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

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.