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 R0a by analyzing the self-consistent equation and the basic reproduction number of disease R0d by using the next generation matrix. The formula of R0d shows that the effect of awareness can reduce the basic reproduction number of disease. In particular, when awareness does not affect epidemic spreading, R0d is shown to match the existing theoretical results. Furthermore, we demonstrate that the disease-free equilibrium is globally asymptotically stable if R0d<1; and the endemic equilibrium is globally asymptotically stable if R0d>1. Finally, numerical simulations show that information plays a vital role in preventing and controlling disease and effectively reduces the final disease scale.