在周期强迫的SIR模型中,双Hopf分叉和混乱动态
João P S Maurício de Carvalho1
1Research on Economics, Management and Information Technologies, Prince Henry Portucalense University, Rua Dr. António Bernardino de Almeida 541, 4200-072, Porto, Portugal. jp.carvalho@upt.pt.
Scientific reports
|December 24, 2025
概括
这项研究分析了与病毒源接触的SIR模型,发现了复杂的流行病动态. 微小的参数变化可能导致不可预测的疾病传播,使控制具有挑战性.
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:
- 该SIR模型是一个基本的流行病学工具.
- 了解疾病动态需要分析传染率和环境因素.
- 定期强制模型可以表现出复杂的行为.
研究的目的:
- 分析具有直接病毒源传播的定期强制SIR模型.
- 在没有季节性的情况下,研究Hopf分叉和周期溶液.
- 在季节性的存在下,探索混乱和奇怪的吸引力的出现.
主要方法:
- 定期强制SIR模型的定性分析.
- 霍夫分叉分析用于研究平衡稳定性.
- 体破裂理论来证明混乱.
- 通过数值模拟支持的分析推导.
主要成果:
- 由于没有季节性,Hopf分叉导致吸引特定传输速率的周期性解决方案.
- 在季节性存在的情况下,模型表现出奇怪的吸引力,表明可观察到的混乱.
- 该系统对参数变化表现出敏感性,导致复杂的流行病动态.
结论:
- 具有病毒源传播的定期强制SIR模型可以显示复杂和不可预测的动态.
- 季节性可以诱导混乱的行为,使疾病控制工作复杂化.
- 分析和数值发现强调了流行病传播的复杂性质.
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