Dynamics analysis of epidemic and information spreading in overlay networks.

We establish an SIS-UAU model to present the dynamics of epidemic and information spreading in overlay networks. The overlay network is represented by two layers: one where the dynamics of the epidemic evolves and another where the information spreads. We theoretically derive the explicit formulas for the basic reproduction number of awareness R0 a by analyzing the self-consistent equation and the basic reproduction number of disease R0 d by using the next generation matrix. The formula of R0 d shows that the effect of awareness can reduce the basic reproduction number of disease. In particular, when awareness does not affect epidemic spreading, R0 d is shown to match the existing theoretical results. Furthermore, we demonstrate that the disease-free equilibrium is globally asymptotically stable if R0 d <1; and the endemic equilibrium is globally asymptotically stable if R0 d >1. Finally, numerical simulations show that information plays a vital role in preventing and controlling disease and effectively reduces the final disease scale.