Falcó Carles, Corral Álvaro
Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, E-08193 Barcelona, Spain.
Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, E-08193 Barcelona, Spain.
Phys Rev E. 2022 Jun;105(6-1):064122. doi: 10.1103/PhysRevE.105.064122.
Epidemics unfold by means of a spreading process from each infected individual to a variable number of secondary cases. It has been claimed that the so-called superspreading events of the COVID-19 pandemic are governed by a power-law-tailed distribution of secondary cases, with no finite variance. Using a continuous-time branching process, we demonstrate that for such power-law-tailed superspreading, the survival probability of an outbreak as a function of both time and the basic reproductive number fulfills a "finite-time scaling" law (analogous to finite-size scaling) with universal-like characteristics only dependent on the power-law exponent. This clearly shows how the phase transition separating a subcritical and a supercritical phase emerges in the infinite-time limit (analogous to the thermodynamic limit). We also quantify the counterintuitive hazards posed by this superspreading. When the expected number of infected individuals is computed removing extinct outbreaks, we find a constant value in the subcritical phase and a superlinear power-law growth in the critical phase.
流行病通过从每个感染者传播到数量可变的二代病例的过程展开。有人声称，新冠疫情中所谓的超级传播事件受二代病例的幂律尾部分布支配，方差无界。我们使用连续时间分支过程证明，对于这种幂律尾的超级传播，疫情的存活概率作为时间和基本再生数的函数，满足一个“有限时间标度”定律（类似于有限尺寸标度），具有仅依赖于幂律指数的类普适特征。这清楚地表明了在无限时间极限（类似于热力学极限）下，区分亚临界和超临界阶段的相变是如何出现的。我们还对这种超级传播带来的反直觉风险进行了量化。当去除灭绝疫情来计算感染个体的预期数量时，我们发现在亚临界阶段有一个恒定值，而在临界阶段有超线性幂律增长。
