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

Abstract

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.

Reconstruction of Epidemiological Data in Hungary Using Stochastic Model Predictive Control

“…where µ u k are free decision variables and K is (not necessarily a closed-form) function of the expected state. Thus, the control input is inherently a random variable and is normally distributed as the state (11) itself is approximated by a Gaussian. If Σ xθ k = (Σ θx k ) denotes the covariance between xk and θk , the joint distribution of xk , ûk , and θk is:…”

“…Due to the rapidly increasing computing power, agent-based models have also become popular for modeling epidemics and studying control possibilities [9,10]. Logistic wavelets were used in [11] to compute the possible cumulative number of people infected with COVID. The application of artificial intelligence and machine learning has also been successful in COVID-related modeling and prediction [12][13][14].…”

A Generalized Logistic Function and Its Applications

“…are described in [19]. We will use them here as well, but multiplied by appropriate factor so that their norms in the space L 2 (R) are equal to 1.…”

“…Then, based on (12), we can redefine, with respect to [19], the logistic mother wavelet ψ n (t) of order n = 2, 3, . .…”

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In this paper we deal with the logistic wavelets introduced in [19]. We modify them by multiplying by appropriate coefficients so that their norm in the space L 2 (R) is equal to 1.

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