  A stochastic model, describing the growth of two competing infections on
$\mathbb{R}^d$, is introduced. The growth is driven by outbursts in the
infected region, an outburst in the type 1 (2) infected region transmitting the
type 1 (2) infection to the previously uninfected parts of a ball with
stochastic radius around the outburst point. The main result is that with the
growth rate for one of the infection types fixed, mutual unbounded growth has
probability zero for all but at most countably many values of the other
infection rate. This is a continuum analog of a result of H\"{a}ggstr\"{o}m and
Pemantle. We also extend a shape theorem of Deijfen for the corresponding model
with just one type of infection.
