在Mittag-Leffler内核中对COVID-19感染的随机分数顺序模型的数值建模和模拟
Muhammad Altaf Khan1,2,3,4, Zain Ul Abadin Zafar5, Irfan Ahmad6
1Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, 602105, Chennai, Tamil Nadu, India. altafdir@gmail.com.
Scientific reports
|September 27, 2025
概括
这项研究引入了一种新的分数随机模型,用于COVID-19的传播,并结合了疫苗接种的影响. 该模型增强了对疾病动态和不确定性下的控制策略的理解.
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:
- COVID-19的传播是复杂的,受到疫苗接种和固有的随机性等因素的影响.
- 经典模型可能无法完全捕捉疾病动态的记忆和遗传性质.
- 随机性在疾病传播中起着至关重要的作用,需要先进的建模技术.
研究的目的:
- 开发和分析COVID-19传播的分数顺序随机模型,包括疫苗接种.
- 调查微积分和随机计算对疾病动态的影响.
- 为评估COVID-19控制战略提供一个更现实的框架.
主要方法:
- 使用Atangana-Baleanu分数导数构建一个分数顺序模型.
- 扩展分数随机微分方程 (FSDE) 来纳入随机性.
- 开发一种用于解决FSDE的新型数值方案.
- 使用来自巴基斯坦的真实COVID-19数据进行参数估计.
主要成果:
- 对确定性分数模型的平衡点和稳定性的分析.
- 确定FSDE模型的解决方案的存在和独特性.
- 数字模拟证明了分数顺序对感染率和趋同的影响.
- 考虑疫苗接种和随机效应的疾病消除条件的探索.
结论:
- 分数随机模型提供了对COVID-19传播动态的更全面的了解.
- 开发的模型和数值方法为分析不确定性下的控制策略提供了灵活的工具.
- 将Atangana-Baleanu衍生品与随机建模的整合为传染病建模提供了一种新的方法.
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