  The two-species symbiotic contact process (2SCP) is a stochastic process
where each vertex of a graph may be vacant or host at most one individual of
each species. Vertices with both species have a reduced death rate,
representing a symbiotic interaction, while the dynamics evolves according to
the standard (single species) contact process rules otherwise. We investigate
the role of dynamical correlations on the 2SCP on homogeneous and heterogeneous
networks using pairwise mean-field theory. This approach is compared with the
ordinary one-site theory and stochastic simulations. We show that our theory
significantly outperforms the one-site theory. In particular, the stationary
state of the 2SCP model on random regular networks is very accurately
reproduced by the pairwise mean-field, even for relatively small values of
vertex degree, where expressive deviations of the standard mean-field are
observed. The pairwise approach is also able to capture the transition points
accurately for heterogeneous networks and provides rich phase diagrams with
transitions not predicted by the one-site method. Our theoretical results are
corroborated by extensive numerical simulations.
