松树病动态的碎形-碎形建模和稳定性分析
Khaled Aldwoah1, Shahid Ahmed2, Shah Jahan2
1Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medinah, Saudi Arabia.
PloS one
|February 12, 2025
概括
这项研究使用碎形微积分计算来建模松病的动态. 这种新的方法通过使用先进的数学技术,提高了对疾病传播和稳定性的理解.
科学领域:
- 数学生物学 数学生物学
- 流行病学 流行病学
- 分数微积分的计算.
背景情况:
- 松病对森林生态系统构成重大威胁.
- 了解疾病传播动态对于有效管理至关重要.
- 传统的数学模型可能无法完全捕捉复杂的疾病传播模式.
研究的目的:
- 开发和分析一种针对松病的新型隔间数学模型.
- 为了研究疾病动态,使用分数-分数运算符来研究疾病动态.
- 探索碎形尺寸和碎形顺序对疾病传播的影响.
主要方法:
- 构建一个六个部分的数学模型 (易受,暴露,感染).
- 分式微积分和分数理论的应用,以建模疾病动态.
- 使用巴纳赫和莱雷-舒德定理分析模型属性 (存在,独特性).
- 对分数模型的Ulam-Hyers稳定性的研究.
- 使用分数亚当斯-巴斯福斯方法开发计算技术.
- 模拟和验证使用MATLAB用于各种碎形顺序和维度.
主要成果:
- 碎形-碎形模型提供了对松病传播的更细致的理解.
- 分析证实了拟议模型的存在,独特性和稳定性.
- 模拟表明了碎形顺序和碎形维度对疾病动态的影响.
结论:
- 碎形微积分提供了一个强大的框架,用于模拟复杂的流行病学现象,如松病.
- 开发的模型和计算技术为预测和管理疾病提供了宝贵的工具.
- 进一步的研究可以探索这种方法的应用到其他传染病.
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