Abstract
Considering the actual behavior of people’s short-term travel, we propose a dynamic small-world community network model with tunable community strength which has constant local links and time varying long-range jumps. Then an epidemic model of susceptible-infected-recovered is established based on the mean-field method to evaluate the inhibitory effects of avoidance and immunization on epidemic spreading. And an approximate formula for the epidemic threshold is obtained by mathematical analysis. The simulation results show that the epidemic threshold decreases with the increase of inner-community motivation rate and inter-community long-range motivation rate, while it increases with the increase of immunization rate or avoidance rate. It indicates that the inhibitory effect on epidemic spreading of immunization works better than that of avoidance.
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References
Cohen R, Havlin S, Ben-Avraham D. Efficient immunization strategies for computer networks and populations [J]. Physical Review Letters, 2003, 91(24): 247901.
Madar N, Kalisky T, Cohen R, et al. Immunization and epidemic dynamics in complex networks [J]. The European Physical Journal B, 2004, 38(2): 269–276.
Mirzasoleiman B, Babaei M, Jalili M. Immunizing complex networks with limited budget [J]. Europhysics Letters, 2012, 98(3): 38004.
Wu Q C, Fu X C, ** Z, et al. Influence of dynamic immunization on epidemic spreading in networks [J]. Physica A: Statistical Mechanics and Its Applications, 2015, 419: 566–574.
Buscarino A, Fortuna L, Frasca M, et al. Disease spreading in populations of moving agents [J]. Europhysics Letters, 2008, 82(3): 38002.
Stone T E, Mckay S R. Critical behavior of disease spread on dynamic small-world networks [J]. Europhysics Letters, 2011, 95(3): 38003.
Funk S, Gilad E, Watkins C, et al. The spread of awareness and its impact on epidemic outbreaks [J]. Proceedings of the National Academy of Sciences of the United States of America, 2009, 106(16): 6872–6877.
Rizzo A, Frasca M, Porfiri M. Effect of individual behavior on epidemic spreading in activity-driven networks [J]. Physical Review E, 2014, 90(4): 042801.
Gross T, Dlima C J D, Blasius B. Epidemic dynamics on an adaptive network [J]. Physical Review Letters, 2006, 96(20): 208701.
Shaw L B, Schwartz I B. Fluctuating epidemics on adaptive networks [J]. Physical Review E, 2008, 77(6): 066101.
Lu Y L, Jiang G P, Song Y R. Stability and bifurcation of epidemic spreading on adaptive network [J]. Acta Physica Sinica, 2013, 62(13): 130202(Ch).
Shaw L B, Schwartz I B. Enhanced vaccine control of epidemics in adaptive networks [J]. Physical Review E, 2010, 81(4): 046120.
Stone T E, Jones M M, Mckay S R. Comparative effects of avoidance and vaccination in disease spread on a dynamic small-world network [J]. Physica A: Statistical Mechanics and Its Applications, 2010, 389(23): 5515–5520.
Newman M E J, Girvan M. Finding and evaluating community structure in networks [J]. Physical Review E, 2004, 69(2): 026113.
Newman M E J. Modularity and community structure in networks [J]. Proceedings of the National Academy of Sciences of the United States of America, 2006, 103(23): 8577–8582.
Li C C, Jiang G P, Song Y R. Epidemic spreading in dynamic small-world networks with community structure [J]. Complex Systems and Complexity Science, 2014, 11(3): 33–39(Ch).
Pastor-Satorras R, Vespignani A. Epidemic spreading in scale-free networks [J]. Physical Review Letters, 2001, 86(14): 3200–3203.
Keeling M. The implications of network structure for epidemic dynamics [J]. Theoretical Population Biology, 2005, 67(1): 1–8.
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Foundation item: Supported by the National Natural Science Foundation of China (61374180, 61373136, 61304169), the Research Foundation for Humanities and Social Sciences of Ministry of Education, China (12YJAZH120), the Six Projects Sponsoring Talent Summits of Jiangsu Province, China (RLD201212) and the Natural Science Foundation of Anhui Province (1608085MF127)
Biography: LI Chanchan, female, Ph.D. candidate, research direction: complex network and information security.
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Li, C., Jiang, G. & Song, Y. Comparative effects of avoidance and immunization on epidemic spreading in a dynamic small-world network with community structure. Wuhan Univ. J. Nat. Sci. 21, 291–297 (2016). https://doi.org/10.1007/s11859-016-1173-6
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DOI: https://doi.org/10.1007/s11859-016-1173-6