期刊
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
卷 3, 期 1, 页码 44-57出版社
IEEE COMPUTER SOC
DOI: 10.1109/TNSE.2016.2516346
关键词
Dynamic random graphs; complex networks; epidemics; stochastic processes; random matrix theory
资金
- NSF [CNS-1302222, IIS-1447470]
- Direct For Computer & Info Scie & Enginr
- Division Of Computer and Network Systems [1302222] Funding Source: National Science Foundation
- Direct For Computer & Info Scie & Enginr
- Div Of Information & Intelligent Systems [1447470] Funding Source: National Science Foundation
In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following limitation: Markovian random graphs can only replicate switching patterns with exponential inter-switching times, while in real applications these times are usually far from exponential. In this paper, we introduce a flexible and tractable extended family of processes able to replicate, with arbitrary accuracy, any distribution of inter-switching times. We then study the stability of spreading processes in this extended family. We first show that a direct analysis based on Ito's formula provides stability conditions in terms of the eigenvalues of a matrix whose size grows exponentially with the number of edges. To overcome this limitation, we derive alternative stability conditions involving the eigenvalues of a matrix whose size grows linearly with the number of nodes. Based on our results, we also show that heuristics based on aggregated static networks approximate the epidemic threshold more accurately as the number of nodes grows, or the temporal volatility of the random graph process is reduced. Finally, we illustrate our findings via numerical simulations.
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