Coevolution of epidemic spreading and opinion dynamics in a two-layer network with media influence

This paper investigates the coupled interplay among public opinion, mass media, and epidemic spreading through a co-evolutionary multilayer network framework. We develop a Susceptible-Alert-Infected-Susceptible (SAIS) model on the physical layer, coupled with a dynamic opinion layer that captures groups’ perceived severity of the epidemic. A key feature of the model is a parameter-level coupling mechanism, whereby opinions—shaped by mass media and social interactions-directly modulate infection and recovery rates. The opinion dynamics evolve on a directed signed graph, incorporating both cooperative and antagonistic inter-group interactions as well as media influence. We rigorously establish the well-posedness of the system and derive opinion-dependent reproduction numbers to characterize epidemic thresholds. Analytical and numerical results reveal that the interaction between media-driven alertness and social influence generates rich dynamical behaviors, leading to multiple stable equilibria. By examining different regimes of the reproduction numbers, we identify diverse epidemic-opinion scenarios and discuss their potential strategic implications.