论文标题
如何减少控制流行病的流行峰
How to reduce epidemic peaks keeping under control the time-span of the epidemic
论文作者
论文摘要
针对COVID-19的流行病的措施的主要挑战之一是在不增加其时间尺度的情况下增加流行峰的幅度。我们使用SIR模型进行流行动态调查了这个问题，为此，仅以增加其出现的时间$ t_p $的价格，才能减少流行峰值$ I_P $。通过时间重新训练，我们将SIR动力学的方程式线性线性化。这使我们能够通过降低感染率$α$并将删除率$β$增加$λ$来确切解决时间域中的动态，并得出大小，时间表和流行速度的缩放行为。我们表明，对于给定尺寸的给定价值（$ i_p $，总计，$ i_e $和平均$ \ hat i_p $受感染的数量），其出现时间$ t_p $和整个时间跨度$ t_e $可以通过因子$ 1/λ$减少，如果减少$ i $通过增加拆除率而不是减少感染率，则可以减少$ 1/λ$。因此，基于追踪的流行遏制措施，与基于社会距离的人相比，迅速隔离感染者的及早检测更有效。我们将结果应用于意大利北部的Covid-19-19。我们表明，峰值时间$ t_p $和整个时间跨度$ t_e $可能会减少$ 0.9 \ le 1/λ\ le 0.34 $，其中包含量的措施旨在增加$β$，而不是减少$α$。
One of the main challenges of the measures against the COVID-19 epidemic is to reduce the amplitude of the epidemic peak without increasing without control its timescale. We investigate this problem using the SIR model for the epidemic dynamics, for which reduction of the epidemic peak $I_P$ can be achieved only at the price of increasing the time $t_P$ of its occurrence and its entire time-span $t_E$. By means of a time reparametrization we linearize the equations for the SIR dynamics. This allows us to solve exactly the dynamics in the time domain and to derive the scaling behaviour of the size, the timescale and the speed of the epidemics, by reducing the infection rate $α$ and by increasing the removal rate $β$ by a factor of $λ$. We show that for a given value of the size ($I_P$, the total, $I_E$ and average $\hat I_P$ number of infected), its occurrence time $t_P$ and entire time-span $t_E$ can be reduced by a factor $1/λ$ if the reduction of $I$ is achieved by increasing the removal rate instead of reducing the infection rate. Thus, epidemic containment measures based on tracing, early detection followed by prompt isolation of infected individuals are more efficient than those based on social distancing. We apply our results to the COVID-19 epidemic in Northern Italy. We show that the peak time $t_P$ and the entire time span $t_E$ could have been reduced by a factor $0.9 \le 1/λ\le 0.34$ with containment measures focused on increasing $β$ instead of reducing $α$.
