  We discuss a box model of migration in channels of networks with possible
application for modelling motion of migrants in migration networks. The channel
consists of nodes of the network (nodes may be considered as boxes representing
countries) and edges that connect these nodes and represent possible ways for
motion of migrants. The nodes of the migration channel have different
"leakage", i.e. the probability of change of the status of a migrant (from
migrant to non-migrant) may be different in the different countries along the
channel. In addition the nodes far from the entry node of the channel may be
more attractive for migrants in comparison to the nodes around the entry node
of the channel. We discuss below channels containing infinite number of nodes.
Two regimes of functioning of these channels are studied: stationary regime and
non-stationary regime. In the stationary regime of the functioning of the
channel the distribution of migrants in the countries of the channel is
described by a distribution that contains as particular case the Waring
distribution. In the non-stationary regime of functioning of the channel one
observes exponential increase or exponential decrease of the number of migrants
in the countries of the channel. It depends on the situation in the entry
country of the channel for which scenario will be realized. Despite the
non-stationary regime of the functioning of the channel the asymptotic
distribution of the migrants in the nodes of the channel is stationary. From
the point of view of the characteristic features of the migrants we discuss the
cases of (i) migrants having the same characteristics and (ii) two classes of
migrants that have differences in some characteristic (e.g., different
religions).
