Combined effect of simplicial complexes and interlayer interaction: An example of information-epidemic dynamics on multiplex networks

In this paper, we investigate the effect of self-awareness (interlayer interaction) for information-epidemic dynamics with simplicial complexes both near and away from the epidemic threshold. It is shown that, contrary to previous views, self-awareness plays a key role near the epidemic threshold. In small homogeneous networks, multiple susceptibility peaks can emerge in the susceptibility of the epidemic layer under the combined effect of simplicial complexes and self-awareness, even two types of multiple susceptibility peaks with completely opposite mechanisms. This means that one needs to be very careful when obtaining epidemic thresholds based on susceptibility. Moreover, the self-awareness can regulate the presence or absence of bistable phenomena both in epidemic prevalence and epidemic threshold. We also found that the time series of disease may be nonmonotonic, with a peak, and that self-awareness is one of the factors controlling the relative height between maximum and steady state. In addition, we modify heterogeneous mean-field theory and partial effective degree theory to accommodate the introduction of simplicial complexes in dynamics. We believe that our study has implications for other dynamics concerning higher-order and interlayer interactions.