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$Multifractal Spectrum Analysis for Assessing Pulmonary Nodule Malignancy$

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A study on fractional COVID-19 disease model by using Hermite wavelets.

Sunil Kumar^1,2, Ranbir Kumar¹, Shaher Momani^2,3

¹Department of Mathematics National Institute of Technology Jamshedpur Jharkhand India.

Mathematical Methods in the Applied Sciences

|April 6, 2021

Summary

This study reveals the speed characteristics of the COVID-19 outbreak in India using a novel wavelet-based approach. The findings offer insights into the dynamics of the novel coronavirus pandemic.

Keywords:

Caputo derivative Hermite wavelets convergence analysis coronavirus mathematical model operational matrix

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Area of Science:

Epidemiology
Mathematical Modeling
Computational Science

Background:

The COVID-19 pandemic, caused by the novel coronavirus, significantly impacted India starting January 2020.
By October 2020, India recorded over 7 million cases and 109,000 deaths, with a substantial number of active infections.

Purpose of the Study:

To determine the speed characteristics of the ongoing COVID-19 outbreak in India.
To analyze the behavior of a fractional-order COVID-19 model using advanced mathematical techniques.

Main Methods:

Utilized Hermite wavelets basis for solving the COVID-19 model with a time-arbitrary Caputo derivative.
Employed an operational matrix with a collocation scheme to convert differential equations into algebraic equations.
Applied a corrector scheme to solve the distinct-value arbitrary-order COVID-19 model.

Main Results:

Investigated various behaviors of the arbitrary-order COVID-19 system, comparing results with existing methods.
Illustrated the dynamics of susceptible, exposed, infected, and recovered individuals across different fractional orders.
Validated the proposed model through numerical simulations and wavelet-based results.

Conclusions:

The Hermite wavelet method effectively models the dynamics of the COVID-19 outbreak.
The study provides valuable insights into the speed and behavior of the pandemic using fractional calculus.
The findings contribute to understanding disease transmission dynamics and can inform public health strategies.