结核病与治疗干预分数模型的综合分析
Benedict Celestine Agbata1, Raimonda Dervishi2, Dennis Ferdinand Agbebaku3
1Department of Mathematics and Statistics, Faculty of Science, Confluence University of Science and Technology, Osara, Nigeria. agbatacelestine92@gmail.com.
BMC infectious diseases
|August 26, 2025
概括
这项研究使用高级数学建模与分数计算来了解结核病 (TB) 的传播. 研究结果表明,提高治疗率和减少传播对于有效控制结核病至关重要.
科学领域:
- 数学生物学
- 流行病学
- 传染病模型
背景情况:
- 结核病 (TB) 是一个主要的传染病杀手,由COVID-19的干扰加剧.
- 有效的结核病控制需要强大而现实的建模方法.
- 包括艾滋病毒感染者在内的弱势群体受到了不成比例的影响.
研究的目的:
- 开发和分析一种新的结核传播数学模型.
- 为了提高准确性,使用分数顺序导数和亚当斯-巴斯福斯法.
- 评估各种干预策略对结核病控制的影响.
主要方法:
- 一个分区模型将人口分为六组:易感,暴露,急性结核病,慢性结核病,治疗和恢复.
- 应用分数顺序导数来捕捉TB传输动态中的记忆效应.
- 用Adams-Bashforth方法进行数值模拟和分析.
- 使用下一代矩阵方法计算基本复制数 (R0).
主要成果:
- 敏感性分析表明,治疗率的增加显著改善了康复.
- 该模型表明,当R0> 1时,结核病持续存在,当R0< 1时,结核病下降.
- 模拟研究了改善治疗和更快诊断等干预措施.
结论:
- 当R0> 1时,特有平衡是全局稳定的,这表明结核病持久.
- 减少传播和加强治疗对于有效控制结核病至关重要.
- 及时干预和加强政策对于管理结核病至关重要.
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