期刊
PHYSICAL REVIEW E
卷 88, 期 2, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.88.022801
关键词
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资金
- ONR [N00014-09-1-0380, N00014-12-1-0548]
- DTRA [HDTRA-1-10-1-0014, HDTRA-1-09-1-0035]
- NSF [CMMI 1125290]
- European EPIWORK project
- European MULTIPLEX project
- European CONGAS project [FP7-ICT-2011-8-317672]
- European MOTIA project [JLS-2009-CIPS-AG-C1-016]
- European LINC project
- Deutsche Forschungsgemeinschaft (DFG)
- Next Generation Infrastructure (Bsik)
- Israel Science Foundation
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [1125290] Funding Source: National Science Foundation
Most real-world networks are not isolated. In order to function fully, they are interconnected with other networks, and this interconnection influences their dynamic processes. For example, when the spread of a disease involves two species, the dynamics of the spread within each species (the contact network) differs from that of the spread between the two species (the interconnected network). We model two generic interconnected networks using two adjacency matrices, A and B, in which A is a 2N x 2N matrix that depicts the connectivity within each of two networks of size N, and B a 2N x 2N matrix that depicts the interconnections between the two. Using an N-intertwined mean-field approximation, we determine that a critical susceptible-infected-susceptible (SIS) epidemic threshold in two interconnected networks is 1/lambda(1)(A + alpha B), where the infection rate is beta within each of the two individual networks and alpha beta in the interconnected links between the two networks and lambda(1)(A + alpha B) is the largest eigenvalue of the matrix A + alpha B. In order to determine how the epidemic threshold is dependent upon the structure of interconnected networks, we analytically derive lambda(1)(A + alpha B) using a perturbation approximation for small and large a, the lower and upper bound for any alpha as a function of the adjacency matrix of the two individual networks, and the interconnections between the two and their largest eigenvalues and eigenvectors. We verify these approximation and boundary values for lambda(1)(A + alpha B) using numerical simulations, and determine how component network features affect lambda(1)(A + alpha B). We note that, given two isolated networks G(1) and G(2) with principal eigenvectors x and y, respectively, lambda(1)(A + alpha B) tends to be higher when nodes i and j with a higher eigenvector component product x(i)y(j) are interconnected. This finding suggests essential insights into ways of designing interconnected networks to be robust against epidemics.
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