Computational modeling of fractional COVID-19 model by Haar wavelet collocation Methods with real data

Area of Science:

• Epidemiology
• Mathematical Biology
• Computational Science

Background:

• The Omicron variant of SARS-CoV-2 presents unique transmission dynamics.
• Fractional-order differential equations offer a more nuanced approach to modeling disease spread.
• Accurate modeling is crucial for effective public health interventions.

Purpose of the Study:

• To develop and analyze a fractional-order COVID-19 model incorporating Omicron variant characteristics.
• To employ the Haar wavelet collocation method for precise numerical solutions.
• To provide data-driven insights for mitigating the impact of the Omicron variant.

Main Methods:

• Utilizing fractional derivatives in the Caputo sense for the COVID-19 epidemic model.
• Establishing the existence and uniqueness of the model solutions via fixed-point theory.
• Applying the Haar wavelet collocation method for numerical simulations and parameter estimation.
• Conducting sensitivity analysis to identify key model parameters.

Main Results:

• The study successfully simulated the spread dynamics of the Omicron variant.
• The Haar wavelet collocation method proved efficient and accurate for the fractional model.
• Sensitivity analysis identified critical parameters influencing virus transmission.
• Parameter estimation was performed using real-world COVID-19 data from India.

Conclusions:

• Fractional-order models provide valuable insights into SARS-CoV-2 variant transmission.
• Numerical simulations aid in understanding epidemic dynamics and informing public health policy.
• The Haar wavelet method is a robust tool for analyzing complex epidemiological models.