Diffusion-reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19,...

Area of Science:

• Epidemiology
• Mathematical Biology
• Continuum Mechanics

Background:

• The COVID-19 pandemic highlighted the need for advanced epidemic modeling.
• Compartmental models are widely used but can be complex to interpret.
• Existing models often lack a unified theoretical framework.

Purpose of the Study:

• To propose a novel formulation of compartmental epidemic models using partial differential equations (PDEs).
• To interpret these models through the lens of continuum mechanics, employing balance and compatibility principles.
• To apply this framework to a COVID-19 compartmental PDE model and analyze its properties.

Main Methods:

• Formulation of compartmental models using partial differential equations (PDEs).
• Application of continuum mechanics concepts (balance, compatibility, constitutive relations).
• Mathematical analysis including stability and sensitivity assessments.
• Numerical simulations to validate model predictions.

Main Results:

• A new PDE-based framework for compartmental epidemic modeling was established.
• The framework provides a physically intuitive interpretation of epidemic dynamics.
• Mathematical analysis revealed key stability and parameter sensitivity insights for a COVID-19 model.
• Numerical simulations supported the theoretical findings.

Conclusions:

• The continuum mechanics-based PDE formulation offers a valuable new perspective on compartmental epidemic models.
• This approach enhances understanding and facilitates interdisciplinary collaboration in epidemic research.
• The developed COVID-19 model provides a robust tool for analyzing disease dynamics and informing public health strategies.