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On nonlinear classical and fractional order dynamical system addressing COVID-19
Kamal Shah1, Rahim Ud Din1, Wejdan Deebani2
1Department of Mathematics, University of Malakand, Chakdara, Dir(L), KPK, Pakistan.
Results in Physics
|March 29, 2021
Summary
This study introduces a new mathematical model for SARS-CoV-2, analyzing how factors like immigration and protection impact disease spread. The model uses fractional calculus to explore epidemic dynamics and stability.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Modeling
Background:
- SARS-CoV-2 (Severe Acute Respiratory Syndrome Coronavirus 2) poses a significant global health challenge.
- Mathematical models are crucial for understanding and predicting infectious disease dynamics.
Purpose of the Study:
- To develop and analyze a novel SEIR (Susceptible-Exposed-Infected-Recovered) mathematical model for SARS-CoV-2.
- To investigate the influence of various parameters on disease transmission and population dynamics.
- To explore the application of fractional calculus in epidemic modeling.
Main Methods:
- Development of a compartmental SEIR model with four classes: susceptible, exposed, infected, and recovered.
- Analysis of local stability using the Jacobian matrix and basic reproduction number.
- Determination of global stability via Lyapunov function theory.
- Numerical interpretation using a fractional-order nonstandard finite difference (NSFD) scheme.
Main Results:
- Identification of key factors affecting SARS-CoV-2 spread, including immigration, protection measures, death rates, and population interactions.
- Calculation of the basic reproduction number and assessment of local and global stability.
- Demonstration of numerical solutions for the fractional-order model.
Conclusions:
- The proposed SEIR model provides insights into SARS-CoV-2 transmission dynamics.
- Fractional calculus offers a valuable framework for analyzing complex epidemic behaviors.
- The study highlights the importance of considering various epidemiological parameters for effective disease control strategies.
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