Epidemic modeling with heterogeneity and social diffusion.

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• Classic Susceptible-Infectious-Recovered/Removed (SIR)-like models lack dynamic heterogeneity in infection risk.
• Emerging infectious diseases, such as COVID-19, exhibit non-canonical dynamics not fully explained by traditional models.

Purpose of the Study:

• To propose and analyze a family of epidemiological models extending SIR-like frameworks to include dynamic heterogeneity in infection risk.
• To investigate how individual behavior and susceptibility influence epidemic trajectories.
• To provide a modeling framework for understanding complex infectious disease dynamics.

Main Methods:

• Developed a system of reaction-diffusion equations coupled with a Fokker-Planck type equation.
• Incorporated macroscopic compartments (S, I, R) and a microscopic variable for the distribution of susceptible individuals' behavior.
• Derived a simplified system of ordinary differential equations by seeking self-similar solutions.

Main Results:

• Proved mathematical properties of the reaction-diffusion system, including convergence to equilibrium.
• The simplified system captures classic SIR dynamics plus the average risk level of the susceptible population.
• Observed rich dynamical behaviors like plateaus, shoulders, rebounds, and oscillations in epidemic curves.

Conclusions:

• The proposed models offer a more nuanced understanding of epidemic spread by accounting for dynamic risk heterogeneity.
• This framework can help interpret non-canonical dynamics observed in emerging infectious diseases.
• The models provide insights into how behavioral changes impact disease transmission and population-level outcomes.