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A robust study on 2019-nCOV outbreaks through non-singular derivative

Muhammad Altaf Khan1,2, Saif Ullah3, Sunil Kumar4

  • 1Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam.

European Physical Journal Plus
|February 8, 2021
PubMed

Insights

This study introduces a novel fractional mathematical model for COVID-19 dynamics using the Atangana-Baleanu derivative. The model helps understand disease transmission and control strategies, emphasizing the importance of memory effects.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Fractional Calculus

Background:

  • The global impact of the COVID-19 pandemic necessitates advanced modeling approaches.
  • Existing models may not fully capture the complex dynamics and memory effects inherent in disease transmission.

Purpose of the Study:

  • To develop and analyze a new fractional mathematical model for COVID-19.
  • To investigate the influence of memory effects and model parameters on disease transmission and control.
  • To establish the global asymptotic stability of the disease-free equilibrium.

Main Methods:

  • Formulation of an integer-order model and its generalization using the Atangana-Baleanu fractional derivative with a non-singular kernel.
  • Analysis of essential mathematical properties of the fractional model.
  • Application of a nonlinear fractional Lyapunov function for stability analysis.
  • Numerical solution using an efficient modified Adams-Bashforth scheme.

Main Results:

  • The study presents a generalized fractional model for COVID-19 dynamics.
  • Demonstration of the global asymptotic stability at the disease-free equilibrium.
  • Numerical simulations highlight the impact of the memory index and model parameters on infection spread and control.

Conclusions:

  • The developed Atangana-Baleanu fractional model provides deeper insights into COVID-19 transmission dynamics.
  • The memory index plays a crucial role in understanding and managing the pandemic.
  • The findings support the development of effective control strategies for infectious diseases.

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