Levy-flight spreading of epidemic processes leading to percolating clusters

We consider two stochastic processes, the Gribov process and the general ep idemic process, that describe the spreading of an infectious disease. In co ntrast 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 1/r(d+sigma). By means of Wilson's moment um shell renormalization-group recursion relations, the critical exponents characterizing the growing fractal clusters are calculated to first order i n an epsilon-expansion. It is shown that the long-range critical behavior c hanges continuously to its short-range counterpart for a decay exponent of the infection sigma = sigma(c) > 2.