对分数的克拉米迪亚流行病模型进行数学分析
Zuhur Alqahtani1, Areej Almuneef2, Mahmoud H DarAssi3
1Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O.Box 84428, 11671, Riyadh, Saudi Arabia. zumalqahtani@pnu.edu.sa.
Scientific reports
|December 28, 2024
概括
这项研究引入了分数性克拉米迪亚流行病模型,证明了其稳定性,并通过先进的分析和模拟来识别影响疾病的关键参数,以获得更好的疾病控制策略.
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:
- 克拉米迪亚感染对全球健康构成重大负担.
- 数学建模对于理解和预测传染病动态至关重要.
- 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:
- 开发和分析一个卡普托分数数学模型,用于克拉米迪亚病毒的传播.
- 为了研究分数克拉米迪亚模型的稳定性.
- 为了确定驱动克拉米迪亚疫情动态的关键参数.
主要方法:
- 开发一个卡普托-分数微分方程模型的克拉米迪亚.
- 分析模型的积极性,边界性,存在性和解决方案的独特性.
- 调查平衡点的局部和全球非对称稳定性.
- 使用拉丁式超立方体采样和PRCCs进行敏感性分析.
- 数字模拟用于探索参数影响.
主要成果:
- 分数克拉米迪亚模型被证明是正的和边界的.
- 没有疾病的平衡是局部异位稳定的.
- 一个独特的特有平衡点在基本繁殖数超过1时,在全球上是异常稳定的.
- 敏感性分析确定了影响疾病传播的关键参数.
结论:
- 开发的分数模型为研究克拉米迪亚流行病提供了一个强大的框架.
- 稳定性分析证实了疾病根除或持续的条件.
- 在克拉米迪亚控制的有针对性的干预策略中,参数识别辅助.
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