  We consider a class of multi-type particle systems having similar structure
to the contact process and show that additivity is equivalent to the existence
of a dual process, extending a result of Harris. We give two additional
characterizations of these systems, in spacetime as percolation models, and
biologically as population models in which the interactions are due to
crowding. We prove a necessary and sufficient condition for the model to
preserve positive correlations. We then show that complete convergence on
$\mathbb{Z}^d$ holds for a large subclass of models including the two-stage
contact process and a household model, and give examples.
