On Existence of Invariant Measures of a Continuous Contact Model in a Periodic Medium

In their previous studies, the authors of the present paper considered contact models in homogeneous and inhomogeneous, deterministic or random media, on graphs and on the Lobachevsky plane. However, the case of contact model with spatially periodic birth rates has not been considered. Here, we study this class of random processes and formulate conditions on the birth and death rates under which there exists a family of invariant measures of a contact model in a periodic medium.