埃博拉病毒流行病模型的计算和稳定性分析,使用碎片式混合分数运算符
Kottakkaran Sooppy Nisar1, Muhammad Farman2,3, Khadija Jamil4
1Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser, Saudi Arabia.
PloS one
|April 16, 2024
概括
这项研究引入了一种非线性分数埃博拉病毒模型,采用碎片式混合技术. 分数计算操作员提高模型准确性,以了解埃博拉传播动态,并为公共卫生战略提供信息.
科学领域:
- 数学建模的数学建模
- 流行病学 流行病学
- 分数微积分的计算.
背景情况:
- 埃博拉病毒病 (EVD) 构成了严重的全球健康威胁,需要精确的动态模型来进行传播分析.
- 传统的流行病学模型往往简化了疾病动态,可能会限制它们对复杂疫情的预测能力.
- 分数计算提供了一个强大的框架,以捕捉疾病传播中固有的记忆效应和非局部行为.
研究的目的:
- 开发和分析埃博拉病毒传播动态的非线性分数顺序数学模型.
- 调查古典和修改的分数运算符,特别是卡普托分数运算符对疾病动态的影响.
- 评估模型的生物可行性,稳定性和对各种参数的敏感性.
主要方法:
- 开发一个八部分非线性分数顺序的埃博拉病毒模型.
- 应用Arzel'a-Ascoli和Schauder条件来确定解决方案的存在和独特性.
- 对古典和修改的分数运算符的研究,包括卡普托分量运算符.
- 基本繁殖数 (R0) 的推导和敏感性分析的执行.
- 应用Matignon方法用于局部稳定性和Lyapunov函数用于全球稳定性分析.
- 使用牛顿的多项式技术进行的数值模拟,用于零碎的卡普托运算符.
主要成果:
- 该研究确定了分数顺序模型的解决方案的存在和独特性.
- 敏感性分析揭示了各种参数对生殖数 (R0) 的影响,表明了传播的关键驱动因素.
- 当地和全球稳定性分析证实了疾病持久性和根除的条件.
- 数字模拟表明,分数运算符显著提高模型捕捉复杂的埃博拉动态的能力.
- 断片式的卡普托运算符在模拟不同分数顺序的疾病传播方面被证明是有效的.
结论:
- 分数计算运算符,特别是分量卡普托运算符,对于准确建模埃博拉病毒传播的复杂动态至关重要.
- 与传统的整数顺序模型相比,开发的模型提供了对疾病传播的更细致的理解.
- 这些发现为完善流行病学模型和加强针对埃博拉病毒控制和预防的公共卫生战略提供了宝贵的见解.
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