在年代年代结构的SIR流行病模型中,Hopf分叉与年龄依赖的传染性
Toshikazu Kuniya1, Hisashi Inaba2
1Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan.
Mathematical biosciences and engineering : MBE
|July 28, 2023
概括
本研究分析了以年龄结构的SIR流行病模型中特有平衡的稳定性. 霍夫分叉分析揭示了稳定性开关的条件,这对于理解疾病动态至关重要.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 动态系统 动态系统
背景情况:
- 地方性平衡对于理解持久性传染病至关重要.
- 根据年龄结构的模型对于捕捉人口对疾病传播的影响至关重要.
- 霍夫分叉分析是研究动态系统中稳定性和振荡的一个关键工具.
研究的目的:
- 在一个按年代结构的SIR流行病模型中研究特有平衡的稳定性.
- 在这个模型中分析Hopf分叉发生的条件.
- 探索依赖年龄的感染率和传播率对疾病动态的影响.
主要方法:
- 开发一个按年代结构的SIR流行病模型.
- 霍夫分支分析应用于特有平衡.
- 使用数值模拟来证实理论发现.
主要成果:
- 当基本生殖数超过1时,就存在特有平衡.
- 当感染力等于去除速率时,Hopf分叉的临界值就存在.
- 即使这些速率不相等,Hopf分叉也可能发生,如果它们的差异很小.
- 数字模拟证实了在特定场景下,特有平衡的多个稳定性切换器.
结论:
- 在年龄结构的SIR模型中,特有平衡的稳定性对控制感染和移除率的参数敏感.
- 霍夫分叉在产生振荡动态和稳定性变化方面发挥着重要作用.
- 年龄相关的传染性和传播率功能会导致复杂的疾病持续性模式.
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