AI 中文总结
该研究针对有限种群SIS和SIR模型，发现不同群体规模分布的相关矩重合时会产生等价动力学，仅高阶机制可区分，这为流行病推断设定了固有局限。
AI 中文摘要
临时群体间的传播并不一定在总体流行病数据中保留群体规模分布的完整信息。我们证明，在有限种群的SIS和SIR模型中，群体规模分布仅通过由非线性传播核阶数选定的有限组矩进入动力学。因此，当相关矩重合时，明显不同的分布可产生相同的随机动力学。这种等价性延伸至暂态演化、涨落、灭绝时间统计以及最终暴发规模。在确定性极限下，一阶矩设定入侵阈值，而二阶矩控制转变的性质以及双稳态和滞后现象的出现。仅当更高阶传播机制激活其首个未匹配矩时，两种分布才变得可区分；即使是微弱的额外通道也能移动相边界，使系统处于不同动力学状态。主方程的解和随机模拟支持这些分析预测。这些结果确立了流行病推断的固有局限：单一总体动力学协议仅能识别群体规模分布的等价类，而非唯一重构完整分布。
英文摘要
Transmission through temporary groups does not necessarily preserve complete information about the group-size distribution in aggregate epidemic data. We show that, in finite-population SIS and SIR models, the group-size distribution enters the dynamics only through a finite set of moments selected by the order of the nonlinear transmission kernel. Consequently, markedly different distributions can generate identical stochastic dynamics when their relevant moments coincide. This equivalence extends to transient evolution, fluctuations, extinction-time statistics, and final outbreak sizes. In the deterministic limit, the first moment sets the invasion threshold, whereas the second controls the nature of the transition and the emergence of bistability and hysteresis. The two distributions become distinguishable only when a higher-order transmission mechanism activates their first unmatched moment; even a weak additional channel can shift the phase boundary and place the systems in different dynamical regimes. Solutions of the master equation and stochastic simulations support these analytical predictions. These results establish an intrinsic limit on epidemic inference: a single aggregate dynamical protocol can identify only an equivalence class of group-size distributions, rather than uniquely reconstructing the full distribution.
Comments17 pages, 6 figures
