  We introduce a model for the spreading of epidemics by long-range infections
and investigate the critical behaviour at the spreading transition. The model
generalizes directed bond percolation and is characterized by a probability
distribution for long-range infections which decays in $d$ spatial dimensions
as $1/r^{d+\sigma}$. Extensive numerical simulations are performed in order to
determine the density exponent $\beta$ and the correlation length exponents
$\nu_{||}$ and $\nu_\perp$ for various values of $\sigma$. We observe that
these exponents vary continuously with $\sigma$, in agreement with recent
field-theoretic predictions. We also study a model for pairwise annihilation of
particles with algebraically distributed long-range interactions.
