结核病和糖尿病共存动态的分数顺序建模
Mohammed S Abdo1, Najla Alghamdi2, Hadeel Z Alzumi2
1Department of Mathematics, Hodeidah University, Al-Hudaydah, 3114, Yemen.
Computers in biology and medicine
|June 22, 2025
概括
这项研究介绍了结核病和糖尿病共同动态的分数顺序模型. 较低的分数顺序减缓了疾病衰变,突出了用于慢性疾病建模和控制的分数计算.
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:
- 结核病 (TB) 和糖尿病 (DM) 是全球重要的健康问题.
- 结核病和DM的共存呈现出复杂的流行病学动态.
- 现有的模型可能无法完全捕捉慢性疾病共同动态的长期,依赖于记忆的性质.
研究的目的:
- 为结核病和DM的协同动力学开发和分析一种新的分数顺序数学模型.
- 研究微积分计算对疾病进展和稳定性的影响.
- 确定影响结核病和DM共存的关键参数.
主要方法:
- 使用阿坦干纳-巴莱努-卡普托 (ABC) 衍生式进行分数建模.
- 使用巴纳赫固定点定理建立了模型定位.
- 获得基本复制数 (R0) 并进行敏感性分析.
- 采用亚当斯-巴什福斯方法进行数值模拟.
主要成果:
- 该模型的解决方案是独特的和积极的.
- 基本的繁殖数量表明了特有状态的潜力.
- 敏感性分析确定了共存的关键参数 (β1, β2, δ1, δ3, δ5).
- 较低的分数顺序 (α ≤ 0.8) 已被证明可以减缓疾病衰变.
结论:
- 分数计算有效地模拟了结核病和DM的慢性共存.
- 该研究提供了有关疾病动态和潜在控制策略的见解.
- 研究结果表明,分数模型固有的记忆属性对于理解慢性疾病相互作用至关重要.
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