Threshold analysis of the susceptible-infected-susceptible model on overlay networks |
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| Institution: | 1. College of Mathematics and Information Science, Jiangxi Normal University, Jiangxi 330022, China;2. School of Mathematical Science, Anhui University, Hefei 230039, China;3. School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia;4. Department of Mathematics, Shanghai University, Shanghai 200444, China;1. Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu 210023, PR China;2. School of Automation, Southeast University, Nanjing, 210096, PR China;3. Institute of Information and Control Engineering Technology, Nanjing Normal University, Nanjing, Jiangsu 210042, PR China;4. College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing, Jiangsu 210042, PR China;1. Université d’Avignon et des Pays de Vaucluse, UMR 1114 EMMAH, F-84018 Avignon Cedex, France;2. UMR 1114 EMMAH, Centre INRA d’Avignon, F-84914 Avignon Cedex 9, France;1. Department of Automatization, Wuhan University, Wuhan 430072, PR China;2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China;3. College of Electrical and Information Engineering, Hunan University, Changsha 410082, PR China;1. Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China;2. Department of Mathematics, Tongji University, Shanghai 200092, China;1. Department of Electrical Engineering, Miyaneh Branch, Islamic Azad University, Miyaneh, Iran;2. School of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran;3. Department of Mathematics and Computer Sciences, Faculty of Art and Sciences, Cankaya University, Ankara, Turkey;4. Institute of Space Sciences, Magurele-Bucharest, Romania;5. Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia |
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| Abstract: | In this paper, we study epidemic spreading on overlay networks in which n multiple sets of links interconnect among the same nodes. By using the microscopic Markov-chain approximation (MMA) approach, we establish the conditions of epidemic outbreak for two kinds of spreading mechanisms in such an overlay network: the concatenation case and the switching case. When a uniform infection rate is set in all the subnetworks, we find the epidemic threshold for the switching case is just n times as large as that of concatenation case. We also find that the overlay network with a uniform infection rate can be considered as an equivalent (in the sense of epidemic dynamics and epidemic threshold) weighted network. To be specific, the concatenation case corresponds to the integer weighted network, while the switching case corresponds to the fractional weighted network. Interestingly, the time-varying unweighted network can be mapped into the static weighted network. Our analytic results exhibit good agreement with numerical simulations. |
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| Keywords: | Complex networks Epidemic spreading Markov-chain model |
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