结核病感染动态的分析使用卡普托的分数顺序模型与诊断和治疗干预措施
Oluwafemi Ezekiel Abiodun1, Morufu Oyedunsi Olayiwola1
1Department of Mathematics, Adeyemi Federal University of Education, Ondo, Nigeria; Department of Mathematical Sciences, Osun State University, Osogbo, Nigeria.
Tuberculosis (Edinburgh, Scotland)
|October 9, 2025
概括
这项研究引入了分数顺序结核病 (TB) 模型与干预措施. 分数计算揭示了记忆效应,表明早期诊断和隔离是控制结核病的关键.
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:
- 结核病 (TB) 仍然是一个重大的全球卫生挑战.
- 数学模型对于理解结核病传播动态至关重要.
- 经典模型可能无法捕捉复杂的疾病行为,如记忆效应.
研究的目的:
- 开发和分析一个卡普托结核病传播的分数级数学模型.
- 包括诸如测试,治疗和隔离等干预措施.
- 评估分数顺序衍生品对TB动态和控制的影响.
主要方法:
- 制定一个五个部分 (易感,暴露,传染,隔离,恢复) 分数顺序模型.
- 分析定性属性:解决方案的积极性,局限性,存在性和独特性.
- 基本复制数 (R0) 的推导和灵敏度分析.
- 使用拉普拉斯-阿多米安分解法 (LADM) 的数值模拟.
主要成果:
- 敏感性分析确定了传播,进展,测试和治疗率作为关键驱动因素.
- 增加分数顺序提高了模型的准确性,并揭示了结核病传播中的记忆效应.
- 早期诊断,治疗和隔离被证明可以显著减少感染并改善恢复.
结论:
- 由于记忆效应,分数顺序模型对结核病动态的经典模型具有优势.
- 该研究为设计有效的结核病控制策略提供了宝贵的见解.
- 早期诊断,治疗和隔离等干预措施对于减轻结核病传播至关重要.
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