识到疾病，而未识别暴露者在三天以上仍未意识到。同时，我们引入了一个暴露后预防（PEP）治疗区室，用P表示，针对已识别暴露类别的个体。这些个体在识别后开始治疗，并持续28天，从而从艾滋病毒中完全康复。此外，我们将感染个体分为两组：治疗不足个体，记为T，以及未接受抗逆转录病毒疗法（ART）治疗的艾滋病完全发展个体，记为A。我们证明了所提出的模型具有唯一、有界且正的解，以及其他基本特征。确定了无病平衡点和地方病平衡点及其相关性质（如繁殖数[公式：见正文]和稳定性分析）。进行了敏感性分析，以评估参数对[公式：见正文]的影响，从而对疾病动态的影响。最后，我们制定了一个分数阶最优控制问题，以研究在使成本最小化的同时将艾滋病毒/艾滋病感染降至最低的策略。我们采用使用避孕套和改变性行为习惯作为最优控制。通过图表展示并讨论了数值结果。
