使用卡普托分数导数进行结核病的数学建模:与真实数据进行比较分析
Sanjay Bhatter1, Sangeeta Kumawat1, Sunil Dutt Purohit2
1Department of Mathematics, Malaviya National Institute of Technology Jaipur, Jaipur, India.
Scientific reports
|April 12, 2025
概括
本研究介绍了中国结核病 (TB) 的小数序流行病学模型. 与传统模型相比,分数模型为结核病传播动态提供了28.5%的精度改进.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 分数微积分的计算.
背景情况:
- 结核病 (TB) 仍然是一个重大的全球卫生挑战.
- 准确的流行病学建模对于有效的公共卫生干预至关重要.
- 传统的整数顺序模型可能无法完全捕捉复杂的疾病动态.
研究的目的:
- 开发和分析一种新的流行病学模型,用于中国的结核病传播,使用卡普托的分数顺序衍生.
- 评估拟议的分数模型的数学特性和稳定性.
- 评估模型在适应真实世界结核病数据方面的准确性和效率.
主要方法:
- 在流行病学模型中应用卡普托分数顺序导数.
- 对模型属性的分析:解决方案的非负性,边界性,存在性和独特性.
- 使用基本复制号和3D图片可视化的灵敏度分析.
- 参数估计,包括最佳分数顺序 (大约. 0.93%) 的情况.
- 使用Adams-Bashforth-Moulton方法进行数值模拟.
- 使用根平均平方误差 (RMSE) 度量与整数顺序模型进行比较.
主要成果:
- 分数顺序的结核病模型被严格分析了它的数学属性.
- 敏感性分析揭示了影响结核病传播动态的关键参数.
- 最优的分数顺序被确定为大约0.93,提供最适合实证数据.
- 数值模拟显示,使用分数模型的效率 (精度) 与整数模型相比提高了28.5%.
- 分数顺序模型在描述结核病传播动态方面表现出卓越的准确性.
结论:
- 分数顺序的流行病学模型为了解传染病动态提供了更精细,更准确的方法.
- 拟议的卡普托分数顺序模型为中国的结核病传播提供了更深入的见解.
- 这些发现凸显了微积分计算在改善公共卫生战略和传染病决策方面的潜力.
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