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Mathematical Biosciences and Engineering (MBE)
 

Structural calculations and propagation modeling of growing networks based on continuous degree
Pages: 1215 - 1232, Issue 5/6, October/December 2017

doi:10.3934/mbe.2017062      Abstract        References        Full text (575.4K)           Related Articles

Junbo Jia - Department of Mathematics, Shanghai University, Shanghai 200444, China (email)
Zhen Jin - Complex Systems Research Center, Shanxi University, Taiyuan, Shan'xi 030006, China (email)
Lili Chang - Complex Systems Research Center, Shanxi University, Taiyuan 030051, Shanxi, China (email)
Xinchu Fu - Department of Mathematics, Shanghai University, Shanghai 200444, China (email)

1 R. Albert and A. L. Barabási, Statistical mechanics of complex networks, Reviews of Modern Physics, 74 (2002), 47-97.       
2 A. L. Barabási, R. Albert and H. Jeong, Mean-field theory for scale-free random networks, Physica A: Statistical Mechanics and its Applications, 272 (1999), 173-187.
3 A. L. Barabási and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509-512.       
4 S. N. Dorogovtsev, J. F. F. Mendes and A. N. Samukhin, Structure of growing networks with preferential linking, Physical Review Letters, 85 (2000), 4633.
5 S. N. Dorogovtsev and J. F. F. Mendes, Scaling properties of scale-free evolving networks: Continuous approach, Physical Review E, 63 (2001), 056125.
6 S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW, Oxford University Press, New York, 2013.       
7 P. Erdős and A. Rényi, On the strength of connectedness of a random graph, Acta Mathematica Hungarica, 12 (1961), 261-267.       
8 M. Faloutsos, P. Faloutsos and C. Faloutsos, On power-law relationships of the internet topology, ACM SIGCOMM Computer Communication Review, 29 (1999), 251-262.
9 M. J. Gagen and J. S. Mattick, Accelerating, hyperaccelerating, and decelerating networks, Physical Review E, 72 (2005), 016123.
10 T. House and M. J. Keeling, Insights from unifying modern approximations to infections on networks, Journal of The Royal Society Interface, 8 (2011), 67-73.
11 M. J. Keeling, The effects of local spatial structure on epidemiological invasions, Proceedings of the Royal Society of London. Series B: Biological Sciences, 266 (1999), 859-867.
12 K. T. D. Ken and M. J. Keeling, Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases, Proceedings of the National Academy of Sciences, 99 (2002), 13330-13335.
13 P. L. Krapivsky, S. Redner and F. Leyvraz, Connectivity of growing random networks, Physical Review Letters, 85 (2000), 4629.
14 P. L. Krapivsky and S. Redner, Organization of growing random networks, Physical Review E, 63 (2001), 066123.
15 J. Lindquist, J. Ma, P. van den Driessche and F. H. Willeboordse, Effective degree network disease models, Journal of Mathematical Biology, 62 (2011), 143-164.       
16 C. Liu, J. Xie, H. Chen, H. Zhang and M. Tang, Interplay between the local information based behavioral responses and the epidemic spreading in complex networks, Chaos: An Interdisciplinary Journal of Nonlinear Science, 25 (2015), 103111, 7 pp.       
17 S. Milgram, The small world problem, Psychology Today, 2 (1967), 60-67.
18 J. C. Miller, A. C. Slim and E. M. Volz, Edge-based compartmental modelling for infectious disease spread, Journal of the Royal Society Interface, 9 (2012), 890-906.
19 J. C. Miller and I. Z. Kiss, Epidemic spread in networks: Existing methods and current challenges, Mathematical Modelling of Natural Phenomena, 9 (2014), 4-42.       
20 Y. Moreno, R. Pastor-Satorras and A. Vespignani, Epidemic outbreaks in complex heterogeneous networks, The European Physical Journal B-Condensed Matter and Complex Systems, 26 (2002), 521-529.
21 M. E. J. Newman, The structure and function of complex networks, SIAM Review, 45 (2003), 167-256.       
22 R. Pastor-Satorras and A. Vespignani, Epidemic spreading in scale-free networks, Physical Review Letters, 86 (2001), 3200.
23 D. Shi, Q. Chen and L. Liu, Markov chain-based numerical method for degree distributions of growing networks, Physical Review E, 71 (2005), 036140.
24 E. Volz, SIR dynamics in random networks with heterogeneous connectivity, Journal of Mathematical Biology, 56 (2008), 293-310.       
25 D. J. Watts and S. H. Strogatz, Collective dynamics of "small-world" networks, Nature, 393 (1998), 440-442.
26 H. Zhang, J. Xie, M. Tang and Y. Lai, Suppression of epidemic spreading in complex networks by local information based behavioral responses, Chaos: An Interdisciplinary Journal of Nonlinear Science, 24 (2014), 043106, 7 pp.       

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