Logistic Wavelets and Their Application to Model the Spread of COVID-19 Pandemic

In the present paper, we model the cumulative number of persons, reported to be infected with COVID-19 virus, by a sum of several logistic functions (the so-called multilogistic function). We introduce logistic wavelets and describe their properties in terms of Eulerian numbers. Moreover, we implement the logistic wavelets into Matlab's Wavelet Toolbox and then we use the continuous wavelet transform (CWT) to estimate the parameters of the approximating multilogistic function. Using the examples of several countries, we show that this method is effective as a method of fitting a curve to existing data. However, it also has a predictive value, and, in particular, allows for an early assessment of the size of the emerging new wave of the epidemic, thus it can be used as an early warning method.

Automated summary

In this paper, we model the cumulative number of COVID-19 infections using a multilogistic function and logistic wavelets, implementing them into Matlab's Wavelet Toolbox. Through examples from several countries, we demonstrate the effectiveness of this method in fitting curves to existing data, as well as its predictive value and early warning capabilities regarding the size of new epidemic waves.