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Modeling the dynamics of COVID-19 using fractal-fractional operator with a case study.
Jian-Cun Zhou1,2, Soheil Salahshour3, Ali Ahmadian4,5
1College of Information and Electronic Engineering, Hunan City University, Yiyang 413000, PR China.
Results in Physics
|January 4, 2022
Summary
This study introduces a new Atangana-Baleanu fractional derivative model to analyze COVID-19 transmission dynamics. The fractal fractional approach provides insights into disease control strategies.
Area of Science:
- Epidemiology
- Mathematical Biology
- Fractional Calculus
Background:
- Coronavirus disease (COVID-19) poses a significant global health challenge.
- Understanding disease transmission dynamics is crucial for effective control.
- Fractional calculus offers advanced tools for modeling complex biological systems.
Purpose of the Study:
- To propose a novel mathematical model for COVID-19 transmission dynamics using the Atangana-Baleanu fractional derivative.
- To analyze the impact of various infection phases and transmission routes on disease spread.
- To investigate the influence of fractional and fractal orders on disease dynamics and control.
Main Methods:
- Formulation of the COVID-19 model using classical integer-order differential equations.
- Application of the Atangana-Baleanu fractal fractional derivative to create a fractional-order model.
- Analysis of basic model properties including equilibria and reproduction number.
- Introduction of a novel Adams-Bashforth fractal-fractional numerical method for iterative solutions.
- Graphical representation and numerical simulations to assess parameter impacts.
Main Results:
- The study presents a fractional-order COVID-19 model with arbitrary order and fractal dimension.
- Equilibria and stability of the model are analyzed.
- Numerical simulations demonstrate the impact of fractional orders on disease dynamics.
- Graphical results illustrate the influence of model parameters on transmission and control.
Conclusions:
- The Atangana-Baleanu fractional derivative provides a robust framework for modeling COVID-19 transmission.
- The fractal fractional approach offers valuable insights into disease mechanisms and control strategies.
- The findings can aid public health practitioners in developing effective interventions.
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