流行病动态与非马科夫感染过程在超人口网络中的流行病动态
Yuan-Hao Xu1, Lele Zhang2, Wei Zhu3
1University of Science and Technology of China, School of Engineering Science, Hefei 230026, People's Republic of China.
Physical review. E
|December 23, 2025
概括
这项研究引入了一个非马科夫SIRS模型,用于在超人口网络中传播流行病. 非马科维感染过程显著改变了流行病的动态,减少了流动性.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 网络科学 网络科学
背景情况:
- 传统的流行病模型通常假定马科维的过程,忽视了时间依赖的传染性.
- 超人口网络和反复的移动模式对于了解疾病传播至关重要.
- 反映真实世界感染动态的非马科夫过程需要先进的建模方法.
研究的目的:
- 开发一种反应-扩散SIRS流行病模型,将非马科维感染过程纳入超人口网络.
- 调查依赖时间的传染性和反复的流动性对流行病传播的影响.
- 从理论上推导出流行病爆发条件,并分析它们对模型参数的依赖性.
主要方法:
- 构建一个非马科夫感染的反应-扩散SIRS模型.
- 使用生成时间分布推导感染率函数.
- 将经常性流动模式纳入一个超人口框架.
- 应用利亚普诺夫稳定性分析来确定流行病爆发条件.
主要成果:
- 非马科维亚感染的特征显著改变了短暂的流行病传播,即使基本的繁殖数量相同.
- 在非马科夫过程中,二次病例生成的平均时间增加减少了流动性对短暂动态的影响.
- 当人口分布高度不对称时,流动性可以抑制流行病的传播.
结论:
- 现实世界非马科维亚感染过程在塑造流行病爆发动态方面发挥着关键作用.
- 了解这些非马科夫效应对于准确的流行病预测和控制至关重要.
- 该模型提供了关于感染持续时间,流动性和疾病在复杂网络中的传播之间的相互作用的见解.
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