复杂网络上非马尔可夫流行病中的极端爆发
Extreme outbreaks in non-Markovian epidemics on complex networks
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中文总结 AI 辅助
研究复杂网络非马尔可夫流行病极端爆发风险，通过映射非马尔可夫SIR动力学为有效马尔可夫描述来确定爆发规模分布，能纳入任意感染和恢复时间统计，为网络级极端爆发风险定量预测提供途径。
中文摘要 AI 辅助
极端疫情风险由爆发规模分布的右尾控制，但对于网络上的非马尔可夫传播，这种分布通常未知。在此，我们通过将非马尔可夫SIR动力学映射到有效的马尔可夫描述来确定此分布。我们表明，任意感染和恢复时间统计可以通过单个边传播率纳入，产生一个有效的马尔可夫过程，该过程再现了完整的爆发规模统计。对于弱异质网络，简化产生了一个由键渗流繁殖数控制的通用充分混合半经典理论。不同等待时间分布和拓扑结构的爆发统计数据汇聚到一条预测曲线上。对于高度异质和经验网络，网络上相应的有效马尔可夫动力学捕获了完整分布。我们的结果提供了一条从测量的等待时间分布到网络级极端爆发风险定量预测的直接途径。
英文摘要
Extreme epidemic risk is controlled by the right tail of the outbreak-size distribution, but this distribution is generally unknown for non-Markovian spreading on networks. Here we determine this distribution by mapping non-Markovian SIR dynamics to an effective Markovian description. We show that arbitrary infection and recovery time statistics can be incorporated through a single edge transmissibility, yielding an effective Markovian process that reproduces the full outbreak-size statistics. For weakly heterogeneous networks, the reduction yields a universal well-mixed semiclassical theory governed by the bond-percolation reproductive number. Outbreak statistics across diverse waiting-time distributions and topologies collapse onto one predictive curve. For highly heterogeneous and empirical networks, the corresponding effective Markovian dynamics on the network captures the complete distribution. Our results provide a direct route from measured waiting-time distributions to quantitative predictions of network-level extreme-outbreak risk.
