Two-stage effects of awareness cascade on epidemic spreading in multiplex networks

Human awareness plays an important role in the spread of infectious diseases and the control of propagation patterns. The dynamic process with human awareness is called awareness cascade, during which individuals exhibit herd-like behavior because they are making decisions based on the actions of other individuals [Borge-Holthoefer et al., J. Complex Networks 1, 3 (2013)]. In this paper, to investigate the epidemic spreading with awareness cascade, we propose a local awareness controlled contagion spreading model on multiplex networks. By theoretical analysis using a microscopic Markov chain approach and numerical simulations, we find the emergence of an abrupt transition of epidemic threshold ${\ensuremath{\beta}}_{c}$ with the local awareness ratio $\ensuremath{\alpha}$ approximating $0.5$, which induces two-stage effects on epidemic threshold and the final epidemic size. These findings indicate that the increase of $\ensuremath{\alpha}$ can accelerate the outbreak of epidemics. Furthermore, a simple 1D lattice model is investigated to illustrate the two-stage-like sharp transition at ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}0.5$. The results can give us a better understanding of why some epidemics cannot break out in reality and also provide a potential access to suppressing and controlling the awareness cascading systems.