Epidemic outbreak for an SIS model in multiplex networks with immunization

•The outbreak condition for the SIS epidemic model in multiplex networks is obtained.•The sensitivity of the outbreak condition on the correlation of two layers is investigated.•A general framework is proposed to analyze the immunization dynamics. The multiplex node-based immunization and the layer node-based immunization are examined.

With the aim of understanding epidemic spreading in a general multiplex network and designing optimal immunization strategies, a mathematical model based on multiple degree is built to analyze the threshold condition for epidemic outbreak. Two kinds of strategies, the multiplex node-based immunization and the layer node-based immunization, are examined. Theoretical results show that the general framework proposed here can illustrate the effect of diverse correlations and immunizations on the outbreak condition in multiplex networks. Under a set of conditions on uncorrelated coefficients, the specific epidemic thresholds are shown to be only dependent on the respective degree distribution in each layer.