两步传染模型中的两个黄金时间
Two golden times in two-step contagion models
摘要：
两步传染模型是一个简单的玩具模型，用于理解现实世界中发生的流行病爆发。该模型考虑到易感者在接触传染性疾病时要么立即被感染，要么变得虚弱。随着身体虚弱的人数增加，他们最终会在短时间内被感染，并发生大流行病爆发。达到这种大流行爆发所需的时间允许进行干预，通常被称为黄金时间。了解黄金时间的规模依赖性对控制流行病爆发是有用的。我们发现两步传染模型中存在两类黄金时间，分别为$O(N^{1/3})$和$O(N^ζ)$，其系统规模为$N$，其中测量的$ζ$略大于$1/4$ .它们分别通过感染节点的初始数量$o(N)$和$O(N)$来区分。虽然黄金时间的$N$依赖性的指数$1/3$是普遍的，即使在其他模型中显示由级联动力学引起的不连续跃迁，测量的$ζ$指数都接近$1/4$，但显示模型依赖性。$ζ$是否在渐近大- $N$限度内降低至$1/4$，这一点仍然是未知的。
英文摘要：
The two-step contagion model is a simple toy model for understanding pandemic outbreaks that occur in the real world. The model takes into account that a susceptible person either gets immediately infected or weakened when getting into contact with an infectious one. As the number of weakened people increases, they eventually can become infected in a short time period and a pandemic outbreak occurs. The time required to reach such a pandemic outbreak allows for intervention and is often called golden time. Understanding the size-dependence of the golden time is useful for controlling pandemic outbreak. Here we find that there exist two types of golden times in the two-step contagion model, which scale as $O(N^{1/3})$ and $O(N^ζ)$ with the system size $N$ on Erdős-Rényi networks, where the measured $ζ$ is slightly larger than $1/4$. They are distinguished by the initial number of infected nodes, $o(N)$ and $O(N)$, respectively. While the exponent $1/3$ of the $N$-dependence of the golden time is universal even in other models showing discontinuous transitions induced by cascading dynamics, the measured $ζ$ exponents are all close to $1/4$ but show model-dependence. It remains open whether or not $ζ$ reduces to $1/4$ in the asymptotically large-$N$ limit.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
