https://doi.org/10.1007/s100510050596
Lévy-flight spreading of epidemic processes leading to percolating clusters
1
Institut für Theoretische Physik III,
Heinrich-Heine-Universität,
40225 Düsseldorf, Germany
2
Laboratoire de Physique Théorique et Hautes Énergies (Laboratoire
associé au Centre National de la Recherche Scientifique -URA D00
63.) ,
Université de Paris-Sud, 91405 Orsay Cedex, France
Received:
17
July
1998
Revised:
20
July
1998
Accepted:
28
July
1998
Published online: 15 January 1999
We consider two stochastic processes, the Gribov process and the
general epidemic process, that describe the spreading of an
infectious disease. In contrast to the usually assumed case of
short-range infections that lead, at the critical point, to
directed and isotropic percolation respectively, we consider
long-range infections with a probability distribution decaying in
d dimensions with the distance as . By means of
Wilson's momentum shell renormalization-group recursion relations,
the critical exponents characterizing the growing fractal clusters
are calculated to first order in an ε-expansion. It is
shown that the long-range critical behavior changes continuously to
its short-range counterpart for a decay exponent of the infection
.
PACS: 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions / 64.60.Ht – Dynamic critical phenomena / 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999