  Epidemic spreading on physical contact network will naturally introduce the
human awareness information diffusion on virtual contact network, and the
awareness diffusion will in turn depress the epidemic spreading, thus forming
the competing spreading processes of epidemic and awareness in a multiplex
networks. In this paper, we study the competing dynamics of epidemic and
awareness, both of which follow the SIR process, in a two-layer networks based
on microscopic Markov chain approach and numerical simulations. We find that
strong capacities of awareness diffusion and self-protection of individuals
could lead to a much higher epidemic threshold and a smaller outbreak size.
However, the self-awareness of individuals has no obvious effect on the
epidemic threshold and outbreak size. In addition, the immunization of the
physical contact network under the interplay between of epidemic and awareness
spreading is also investigated. The targeted immunization is found performs
much better than random immunization, and the awareness diffusion could reduce
the immunization threshold for both type of random and targeted immunization
significantly.
