Epidemic outbreak for an SIS model in multiplex networks with immunization.

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.