A computational supervised neural network procedure for the fractional SIQ mathematical model

Area of Science:

• Mathematical modeling
• Epidemiology
• Artificial Intelligence

Background:

• Fractional calculus offers a more accurate approach to modeling complex dynamical systems.
• Understanding the impact of interventions like lockdowns on disease spread is crucial.

Purpose of the Study:

• To provide accurate numerical solutions for the fractional susceptible, infected, and quarantine (SIQ) model.
• To investigate the effects of lockdown measures on disease dynamics.
• To apply artificial intelligence techniques for solving the fractional SIQ model.

Main Methods:

• Utilized fractional-order derivatives to solve nonlinear SIQ differential models.
• Employed an artificial intelligence approach with the scale conjugate gradient (AI-SCG) design.
• Trained, validated, and tested the AI-SCG model with specific data percentages (82% train, 7% validation, 11% test).

Main Results:

• Achieved accurate and realistic numerical solutions for the fractional SIQ model.
• Demonstrated the effectiveness of the AI-SCG method by comparing results with Adam solutions.
• Validated the AI-SCG solver's performance using error histograms, state transition measures, and regression values.

Conclusions:

• The AI-SCG method provides a reliable and efficient approach for solving fractional dynamical systems.
• Fractional SIQ models with lockdown effects offer a more precise representation of disease spread.
• The study validates the use of AI in epidemiological modeling for public health insights.