Diffusion processes widely exist in nature. Some recent papers concerning diffusion processes focus their attention on multiplex networks. Superdiffusion, a phenomenon by which diffusion processes converge to equilibrium faster on multiplex networks than on single networks in isolation, may emerge because diffusion can occur both within and across layers. Some studies have shown that the emergence of superdiffusion depends on the topology of multiplex networks if the interlayer diffusion coefficient is large enough. This paper proposes some superdiffusion criteria relating to the Laplacian matrices of the two layers and provides a construction mechanism for generating a superdiffusible two-layered network. The method we proposed can be used to guide the discovery and construction of superdiffusible multiplex networks without calculating the second smallest Laplacian eigenvalues.
After the groundbreaking work by Gómez et al., the superdiffusion phenomenon on multiplex networks begins to attract researchers’ attention. The emergence of superdiffusion means that the time scale of the diffusion process of the multiplex network is shorter than that of each layer. Using the optimization theory, the manuscript studies the greatest impact of one edge on the network diffusion speed. It is proved that by deleting any edge from a given network, the drop of the second smallest eigenvalue of its Laplacian matrix is at most 2. Based on the conclusion, the relation between the complete structure and the superdiffusible network is studied, and, further, some superdiffusion criteria on general duplex networks are proposed. Interestingly, the theoretical results indicate that the emergence of superdiffusion depends on the complete structure rather than the overlap one. Some numerical examples are shown to verify the effectiveness of the theoretical results.
Complex networks have become an important tool for investigating epidemic dynamics. A widely concerned research field for epidemics is to develop and study mitigation strategies or control measures. In this paper, we devote our attention to ring vaccination and targeted vaccination and consider the combination of them. Based on the different roles ring vaccination plays in the mixed strategy, the whole parameter space can be roughly divided into two regimes. In one regime, the mixed strategy performs poorly compared with targeted vaccination alone, while in the other regime, the addition of ring vaccination can improve the performance of targeted vaccination. This result gives us the more general and overall comparison between targeted and ring vaccination. In addition, we construct a susceptible–infected–recovered epidemic model coupled with the immunization dynamics on random networks. The comparison between stochastic simulations and numerical simulations confirms the validity of the model we propose.
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