  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.
