A coupled awareness-epidemic model on a multi-layer time-varying network.

Social interactions have become more complicated and changeable under the influence of information technology revolution. We, thereby, propose a multi-layer activity-driven network with attractiveness considering the heterogeneity of activated individual edge numbers, which aims to explore the role of heterogeneous behaviors in the time-varying network. Specifically, three types of individual behaviors are introduced: (i) self-quarantine of infected individuals, (ii) safe social distancing between infected and susceptible individuals, and (iii) information spreading of aware individuals. Epidemic threshold is theoretically derived in terms of the microscopic Markov chain approach and the mean-field approach. The results demonstrate that performing self-quarantine and maintaining safe social distance can effectively raise the epidemic threshold and suppress the spread of diseases. Interestingly, individuals' activity and individuals' attractiveness have an equivalent effect on epidemic threshold under the same condition. In addition, a similar result can be obtained regardless of the activated individual edge numbers. The epidemic outbreak earlier in a situation of the stronger heterogeneity of activated individual edge numbers.