通过使用人工深度神经网络研究分数顺序的流行病分区模型
Eiman1, Kamal Shah2, Muhammad Sarwar2
1Department of Mathematics, University of Malakand, Chakdara Dir(L) 18000, Khyber, Pakhtunkhwa, Pakistan.
概括
这项研究使用碎形微分方程和深度神经网络 (DNN) 建模了轮状病毒传播. 这些发现为疾病动态和潜在的控制策略提供了新的见解.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 计算科学 计算科学
背景情况:
- 在全球范围内,罗塔病毒胃肠炎仍然是一个重大的公共卫生问题.
- 数学建模对于理解传染病动态至关重要.
- 分形微积分计算为模拟复杂的生物系统提供了先进的工具.
研究的目的:
- 开发和分析罗塔病毒传播的碎形分数顺序数学模型,包括接种疫苗的班级.
- 研究深度神经网络 (DNN) 的应用,以分析轮状病毒传播的动态系统.
- 为了比较基于DNN的预测与从碎形分数模型中得出的数值解决方案.
主要方法:
- 在卡普托·法布里齐奥 (Caputo Fabrizio) 的意义上,利用了带有指数内核 (FFE) 的分数微分导数.
- 运用固定点理论来证明解决方案的存在,并使用欧勒的数值解释方法.
- 应用深度神经网络,特别是Levenberg-Marquardt算法,用于模型分析和预测.
主要成果:
- 确定了罗塔病毒传播模型的解决方案的存在.
- 呈现了数值模拟,展示了不同碎形分数顺序对疾病动态的影响.
- 证明了DNN在预测模型行为的准确性和有效性,通过回归 (R),MSE和RMSE指标验证.
结论:
- 碎形分数模型为研究轮状病毒传播动态提供了一个强大的框架.
- 深度神经网络为分析复杂的流行病学模型提供了强大而准确的替代方案.
- 这种综合方法提高了我们对疾病传播的理解,并为公共卫生干预提供了信息.
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