艾滋病毒和结核病共感染动态的数学框架
Nauman Raza1, Shaiza Irum2, Shafiullah Niazai3
1Department of Mathematics, University of the Punjab, Lahore, Pakistan.
Scientific reports
|April 3, 2025
概括
这项研究引入了一种新的分数数学模型,以了解艾滋病毒和结核病共感染的动态和治疗效应. 模型 模型的模型
科学领域:
- 数学生物学 数学生物学
- 流行病学 流行病学
- 传染病建模 传染病建模
背景情况:
- 人类免疫缺陷病毒 (HIV) 和结核病 (TB) 的联合感染对全球健康构成了重大挑战.
- 了解共同感染的复杂相互作用和动态对于有效的疾病控制策略至关重要.
- 现有的数学模型可能无法完全捕捉复杂的动态,需要先进的方法.
研究的目的:
- 开发和分析HIV和结核病共感染的新型分数顺序数学模型.
- 将治疗效应,特别是抗逆转录病毒疗法 (ART) 纳入共感染模型.
- 调查拟议的分数模型解决方案的存在,独特性,积极性和局限性.
主要方法:
- 用分数计算,特别是卡普托分数导数,来制定模型.
- 采用下一代矩阵技术来确定结核病和艾滋病毒的基本繁殖数 (R0).
- 应用了Routh-Hurwitz标准和Lyapunov函数来分析无疾病平衡的稳定性.
- 使用美国 (1999-2022) 的真实世界数据估计的模型参数.
主要成果:
- 证明了分数共感染模型的基本数学属性 (存在,独特性,积极性,边界性).
- 确定无病和特有平衡,以及结核病和艾滋病毒的R0值.
- 确定了无病平衡点的本地和全球稳定性.
- 使用美国流行病学数据证明了模型与数据的匹配,验证了模型的预测能力.
- 计算模拟说明了分数顺序和稳定点对疾病动态的影响.
结论:
- 开发的分数顺序模型为分析在治疗中的HIV和结核病共感染动态提供了强大的框架.
- 稳定性分析证实了这种疾病可以根除的条件.
- 模型与真实数据的验证支持其在公共卫生政策和干预计划中的潜在应用.
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