Abstract
The study compares the epidemic spread on static and dynamic small-world networks. They are constructed as a 2-dimensional Newman and Watts model (500 × 500 square lattice with additional shortcuts), where the dynamics involves rewiring shortcuts in every time step of the epidemic spread. We assume susceptible-infectious-removed (SIR) model of the disease. We study the behaviour of the epidemic over the range of shortcut probability per underlying bond ϕ = 0–0.5. We calculate percolation thresholds for the epidemic outbreak, for which numerical results are checked against an approximate analytical model. We find a significant lowering of percolation thresholds on the dynamic network in the parameter range given. The result shows the behaviour of the epidemic on dynamic network is that of a static small world with the number of shortcuts increased by 20.7±1.4 %, while the overall qualitative behaviour stays the same. We derive corrections to the analytical model which account for the effect. For both dynamic and static small worlds we observe suppression of the average epidemic size dependence on network size in comparison with the finite-size scaling known for regular lattice. We also study the effect of dynamics for several rewiring rates relative to infectious period of the disease.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
World Health Organization, Avian influenza (H5N1), http://www.who.int/csr/disease/avian_influenza/en/ (2010)
World Health Organization, Swine influenza (H1N1), http://www.who.int/csr/disease/swineflu/en/ (2010)
World Health Organization, Severe acute respiratory syndrome (SARS), http://www.who.int/csr/sars/en/ (2010)
C. Dye, N. Gay, Science 300, 1884 (2003)
M.J. Keeling, M.E.J. Woolhouse, D.J. Shaw, L. Matthews, M. Chase-Topping, D.T. Haydon, S.J. Cornell, J. Kappey, J. Wilesmith, B.T. Grenfell, Science 294, 813 (2001)
J. Swinton, C.A. Gilligan, Proc. Trans. R. Soc. B 351, 605 (1996)
A.J. Stacey, J.E. Truscott, M.J.C. Asher, C.A. Gilligan, Phytopathology 94, 209 (2004)
R.M. May, R.M. Anderson, Nature 326, 137 (1987)
G.P. Garnett, S.O. Aral, D.V. Hoyle, W. Cates Jr, R.M. Anderson, Sex. Transm. Dis. 24, 185 (1997)
T. Gross, C.J.D. D’Lima, B. Blasius, Phys. Rev. Lett. 96, 208701 (2006)
B. Dybiec, A. Kleczkowski, C.A. Gilligan, J. R. Soc. Interface 6, 941 (2009)
J. Saramäki, K. Kaski, J. Theor. Biol. 234, 413 (2005)
E. Volz, L.A. Meyers, Proc. R. Soc. B 274, 2925 (2007)
J.M. Read, K.T.D. Eames, W.J. Edmunds, J. R. Soc. Interface 5, 1001 (2008)
M.E.J. Newman, I. Jensen, R.M. Ziff, Phys. Rev. E 65, 021904 (2002)
D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)
M.E.J. Newman, D.J. Watts, Phys. Lett. A 263, 341 (1999)
P. Grassberger, Math. Biosci. 63, 157 (1983)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Ochab, J.K., Góra, P.F. Shift of percolation thresholds for epidemic spread between static and dynamic small-world networks. Eur. Phys. J. B 81, 373–379 (2011). https://doi.org/10.1140/epjb/e2011-10975-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2011-10975-6