Normalized Gompertz wavelets and their application

TL;DR

This paper introduces Gompertz wavelets, proves their mathematical properties, and applies them to analyze Covid-19 spread in Saudi Arabia using Matlab implementation.

Contribution

It defines and analyzes Gompertz wavelets, providing explicit normalization formulas and demonstrating their practical application in pandemic modeling.

Findings

Gompertz wavelets satisfy admissibility conditions.

Explicit normalization formulas involve Bernoulli numbers.

Applied to Covid-19 data in Saudi Arabia with successful results.

Abstract

In the present paper, we define the Gompertz wavelets and show their basic properties. In particular, we prove that the admissibility condition holds for them. We also compute the normalizing factors in the space of square intergrable functions $L^{2}(\mathbb{R})$ and present an explicit formula for them in terms of the Bernoulli numbers. Then, after implementing the second-order Gompertz wavelets into Matlab's Wavelet Toolbox, we apply them to study the spread of the Covid-19 pandemic in Saudi Arabia.