A social structure description of epidemics propagation with the mean field game paradigm

TL;DR

This paper models epidemic spread using a mean field game approach that incorporates social structure and individual decision-making, analyzing the impact of social costs and policies on epidemic dynamics.

Contribution

It introduces a novel mean field game framework for epidemic modeling that accounts for social structure and individual strategic behavior.

Findings

Nash equilibrium strategies differ from societal optimum.

Social policies like lockdown can approximate societal optimal strategies.

Model highlights the impact of individual choices on epidemic outcomes.

Abstract

We consider the spread of infectious diseases through a Mean Field Game version of a SIR compartmental model with social structure, in which individuals are grouped by their age class and interact together in different settings. In our game theoretical approach, individuals can choose to limit their contacts if the epidemic is too virulent, but this effort comes with a social cost. We further compare the Nash equilibrium obtained in this way with the societal optimum that would be obtained if a benevolent central planner could decide of the strategy of each individual, as well as to the more realistic situation where an approximation of this optimum is reached through social policies such as lockdown.