Optimizing spreading dynamics in interconnected networks

Adding edges between layers of interconnected networks is an important way to optimize the spreading dynamics. While previous studies mostly focus on the case of adding a single edge, the theoretical optimal strategy for adding multiple edges still need to be studied. In this study, based on the susceptible-infected-susceptible (SIS) model, we investigate the problem of maximizing the stationary spreading prevalence in interconnected networks. For two isolated networks, we maximize the spreading prevalence near the critical point by choosing multiple interconnecting edges. We present a theoretical analysis based on the discrete-time Markov chain approach to derive the approximate optimal strategy. The optimal inter-layer structure predicted by the strategy maximizes the spreading prevalence, meanwhile minimizes the spreading outbreak threshold for the interconnected network simultaneously. Numerical simulations on synthetic and real-world networks show that near the critical point, the proposed strategy gives better performance than connecting large degree nodes and randomly connecting.