We consider a pure-jump Markov generator that which can be seen as a generalization of the spatial birth-and-death generator, which allows for mobility of particles. Conditions for the regularity of this generator and for its ergodicity are established. We also give the conditions under which its stationary distribution is a Gibbs measure. This extends previous work in~\cite{Preston1977} by allowing particle mobility. Such spatial birth-mobility-and-death processes can also be seen as generalizations of the spatial queueing systems considered in~\cite{Serfozo1999}. So our approach yields regularity conditions and alternative conditions for ergodicity of spatial open Whittle networks, complementing the results in~\cite{SerfozoHuang1999}. Next we show how our results can be used to model wireless communication networks. In particular we study two spatial loss models for which we establish an expression for the blocking probability that might be seen as a spatial version of the classical Erlang loss formula. Some specific applications to CDMA (Code Division Multiple Access) networks are also discussed.