在结核病模型中探索霍夫分叉和特有气泡,包括行为变化和治疗和度
Saduri Das1, Prashant K Srivastava2, Pankaj Biswas1
1National Institute of Technology Silchar, Silchar 788010, Assam, India.
Chaos (Woodbury, N.Y.)
|January 22, 2024
概括
这项研究引入了一种结核病模型,具有和的再感染和治疗,揭示了结核病即使由于这些因素导致基本生殖数量低,也可以持续存在,从而导致复杂的疾病动态.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 传染病建模 传染病建模
背景情况:
- 传染性疾病的传播受到行为变化的影响,例如减少接触.
- 疾病传播模型通常通过发病和结合行为变化.
- 了解结核病 (TB) 动态需要考虑再感染和治疗和.
研究的目的:
- 提出和分析结核病传播的数学模型.
- 调查和外源性再感染和治疗对结核病动态的影响.
- 检查结核病模型中稳定状态和分叉的稳定性.
主要方法:
- 开发结核病传播的数学模型.
- 对模型的无病和特有平衡点进行严格的稳定性分析.
- 使用分析和数值技术,研究向后和霍夫分叉.
- 用各种参数集对分析结果进行数值验证.
主要成果:
- 当再感染不存在,治疗是普遍的 (R0 < 1 和 R0 > 1,分别) 时,无病和特有平衡点在全球上是异常稳定的.
- 结核病的持续性即使在R0 < 1的情况下也可能发生,这是由于和的再感染和治疗,导致向后分叉.
- 分析了Hopf分叉,随着传输速率 (β) 的增加,导致前进的Hopf分叉和潜在的稳定性恢复,形成一个特有泡.
结论:
- 和的外部再感染和治疗和可以导致持续的结核病,即使低于关键的R0值.
- 该模型展示了复杂的动态,包括向后和向前的Hopf分叉和特有气泡,突出了和效应的重要性.
- 数字模拟证实了分析结果,强调了疾病参数和结核病持续性之间的复杂关系.
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