在非线性分数双易感模型中探索最佳控制策略,用于使用阿坦甘娜-巴莱努衍生物的Covid-19动态
Azhar Iqbal Kashif Butt1, Waheed Ahmad2, Hafiz Ghulam Rabbani3
1Department of Mathematics and Statistics, College of Science, King Faisal University, 31982, Al-Ahsa, Saudi Arabia. aikhan@kfu.edu.sa.
Scientific reports
|December 31, 2024
概括
这项研究介绍了使用阿坦干纳-巴莱努衍生物的COVID-19动态的分数数学模型. 数字模拟表明,疫苗接种和住院控制可以加快流行病的消除.
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:
- 由于COVID-19的流行,我们需要先进的数学模型来理解疾病的动态.
- 分数计算为捕捉流行病学系统中复杂的非局部行为提供了一个强大的框架.
研究的目的:
- 开发和分析一个非线性分数双易感性模型用于COVID-19使用卡普托意义上的Atangana-Baleanu衍生 (ABC).
- 调查疫苗接种和住院治疗等控制策略对大流行病减缓的影响.
- 制定和解决一个最佳的控制问题,以尽量减少感染率和成本.
主要方法:
- 开发一种非线性分数双敏感的COVID-19模型,采用ABC衍生物.
- 分析基本属性,包括积极性和局限性.
- 在平衡状态下使用值参数确定非对称稳定性.
- 应用Toufik-Atangana数值技术进行验证.
- 灵敏度分析以确定关键模型参数.
- 用Pontryagin的最小原则制定一个最佳控制问题.
主要成果:
- 该模型的基本属性 (积极性,局限性) 已被证明.
- 确定了平衡状态的非对称稳定性.
- 数字实验表明,联合疫苗接种和住院策略可以加速COVID-19的消除.
- 敏感性分析确定了影响疾病传播的关键参数.
- 发现最佳的控制策略有效降低了感染率和相关成本.
结论:
- 开发的分数模型为研究COVID-19提供了一个强大的框架.
- 阿坦干纳-巴莱努分数导数和图菲克-阿坦干纳数值方案为分析流行病动态提供了显著的优势.
- 实施疫苗接种和住院控制,以最佳控制策略为指导,对于有效的流行病管理至关重要.
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