We consider a class of multi-type particle systems whose structure is similar to that of a contact process and show that additivity is equivalent to the existence of a dual process, extending a result of Harris. We prove a necessary and sufficient condition for the model to preserve positive correlations. We then show that complete convergence on Zd holds for a large subclass of models including the two-stage contact process and a household model, and give examples.
"Duality and complete convergence for multi-type additive growth models." Adv. in Appl. Probab. 48 (1) 32 - 51, March 2016.