Heterogeneous propagation processes between awareness and epidemic on signed multiplex networks

In recent years, modeling the coupled spread of awareness and epidemic has become an active topic in the field of network science. Many researches have pointed out that individual heterogeneity is often a significant factor influencing the epidemic transmission, due to variations in the responses of different individuals confronting epidemics. In addition, in social networks there are not only simple friendly interactions, but also hostile relationships that contain negative feelings. Therefore, we construct a two-layered network model of information diffusion and epidemics spreading on signed networks. The top layer denotes the diffusion of awareness, which is constructed as a signed network and is based on structural balance theory, here we assume that the information acceptance rate varies between individuals as a result of positive and negative relationships. The bottom layer characterizes the epidemic transmission layer, which defines that the individual precaution intensity will differ according to local and global disease proportion. We utilize the Microscopic Markov Chain approach to theoretically analyze the model and solve the epidemic threshold, which is in good accordance with the Monte Carlo simulations. Our findings indicate that increasing the proportion of positive edges could promote the diffusion of awareness, thereby inhibiting epidemics spread and raising outbreak thresholds. As the impact of local and global disease proportion on individual response strength increases, it reduces the proportion of eventual infectives of epidemics but does not have any effect on thresholds. The results of our study can provide some theoretical support for the public health authorities to develop effective prevention and control strategies.