模拟COVID-19疾病的动态一致的数值方法与成本效益战略
Shuo Li1, Muhammad Amjad Abbas2, Ihsan Ullah Khan2
1School of Mathematics and Data Sciences, Changji University, Changji, 831100, Xinjiang, China.
Scientific reports
|September 30, 2025
概括
这项研究比较了模拟COVID-19传播的数值方法. 非标准的有限差异 (NSFD) 方案准确地追踪疾病,超过了流行病建模的欧勒和RK-4方法.
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:
- 由SARS-CoV-2引起的COVID-19通过接触迅速传播.
- 准确的数学模型对于理解和控制流行病动态至关重要.
- 现有的数值方案可能无法完全捕捉连续流行病模型的复杂性.
研究的目的:
- 评估和比较不同数值方案的性能,以确定COVID-19SEIHR流行病模型.
- 评估非标准有限差异 (NSFD) 方案与传统方法 (如欧勒和顺序4的Runge-Kutta) (RK-4) 相比的有效性.
- 使用NSFD方案分析无病和特有平衡的稳定性.
主要方法:
- 为COVID-19开发和应用一个确定性的SEIHR流行病模型.
- 使用下一代矩阵计算基本复制数 (R0).
- 实施和比较欧勒,RK-4和非标准有限差异 (NSFD) 数值方案.
- 对模型平衡局部和全球稳定性的分析.
主要成果:
- 欧勒和RK-4方案产生了从连续模型的行为偏离的数值解决方案.
- 该NSFD方案表现出卓越的准确性,提供与连续模型类似的结果.
- 该NSFD方案有效地捕捉了SEIHR模型的动态,并提供了精确的数学结果.
结论:
- 非标准有限差异 (NSFD) 方案是模拟COVID-19传播动态的强大而准确的工具.
- NSFD方案为模拟流行病模型提供了一种可靠的方法,确保数学精度.
- 这项研究验证了NSFD方法在了解和管理COVID-19等传染病爆发方面的实用性.
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