Analysis of epidemic outbreaks in two-layer networks with different structures for information spreading and disease diffusion

A two-layer susceptible-infected-recovered/unaware-aware (SIR-UA) epidemic model is presented to analyze the effect of different heterogeneous networks in a population. Random, scale-free, and small-world network topologies are tested to investigate the impact of awareness on the spread of epidemics in a two-layer network with diverse combinations of degree and structure. Susceptible and infected (both unaware and aware) individuals are associated with their neighboring nodes in a social network structure with various degree distributions. In the two-layer SIR-UA epidemic model, a virtual network represents the connections that spread information, while a physical network represents the physical social interactions that spread diseases. We test various combinations of network structures in virtual or physical networks, to understand the impact of information diffusion on the spread of epidemics in a heterogeneous network structure. Then, the effects of awareness on the spread of a disease are discussed. Finally, phase diagrams are illustrated to reveal the final regions covered by an epidemic with various network parameters. We find that a disease spreads less if the virtual social network is more connected than the network of physical connections.