Logistic wavelets and logistic function: An application to model the spread of SARS-CoV-2 virus infections

Abstract

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.