Yasir Nadeem Anjam, Rubayyi Turki Alqahtani, N. Alharthi, Saira Tabassum
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引用次数: 0
摘要
本文介绍了一个非线性确定性数学模型,该模型捕捉了艾滋病传播的演变动态,考虑了人群中的三个感染水平。该模型利用卡普托算子整合了分形-分数阶导数,并通过定点理论进行定性分析,以确定解的存在性和唯一性。通过非线性函数分析确认了 Ulam-Hyer 稳定性,并考虑了小扰动。利用分数 Adam-Bashforth 迭代方案获得了数值解,并通过 MATLAB 仿真加以证实。不同分数阶数和分形维数的结果与整数阶数的结果进行了比较,揭示了感染人群和康复人群向无 HIV 疾病平衡点发展的趋势。同时,易感个体向这一平衡状态减少,表明艾滋病毒暴露的稳定性。这项研究强调了控制传播率对减少死亡、遏制艾滋病毒传播和提高康复率的关键作用。这一建议的策略具有竞争优势,可增强对模型复杂动态的理解。
Unveiling the Complexity of HIV Transmission: Integrating Multi-Level Infections via Fractal-Fractional Analysis
This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. This proposed strategy offers a competitive advantage, enhancing comprehension of the model’s intricate dynamics.