Abstract A number of particles in a multiplying medium under rather general conditions is asymptotically exponential with respect to time t with the parameter λ, i.e., with the index of power λ ⁢ t {\lambda t} . If the medium is random, then the parameter λ is the random variable. To estimate the temporal asymptotics of the mean particles number (via the medium realizations), it is possible to average the exponential function via the corresponding distribution. Assuming that this distribution is Gaussian, the super-exponential estimate of the mean particle number could be obtained and expressed by the exponent with the index of power t ⁢ E ⁢ λ + t 2 ⁢ D ⁢ λ 2 {t{\rm E}\lambda+t^{2}{\rm D}\frac{\lambda}{2}} . The application of this new formula to investigation of the COVID-19 pandemic is performed.

中文翻译：

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COVID-19 大流行（全球）中部分超指数增长率的数值统计调查

摘要 在相当一般的条件下，倍增介质中的许多粒子相对于时间 t 呈渐近指数，参数为 λ，即幂指数为 λ ⁢ t {\lambda t} 。如果介质是随机的，则参数 λ 是随机变量。为了估计平均粒子数的时间渐近（通过介质实现），可以通过相应的分布平均指数函数。假设这个分布是高斯分布，可以得到平均粒子数的超指数估计，并用幂指数 t ⁢ E ⁢ λ + t 2 ⁢ D ⁢ λ 2 {t{\rm E} \lambda+t^{2}{\rm D}\frac{\lambda}{2}} 。执行了此新公式在 COVID-19 大流行调查中的应用。