Macroscopic growth laws describe in an effective way the underlying complex dynamics of the spreading of infections, as in the case of Covid-19, where the counting of the cumulative number [Formula: see text] of detected infected individuals is a generally accepted variable to understand the epidemic phase. However, [Formula: see text] does not take into account the unknown number of asymptomatic cases [Formula: see text]. The considered model of Covid-19 spreading is based on a system of coupled differential equations, which include the dynamics of the spreading among symptomatic and asymptomatic individuals and the strong containment effects due to the social isolation. The solution has been compared with [Formula: see text], determined by a single differential equation with no explicit reference to [Formula: see text], showing the equivalence of the two methods. The model is applied to Covid-19 spreading in Italy where a transition from an exponential behavior to a Gompertz growth for [Formula: see text] has been observed in more recent data. The information contained in the time series [Formula: see text] turns out to be reliable to understand the epidemic phase, although it does not describe the total infected population. The asymptomatic population is larger than the symptomatic one in the fast growth phase of the spreading.

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宏观法律如何描述复杂的动态：无症状人群和 Covid-19 传播

宏观增长规律有效地描述了感染传播的潜在复杂动态，例如 Covid-19，其中检测到的受感染个体的累积数量 [公式：见文本] 的计数是普遍接受的变量了解流行阶段。但是，【公式：见正文】没有考虑到未知数量的无症状病例【公式：见正文】。所考虑的 Covid-19 传播模型基于耦合微分方程系统，其中包括有症状和无症状个体之间的传播动态以及由于社会隔离而产生的强烈遏制效应。解决方案已与 [公式：参见文本] 进行比较，由单个微分方程确定，没有明确参考 [公式：参见文本]，显示两种方法的等价性。该模型应用于在意大利传播的 Covid-19，在最近的数据中观察到 [公式：见文本] 从指数行为到 Gompertz 增长的转变。时间序列 [公式：见正文] 中包含的信息被证明对于理解流行阶段是可靠的，尽管它没有描述总感染人口。在传播的快速增长阶段，无症状人群大于有症状人群。尽管它没有描述受感染的总人口。在传播的快速增长阶段，无症状人群大于有症状人群。尽管它没有描述受感染的总人口。在传播的快速增长阶段，无症状人群大于有症状人群。