  The Markov evolution of states of a continuum migration model is studied. The
model describes an infinite system of entities placed in $\mathds{R}^d$ in
which the constituents appear (immigrate) with rate $b(x)$ and disappear, also
due to competition. For this model, we prove the existence of the evolution of
states $\mu_0 \mapsto \mu_t$ such that the moments $\mu_t(N_\Lambda^n)$, $n\in
\mathds{N}$, of the number of entities in compact $\Lambda \subset
\mathds{R}^d$ remain bounded for all $t>0$. Under an additional condition, we
prove that the density of entities and the second correlation function remain
bounded globally in time.
