On the Mathematical Theory of Human Migration: Model of a Migration Channel with a Secondary and a Tertiary Arm

We study the motion of substance in a finite channel that belongs to a network. The channel splits to two arms in a node of the network. There is an additional split of the secondary arm. We obtain analytical relationships for the distribution of the substance in the nodes of the channel for the case of stationary regime of the motion of the substance in the arms of the channel. The obtained results are discussed from the point of view of application of the model to migration dynamics: model of motion of migrants in a channel consisting of chains of countries with different probabilities for obtaining permission to stay for the migrants in the different countries of the channel