SIQR流行病模型的动态与分数顺序导数
Subrata Paul1, Animesh Mahata2, Supriya Mukherjee3
1Department of Mathematics, Arambagh Government Polytechnic, Arambagh, West Bengal, India.
概括
这项研究使用分数顺序SIQR模型来分析COVID-19传播动态. 分数衍生品在模拟2019年新冠病毒病的传播方面被证明比整数订单更有效.
科学领域:
- 流行病学 流行病学
- 数学建模的数学建模
- 分数微积分的计算.
背景情况:
- 新型冠状病毒疾病-2019 (COVID-19) 构成了重大的全球健康挑战.
- 了解传播动态对于有效的控制策略至关重要.
- 传统的流行病学模型可能无法完全捕捉疾病传播的复杂性.
研究的目的:
- 应用一个分数顺序的易受感染-隔离-恢复 (SIQR) 模型来研究COVID-19传播.
- 分析拟议的分数模型的稳定性.
- 为了比较分数顺序导数与整数顺序导数在建模COVID-19动态中的有效性.
主要方法:
- 对半分析性溶液实施代拉普拉斯变换法 (ILTM).
- 利用来自印度和巴西的实时COVID-19数据进行参数估计.
- 采用亚当-巴什福斯-穆尔顿预测器-校正器技术用于数值解决方案.
- 在ILTM和数值解决方案之间进行比较分析.
主要成果:
- 分数顺序SIQR模型有效地描述了COVID-19传播动态.
- 通过使用现实世界的数据成功进行了参数估计.
- 该ILTM提供了可靠的半分析解决方案.
- 分数顺序衍生品与整数顺序衍生品相比,显示出更高的效率.
结论:
- 分数计算为模拟COVID-19等传染病动态提供了一种更细微的方法.
- 分数SIQR模型与ILTM结合,为分析和预测疾病传播提供了一个强大的框架.
- 这些发现凸显了分数计算在流行病学研究中的重要性.
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