We investigate an SIR model of epidemic propagation on networks in the context of mean-field games. In a real epidemic, individuals adjust their behavior depending on the epidemic level and the impact it might have on them in the future. These individual behaviors, in turn, affect the epidemic dynamics. Mean-field games are a framework in which these retroaction effects can be captured. We derive dynamical equations for the epidemic quantities in terms of individual contact rates, and via mean-field approximations, we obtain the Nash equilibrium associated with the minimization of a certain cost function. We first consider homogeneous networks, where all individuals have the same number of neighbors, and discuss how the individual behaviors are modified when that number is varied. We then investigate the case of a realistic heterogeneous network based on real data from a social contact network. Our results allow us to assess the potential of such an approach for epidemic mitigation in real-world implementations.

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• Epidemic
• Complex networks
• Mean field theory