Epidemic dynamics prediction using fractional SIRD and deep learning.

Area of Science:

• Epidemiology
• Mathematical Biology
• Computational Science

Background:

• Traditional SIRD models often lack memory effects and detailed mortality tracking.
• Fractional calculus offers a framework to incorporate memory into epidemic dynamics.
• Accurate epidemic forecasting is crucial for public health interventions.

Purpose of the Study:

• To introduce and analyze a fractional-order SIRD epidemic model using the normalized Caputo-Fabrizio derivative.
• To incorporate memory effects and disease-induced mortality into the SIRD framework.
• To develop and validate a numerical scheme and integrate deep learning for enhanced prediction.

Main Methods:

• Development of a fractional-order SIRD model with a normalized Caputo-Fabrizio derivative.
• Establishment of existence, uniqueness, positivity, and population conservation properties.
• Implementation of a robust numerical scheme and deep neural network (DNN) for approximation.
• Simulation analysis to demonstrate the influence of memory parameters and kernel normalization.

Main Results:

• The fractional SIRD model with NCF derivative successfully incorporates memory effects and mortality.
• The numerical scheme proved robust, and the DNN accurately approximated fractional SIRD dynamics.
• Simulations highlighted the significance of memory parameters for epidemic forecasting.
• The integrated model achieved high predictive accuracy with low mean square error (0.00027) and root mean square error (<0.17).

Conclusions:

• The proposed fractional SIRD model provides a more comprehensive framework for understanding epidemic dynamics.
• The integration of fractional calculus and deep learning offers a powerful tool for accurate epidemic prediction.
• This approach yields valuable insights for public health decision-making and disease control strategies.