New applications related to Covid-19

Area of Science:

• Epidemiology
• Mathematical Biology
• Dynamical Systems

Background:

• Mathematical models are crucial for understanding COVID-19 dynamics.
• Existing models often use standard derivatives, potentially limiting their ability to capture complex disease behaviors.

Purpose of the Study:

• To analyze a novel COVID-19 mathematical model incorporating fractal-fractional derivatives.
• To investigate the equilibria and stability of the proposed model.
• To provide numerical simulations for validating the model's predictions.

Main Methods:

• Development of a COVID-19 model utilizing fractal-fractional derivatives.
• Analysis of the model's equilibrium points.
• Conducting a detailed stability analysis of the equilibria.
• Application of an effective numerical method for simulation.

Main Results:

• The study successfully analyzed the equilibria of the fractal-fractional COVID-19 model.
• Detailed stability analysis was performed, providing insights into disease dynamics.
• Numerical simulations demonstrated the model's behavior and validated the analytical findings.

Conclusions:

• The fractal-fractional derivative approach offers a valuable framework for modeling COVID-19.
• The analysis of equilibria and stability provides a deeper understanding of disease transmission.
• Numerical simulations confirm the utility of the proposed mathematical model.