论文标题
在扩展的参数空间中流行病扩散：超临界尺度定律和亚临界阶段
Epidemic spreading in an expanded parameter space: the supercritical scaling laws and subcritical metastable phases
论文作者
论文摘要
到目前为止，冠状病毒2020年流行病数据的大多数分析一直集中在短时窗口上，因此目前缺乏对冠状病毒流行病的统计物理定律（CEWCM）的定量测试。在这里，我们报告了230天内CEWCM的定量分析，涵盖了第一次流行波浪的全职失效。我们使用3D相图跟踪双倍时间TD（T）和生殖数RT（T）的同时演变，以表明CEWCP的生物物理学需要此扩展的参数空间。我们已经证实，在超临界[rt（t）> 1，td（t）<40天] i）i）总受感染案件的曲线z（t）遵循称为奥斯特瓦尔德·法（Ostwald Law）的增长率； ii）加倍时间遵循指数定律td（t）= a exp（（（t-t-t0）/s）作为时间的函数和iii）幂律td（t）= c（rt（t）-1）^ - n通过指数n验证，取决于RT（t）的定义。在亚临界状态[TD（t）> 100天]中第二2020年流行病波揭开第二个2020流行波揭开的对数图图（t）与（rt-1），以RT> 1捕捉的可稳态阶段，其中TD（t）保持恒定，其爆炸及其在第一波的强力范围之后，其爆炸及其在第一波的强力法律之后，
So far most of the analysis of coronavirus 2020 epidemic data has been focusing on a short-time window and consequently a quantitative test of statistical physical laws of Coronavirus Epidemics with Containment Measures (CEwCM) is currently lacking. Here we report a quantitative analysis of CEwCM over 230 days, covering the full-time lapse of the first epidemic wave. We use a 3D phase diagram tracking the simultaneous evolution of the doubling time Td(t) and reproductive number Rt(t) showing that this expanded parameter space is needed for biological physics of CEwCP. We have verified that in the supercritical [Rt(t)>1, Td(t)<40 days] regime i) the curve Z(t) of total infected cases follows the growth rate called Ostwald law; ii) the doubling time follows the exponential law Td(t)=A exp((t-t0)/s) as a function of time and iii) the power law Td(t)=C(Rt(t)-1)^-n is verified with the exponent n depending on the definition of Rt(t). The log-log plots Td(t) versus (Rt-1) of the second 2020 epidemic wave unveil in the subcritical regime [Td(t)>100 days] arrested metastable phases with Rt>1 where Td(t) was kept constant followed by its explosion and its containment following the same power law as in the first wave
