Abstract:
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 -expansion. It is shown that the long-range critical behavior changes continuously to its short-range counterpart for a decay exponent of the infection .
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Received: 17 July 1998 / Revised: 20 July 1998 / Accepted: 28 July 1998
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Janssen, H., Oerding, K., van Wijland, F. et al. Lévy-flight spreading of epidemic processes leading to percolating clusters. Eur. Phys. J. B 7, 137–145 (1999). https://doi.org/10.1007/s100510050596
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DOI: https://doi.org/10.1007/s100510050596