Immunity of multiplex networks via acquaintance vaccination

How to find the effective approach of immunizing a population is one open question in the research of complex systems. Up to now, there have been a great number of works focusing on the efficiency of various immunization strategies. However, the majority of these existing achievements are limited to isolated networks, how immunization affects disease spreading in multiplex networks seems to need further exploration. In this letter, we explore the impact of the acquaintance immunization in multiplex networks, where two kinds of immunization strategies, multiplex node-based acquaintance immunization and layer node-based acquaintance immunization, are proposed. With the generating function method, our theoretical framework is able to accurately calculate the critical immunization threshold which is one of the most important indexes to predict the epidemic regime. Moreover, we further uncover that, with the increment of degree correlation between network layers, the immunization threshold declines for multiplex node-based acquaintance immunization, but slowly increases for layer node-based acquaintance immunization