分数顺序HIV/AIDS模型与使用莱文伯格-马奎特反向传播方法治疗的数值近似
Muhammad Awais1, Tayyab Nawaz2, Abu Safyan Ali1
1Department of Mathematics and Computer Science, University of Ferrara, Via Machiavelli 30, Ferrara 44121, Italy.
这项研究引入了一种新的分数顺序模型来分析艾滋病毒的扩散和控制. 该模型与人工神经网络相结合,可以准确预测艾滋病毒的进展,并有助于优化治疗策略.
科学领域:
- 数学生物学 数学生物学
- 病毒学 病毒学
- 计算科学 计算科学
背景情况:
- 艾滋病毒向CD4+T细胞,导致免疫缺陷和艾滋病.
- 了解艾滋病毒传播动态对于有效的治疗和控制至关重要.
- 现有的模型可能无法完全捕捉HIV的复杂,长期进展.
研究的目的:
- 开发和分析一种新的非线性分数顺序模型,用于艾滋病毒的扩散.
- 调查无病和特有平衡状态的稳定性.
- 采用人工神经网络来准确预测和控制艾滋病毒的进展.
主要方法:
- 一个使用卡普托导数的四个部分 (S,I1,I2,A) 非线性分数顺序模型.
- 数学属性的分析 (积极性,边界性) 和平衡状态 (DFE,EE).
- 应用亚当斯-巴什福斯-穆尔顿 (ABM) 数值解决方案和莱文伯格-马奎特反向传播 (LMBNN) 提高精度.
主要成果:
- 该模型的稳定性分析证实了R0<1的DFE和R0>1.1的EE.
- 在预测艾滋病毒动态方面,LMBNN方法实现了高精度 (MSE ~10^-3,R^2 ≈1).
- 研究了微分衍生品订单 (0.55,0.7,0.9),显示出有效的预测能力.
结论:
- 拟议的分数顺序模型和LMBNN技术为预测和控制艾滋病毒/艾滋病的进展提供了一个强大的框架.
- 这种方法可以显著帮助优化治疗策略和管理疾病负担.
- 该研究将数学建模与实际的疾病控制措施相结合,以改善公共卫生结果.
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