On quasi-linear reaction diffusion systems arising from compartmental SEIR models.

Area of Science:

• Mathematical Biology
• Epidemiology
• Reaction-Diffusion Systems

Background:

• Investigates quasi-linear reaction-diffusion systems from infectious disease compartmental models.
• Previous work assumed uniform diffusion rates, avoiding degeneracy.
• The current model features diffusion dependent on total population, leading to potential degeneracy.

Purpose of the Study:

• To analyze global existence and boundedness of solutions for degenerate quasi-linear reaction-diffusion systems.
• To remove the assumption of uniform diffusion rates present in prior analyses.
• To extend the applicability of mathematical methods to a broader range of models.

Main Methods:

• Utilizes a recently developed $$-energy method.
• Focuses on mathematical analysis of reaction-diffusion systems.
• Applies techniques to address degeneracy in diffusion terms.

Main Results:

• Demonstrates global existence and boundedness of solutions.
• Successfully removes the assumption of uniform diffusion rates.
• Establishes a robust analytical framework for degenerate systems.

Conclusions:

• The $$-energy method provides a powerful tool for analyzing degenerate quasi-linear reaction-diffusion systems.
• The findings are applicable to a wider class of models and boundary conditions.
• Advances the mathematical understanding of infectious disease spread models.