脊髓灰质炎动态与分数顺序导数和深度神经网络
Ashraf Al-Quran1, Ramsha Shafqat2, Ateq Alsaadi3
1Department of Mathematics and Statistics, King Faisal University, 31982, Hofuf, Saudi Arabia.
Scientific reports
|August 31, 2025
概括
本研究使用分数顺序模型与阿坦甘纳-巴莱努衍生品来分析脊髓灰质炎 (脊髓灰质炎) 的传播. 较低的分数顺序和深度神经网络改善了疾病预测和控制策略.
科学领域:
- 流行病学
- 数学生物学
- 计算动力学
背景情况:
- 脊髓灰质炎的传播动态很复杂,受疫苗接种和疾病记忆等因素的影响.
- 分数顺序微分方程提供了先进的工具来模拟疾病传播中的遗传性质.
研究的目的:
- 开发和分析包含疫苗接种和后效应的脊髓灰质炎传播的分数级模型.
- 整合深度神经网络技术以提高疾病动态的预测和数据驱动模拟.
主要方法:
- 使用了两个分数顺序模型,其中包括阿坦加纳-巴莱努衍生 (ABC) 和米塔格-莱弗勒内核.
- 使用固定点理论和非线性技术建立了模型存在,独特性和Ulam-Hyers稳定性.
- 采用代的亚当斯-巴什福斯方案进行数值近似和深度神经网络 (DNN) 进行分类和预测.
主要成果:
- 分数模型有效地捕捉复杂的疾病行为,较低的分数顺序显示更快的稳定性.
- 所有模型组件都显示出与时间的趋同和动态稳定性.
- 基于DNN的预测与数值模拟密切结合,验证了混合方法.
结论:
- 使用ABC衍生品的分数顺序建模为分析脊髓灰质炎提供了强大的框架.
- 整合DNN可以提高传染病动态的预测准确度.
- 这种混合方法为了解和管理疫苗接种下脊髓灰质炎的传播提供了强大的工具.
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