  The contact process is a particular case of birth-and-death processes on
infinite particle configurations. We consider the contact models on locally
compact separable metric spaces. We prove the existence of a one-parameter set
of invariant measures in the critical regime under the condition imposed on the
associated Markov jump process. This condition, roughly speaking, requires the
separation of any pair of trajectories of this jump process. The general scheme
can be applied to the contact process on the lattice in a heterogeneous and
random environments as well as to the contact process on graphs and on
manifolds.
