Up to now, immunization of disease propagation has attracted great attention in both theoretical and experimental researches. However, vast majority of existing achievements are limited to the simple assumption of single layer networked population, which seems obviously inconsistent with recent development of complex network theory: each node could possess multiple roles in different topology connections. Inspired by this fact, we here propose the immunization strategies on multiplex networks, including multiplex node-based random (targeted) immunization and layer node-based random (targeted) immunization. With the theory of generating function, theoretical analysis is developed to calculate the immunization threshold, which is regarded as the most critical index for the effectiveness of addressed immunization strategies. Interestingly, both types of random immunization strategies show more efficiency in controlling disease spreading on multiplex Erdös-Rényi (ER) random networks; while targeted immunization strategies provide better protection on multiplex scale-free (SF) networks.

Efficient security patch distribution is of essential importance for updating anti-virus software to ensure effective and timely virus detection and cleanup. In this paper, we propose a mixed strategy of patch distribution to combine the advantages of the traditional centralized patch distribution strategy and decentralized patch distribution strategy. A novel network model that contains a central node and a multiplex network composed of patch dissemination network layer and virus propagation network layer is presented, and a competing spreading dynamical process on top of the network model that simulates the interplay between virus propagation and patch dissemination is developed. Such a new framework helps effectively analyzing the impacts of patches distribution on virus propagation, and developing more realizable schemes for restraining virus propagation. Furthermore, considering the constrains of capacity of central node and the bandwidth of network links, an optimal allocation approach of patches is proposed, which could simultaneously optimize multiple dynamical parameters to effectively restrain the virus propagation with a given budget.