Mean Field Game description of virus propagation
This thesis investigates the role of human behavior in epidemic modeling. Epidemics are influenced by both individuals’ spontaneous responses and government-imposed measures, creating a feedback loop that shapes the outbreak’s progression. However, many existing models treat human behavior as an external factor, limiting their realism. To address this gap, the thesis applies the Mean Field Game (MFG) framework, a theoretical tool for incorporating individual decision-making into epidemic models.
The first part of the thesis applies the MFG approach to an SIR (Susceptible-Infected-Recovered) model with a social structure. Individuals balance infection risk against the social and economic costs of reducing contact. Numerical simulations with realistic parameters identify a Nash equilibrium, reflecting self-interested behavior, and we compare it to the social optimum, which minimizes overall societal costs. The gap between these scenarios is narrowed through constrained Nash equilibria, which include government interventions. The analysis also reveals that changes in population size or model duration can lead to phase transitions in optimal strategies, emphasizing the need for adaptive policies.
In the second part, the MFG framework is extended to complex networks, where individuals differ in connectivity. Using pairwise approximation, we derive epidemic dynamics and integrate MFG principles. Simulations on realistic contact networks highlight how variations in social cost structures influence individual behavior, with significant differences observed based on connectivity levels. A related project provides new analytical insights into the SIR model on regular networks.
Jury : Alain Barrat (examinateur), Marc Barthelemy (président du Jury), Laura di Domenico (examinatrice), Olivier Giraud (co-directeur de thèse), Sergio Gomez (rapporteur), Gabriel Turinici (rapporteur), Denis Ullmo (directeur de thèse)