We study the ergodic theory of a multitype contact process with equal death rates and unequal birth rates on the d-dimensional integer lattice and regular trees. We prove that for birth rates in a certain interval there is coexistence on the tree, which by a result of Neuhauser is not possible on the lattice. We also prove a complete convergence result when the larger birth rate falls outside of this interval.
"Survival and coexistence for a multitype contact process." Ann. Probab. 37 (3) 853 - 876, May 2009. https://doi.org/10.1214/08-AOP422