A Mean-Field Analysis of a Network Behavioral–Epidemic Model

The spread of an epidemic disease and the population’s collective behavioral response are deeply intertwined, influencing each other’s evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their real-world applicability. To address this gap, we propose and analyse a behavioral–epidemic model, in which a susceptible–infected–susceptible epidemic model and an evolutionary game-theoretic decision-making mechanism concerning the use of self-protective measures are coupled. Through a mean-field approach, we characterize the asymptotic behavior of the system, deriving conditions for global convergence to a disease-free equilibrium and characterizing the endemic equilibria of the system and their (local) stability properties. Interestingly, for a certain range of the model parameters, we prove global convergence to a limit cycle, characterized by periodic epidemic outbreaks and collective behavioral response.