This title appears in the Scientific Report :
2013
Please use the identifier:
http://dx.doi.org/10.1007/s1095501308247 in citations.
TwoDimensional SIR Epidemics with Long Range Infection
TwoDimensional SIR Epidemics with Long Range Infection
We extend a recent study of susceptibleinfectedremoved epidemic processes with long range infection (referred to as I in the following) from 1dimensional lattices to lattices in two dimensions. As in I we use hashing to simulate very large lattices for which finite size effects can be neglected,...
Personal Name(s):  Grassberger, Peter (Corresponding author) 

Contributing Institute: 
Jülich Supercomputing Center; JSC 
Published in:  Journal of statistical physics, 153 (2013) 2, S. 289  311 
Imprint: 
New York, NY [u.a.]
Springer Science + Business Media B.V.
2013

DOI: 
10.1007/s1095501308247 
Document Type: 
Journal Article 
Research Program: 
Computational Science and Mathematical Methods 
Publikationsportal JuSER 
We extend a recent study of susceptibleinfectedremoved epidemic processes with long range infection (referred to as I in the following) from 1dimensional lattices to lattices in two dimensions. As in I we use hashing to simulate very large lattices for which finite size effects can be neglected, in spite of the assumed power law p(x)∼x−σ−2 for the probability that a site can infect another site a distance vector x apart. As in I we present detailed results for the critical case, for the supercritical case with σ=2, and for the supercritical case with 0<σ<2. For the latter we verify the stretched exponential growth of the infected cluster with time predicted by M. Biskup. For σ=2 we find generic power laws with σdependent exponents in the supercritical phase, but no KosterlitzThouless (KT) like critical point as in 1d. Instead of diverging exponentially with the distance from the critical point, the correlation length increases with an inverse power, as in an ordinary critical point. Finally we study the dependence of the critical exponents on σ in the regime 0<σ<2, and compare with field theoretic predictions. In particular we discuss in detail whether the critical behavior for σ slightly less than 2 is in the short range universality class, as conjectured recently by F. Linder et al. As in I we also consider a modified version of the model where only some of the contacts are long range, the others being between nearest neighbors. If the number of the latter reaches the percolation threshold, the critical behavior is changed but the supercritical behavior stays qualitatively the same. 