一个分数COVID-19模型的动力学与免疫使用和发病率平均类型的免疫力
Nandhini Mohankumar1, Lavanya Rajagopal1
1Department of Mathematics, Coimbatore Institute of Technology, Civil Aerodrome (PO), Coimbatore, Tamilnadu 641014 India.
概括
这项研究模型COVID-19的传播使用一个分数模型与免疫. 协调发病率旨在消除暴露和感染的个体,实现疾病控制.
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 传播动态需要强大的数学模型.
- 了解获得免疫力对于疾病控制策略至关重要.
- 分数计算为模拟复杂的生物系统提供了先进的工具.
研究的目的:
- 通过阿坦干纳-巴莱努分数模型调查COVID-19传播动态.
- 分析获得免疫对疾病传播的影响.
- 制定最佳的疾病根除控制策略.
主要方法:
- 使用了与获得免疫力的Atangana-Baleanu分数模型.
- 在人口动态中使用的和发病率平均类型.
- 使用下一代矩阵计算了基本的复制数.
- 应用卡斯蒂略-查韦斯和添加剂化合物矩阵方法进行稳定性分析.
- 实现了Pontryagin的最大原则,以实现最佳控制.
- 使用拉普拉斯变换进行分数导数的分析模拟.
主要成果:
- 证明了和发病率可以将暴露和感染的人口驱使到灭绝.
- 在无疾病和特有平衡点之间建立了全球稳定性.
- 确定了管理COVID-19传播的最佳控制策略.
- 图形分析提供了有关疾病传播动态的见解.
结论:
- 阿坦加纳-巴莱努分数模型有效地捕获了COVID-19传播动态.
- 获得的免疫力在疾病控制中起着重要作用.
- 从模型中获得的最佳控制策略可以帮助消除疾病的努力.
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