Social structure description of epidemic propagation with a mean-field game paradigm

As emphasized by the recent pandemic crisis, the design of coherent policies against epidemic propagation is of major importance and required to model both epidemic quantities and individuals behavior because the latter has a strong influence on the former. To address this issue, 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 on 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.