  The non-equilibrium phase transition in models for epidemic spreading with
long-range infections in combination with incubation times is investigated by
field-theoretical and numerical methods. Here the spreading process is modelled
by spatio-temporal Levy flights, i.e., it is assumed that both spreading
distance and incubation time decay algebraically. Depending on the infection
rate one observes a phase transition from a fluctuating active phase into an
absorbing phase, where the infection becomes extinct. This transition between
spreading and extinction is characterized by continuously varying critical
exponents, extending from a mean-field regime to a phase described by the
universality class of directed percolation. We compute the critical exponents
in the vicinity of the upper critical dimension by a field-theoretic
renormalization group calculation and verify the results in one spatial
dimension by extensive numerical simulations.
