Investigation of a time-fractional COVID-19 mathematical model with singular kernel

Area of Science:

• Mathematical Biology
• Fractional Calculus
• Epidemiology

Background:

• Mathematical models are crucial for understanding infectious disease dynamics.
• Fractional calculus offers a more nuanced approach to modeling complex phenomena like disease spread.
• Previous models often use integer-order derivatives, potentially missing finer dynamic details.

Purpose of the Study:

• To investigate the fractional dynamics of a coronavirus mathematical model using the Caputo derivative.
• To develop and validate approximate analytical solutions for the fractional model.
• To assess the existence, uniqueness, and stability of the model's solutions.

Main Methods:

• Application of Laplace-Adomian decomposition and Homotopy perturbation techniques for approximate series solutions.
• Utilizing the Banach fixed-point theorem to establish existence and uniqueness of solutions.
• Investigating Ulam-Hyers-type stability for the fractional coronavirus model.

Main Results:

• Approximate series solutions were successfully obtained for the fractional coronavirus model.
• The existence, uniqueness, and stability of the solutions were rigorously demonstrated.
• Comparisons between approximate solutions, numerical simulations, and real-world data showed strong agreement across various fractional orders.

Conclusions:

• Fractional calculus provides a powerful framework for modeling coronavirus dynamics with enhanced accuracy.
• The applied analytical techniques effectively approximate the complex behavior of the fractional model.
• The study validates the use of fractional-order models in epidemiological research, showing good agreement with integer-order models and real data.