Eur. Phys. J. B 81, 373-379 (2011)
https://doi.org/10.1140/epjb/e2011-10975-6

Shift of percolation thresholds for epidemic spread between static and dynamic small-world networks

¹ M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
² Mark Kac Complex Systems Research Centre, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Corresponding author: ^a jeremi.ochab@uj.edu.pl

Received: 13 December 2010
Revised: 23 April 2011
Published online: 7 June 2011

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.