While the mathematical laws of uncontrolled epidemic spreading are well known, the statistical physics of coronavirus epidemics with containment measures is currently lacking. The modelling of available data of the first wave of the Covid-19 pandemic in 2020 over 230 days, in different countries representative of different containment policies is relevant to quantify the efficiency of these policies to face the containment of any successive wave. At this aim we have built a 3D phase diagram tracking the simultaneous evolution and the interplay of the doubling time, T _d, and the reproductive number, R _t measured using the methodological definition used by the Robert Koch Institute. In this expanded parameter space three different main phases, supercritical, critical and subcritical are identified. Moreover, we have found that in the supercritical regime with R _t > 1 the doubling time is smaller than 40 days. In this phase we have established the power law relation between T _d and (R _t − 1)^−ν with the exponent ν depending on the definition of reproductive number. In the subcritical regime where R _t < 1 and T _d > 100 days, we have identified arrested metastable phases where T _d is nearly constant.

虽然不受控制的流行病传播的数学规律是众所周知的，但目前缺乏控制措施的冠状病毒流行的统计物理学。在代表不同遏制政策的不同国家，对 2020 年第一波 Covid-19 大流行的可用数据进行建模，该模型代表不同的遏制政策，这与量化这些政策面对任何连续波遏制的效率有关。为此，我们构建了一个 3D 相图，用于跟踪倍增时间T _d和再生数R _t的同时演化和相互作用，使用罗伯特科赫研究所使用的方法学定义进行测量。在这个扩展的参数空间中，三个不同的主要阶段， 确定了超临界、临界和亚临界。此外，我们发现在R _t > 1 的超临界状态下，倍增时间小于 40 天。在这个阶段，我们建立了T _d和 ( R _t − 1) ^{− ν}之间的幂律关系，其中指数ν取决于再生数的定义。在R _t < 1 和T _d > 100 天的亚临界状态中，我们已经确定了停滞的亚稳相，其中T _d 几乎是恒定的。