分数微分方程的决定性-随机分析营养不良模型与随机扰动和交叉效应
Yu-Ming Chu1, Saima Rashid2,3, Shazia Karim4
1Department of Mathematics, Faculty of Sciences, Huzhou University, Huzhou, China.
Scientific reports
|September 8, 2023
概括
这项研究引入了一种新的数学模型,使用分数微积分来理解和预测营养不良的动态,特别是在孕妇中. 这些发现旨在通过更好的营养策略来改善社区健康和福祉.
科学领域:
- 数学生物学 数学生物学
- 分数微积分的计算.
- 公共卫生建模公共卫生建模
背景情况:
- 营养不良对社区福祉构成重大风险,特别是对妇女和儿童来说.
- 现有的模型可能无法完全捕捉营养不良的复杂动态,包括随机因素.
- 准确的建模对于开发有效的干预措施和改善公共卫生结果至关重要.
研究的目的:
- 开发和分析一个确定性-随机性营养不良模型,使用分数运算符.
- 调查行为和预测营养不良的进展,重点是孕妇.
- 探索微积分计算在模拟健康相关现象中的应用.
主要方法:
- 探索一个具有非线性扰动的确定性-随机性营养不良模型.
- 部分分数运算符的应用 (古典,卡普托,卡普托-法布里齐奥,阿坦加纳-巴莱努,随机导数).
- 对积极性和全球性的模型解决方案的分析,并使用随机莱普诺夫函数检查 ergodic 静止分布.
主要成果:
- 证明了随机模型的解决方案是正的和全局的.
- 证实了对随机系统的独特的ergodic静止分布的存在.
- 图形表示说明了混乱和随机扰动模式,验证了模型的有效性.
结论:
- 碎微积分计算提供了一个灵活而强大的框架,用于建模复杂的系统动态,如营养不良.
- 开发的模型提供了对孕妇营养缺乏的见解,有助于设计有针对性的干预措施.
- 这种方法提高了在不同时间间隔的现实世界健康场景中捕捉各种行为的能力.
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