一个数值研究SIR流行病模型的动态通过Genocchi波纹拼接方法
Darshan Kumar Chiranahalli Vijaya1, Prakasha Doddabhadrappla Gowda1, Balachandra Hadimani2
1Department of Mathematics, Davangere University, Shivagangotri, Davangere, 577007, India.
Scientific reports
|March 22, 2025
概括
这项研究引入了一种新的数值方法来分析分数顺序的流行病模型. 热诺基波列聚合方法提供了一种准确而有效的方法来了解疾病传播动态.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 数字分析 数字分析
背景情况:
- 数学模型对于了解疾病传播和公共卫生至关重要.
- 分数顺序微分方程越来越多地用于模拟疾病动态中的复杂,非局部现象.
研究的目的:
- 应用 Genocchi 波纹聚合方法来解决任意分数顺序的 SIR (易感染-复原) 流行病模型.
- 通过使用卡普托分数导数来研究SIR模型的动态行为.
- 为了证明拟议的数值方法的效率和准确性.
主要方法:
- 采用Genocchi波形聚合方法,将分数顺序的非线性普通微分方程转换为代数方程.
- 这种方法将操作矩阵与拼接技术合并为高效的计算.
- 生成数值解决方案并与已建立的方法比较,如Runge-Kutta和剩余功率序列.
主要成果:
- 热诺基波列拼接方法为分数顺序的SIR模型提供了精确和可靠的结果.
- 该方法在计算上是高效的,比传统技术需要更少的资源.
- 对各种分数顺序的数值结果的图形表示说明了模型的动态.
结论:
- 热诺基波列聚合方法是分析流行病和生物模型中的非线性并发症的高效和准确技术.
- 这种方法为研究复杂的现实世界疾病动态提供了更简单,更快速和无参数的替代方案.
- 该研究验证了在流行病学建模中分数计算的实用性,并提供了一个强大的数值工具.
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