使用分数流行病学建模方法对麻疹病的数学评估与疫苗接种的影响
Botao Liu1, Samreen Farid2, Saif Ullah3
1School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People's Republic of China.
Scientific reports
|August 20, 2023
概括
这项研究使用分数计算来模拟 (一种病毒感染),揭示了参数和分数顺序如何影响疾病动态和控制策略.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 分数微积分的计算.
背景情况:
- (一种病毒感染) 给公共卫生带来了重大挑战.
- 数学建模对于理解疾病传播动态至关重要.
- 分数顺序模型为复杂的生物系统提供了先进的见解.
研究的目的:
- 开发和分析一个分数顺序的数学模型,用于麻疹.
- 调查麻疹传播的流行病学方面.
- 评估不完美的疫苗接种对疾病动态的影响.
主要方法:
- 整数顺序非线性微分方程模型的制定.
- 使用分数顺序导数进行重构 (卡普托用乘法).
- 参数估计使用美国麻疹病例数据 (2022年5月至10月).
- 为分数模型建立存在和独特性条件.
- 使用Lyapunov函数对特有平衡稳定的分析.
- 通过 Adams-Bashforth-Moulton 分数方法进行数值模拟.
主要成果:
- 为解决方案的存在和独特性建立了足够的条件.
- 证明了分数水模型平衡的全球稳定性.
- 数字模拟突出了模型参数和分数顺序对疾病动态的影响.
- 该研究量化了不完美的疫苗接种对麻疹传播的影响.
结论:
- 分数顺序建模为分析麻疹流行病学提供了强大的框架.
- 模型参数和分数顺序显著影响疾病传播和控制.
- 这些发现为针对水的公共卫生干预提供了有价值的见解.
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