论文标题
逻辑小波和逻辑功能：建模SARS-COV-2病毒感染传播的应用
Logistic wavelets and logistic function: An application to model the spread of SARS-CoV-2 virus infections
论文作者
论文摘要
在本文中，我们通过一系列logistic函数的总和对据报道被SARS-COV-2病毒感染的人累积数量。对于给定的逻辑函数，使用Eulerian数字，我们找到了其连续的导数的零及其与此功能的饱和水平的关系。在给定的时间序列中，具有潜在的逻辑趋势，我们使用其第二个差异来确定与这些零相对应的点。为了估计近似logistic函数的参数，我们定义和使用逻辑小波。然后，我们将该理论应用于美国和英国的SARS-COV-2感染案例。
In the present paper, we model the cumulative number of persons reported to be infected by the SARS-CoV-2 virus, in a country or a region, by a sum of logistic functions. For a given logistic function, using Eulerian numbers, we find the zeros of its successive derivatives and their relationship with the saturation level of this function. In a given time series, having potentially the logistic trend, we use its second differences to determine points corresponding to these zeros. To estimate the parameters of the approximating logistic function, we define and use logistic wavelets. Then we apply the theory to the cases of SARS-CoV-2 infections in the United States and the United Kingdom.
