A Unified Inferring Framework of Multiplex Epidemic Networks Under Multiple Interlayer Interaction Modes

Different epidemic transmissions on multiplex networks may interact and display intertwined effects, leading to a challenge and urgently needed problem of the inference of multiplex epidemic network structures under multiple interlayer interaction modes (IIMs). However, in reality, few existing studies have focused on multiplex epidemic network inference responding to the intertwined IIMs, much less the corresponding consistency analysis. To fill these two gaps, we first propose an inference framework of multiplex epidemic networks under a unified form of IIMs. In particular, we develop a Hamming distance-based two-step estimator for an intricate IIM called infection-probability-dependent interaction (IPDI). The proposed two-step estimator overcomes the problems of unobservable and time-varying variable inference in the IPDI mode. Second, we solve the theoretical difficulty of consistency analysis for the network inference under multiple IIMs and obtain sufficient conditions for exponentially decaying inferring error. Under the guarantee of consistently sufficient conditions, the sample size scale enables our framework's high-dimensional inferring ability. The synthetic network simulations show the validity of the proposed algorithm and consistency analysis. In addition, the analysis of real data of Twitter and Foursquare indicates the effectiveness and practicality of the proposed inferring framework.