Stability analysis and numerical simulation of nonlocal extended epidemic models using positivity-preserving scheme

Area of Science:

• Mathematical Biology
• Computational Epidemiology
• Numerical Analysis

Background:

• Epidemic modeling is crucial for understanding disease spread.
• Traditional models often simplify spatial-temporal dynamics.
• Fractional calculus offers a powerful tool to capture complex disease transmission patterns.

Purpose of the Study:

• To develop a robust numerical framework for nonlocal extended epidemic models with fractional diffusion.
• To investigate the impact of fractional diffusion on disease transmission dynamics.
• To provide a computational tool for public health policy and epidemic control.

Main Methods:

• Fourier spectral approach for spatial discretization.
• Positivity-preserving exponential time differencing for temporal integration.
• Analysis of SIR and SEIR fractional epidemic models.

Main Results:

• The numerical scheme is L-stable and positivity-preserving.
• Fractional diffusion significantly influences the spatial distribution and temporal evolution of diseases.
• The developed method achieves second-order accuracy.

Conclusions:

• Fractional diffusion plays a critical role in epidemic modeling.
• The proposed numerical framework is effective for simulating complex disease dynamics.
• This research provides a foundation for future studies in public health and epidemic control.