Discrete-time model for a substance motion in a channel of a network. Application to a human migration channel

TL;DR

This paper introduces a discrete-time network model for substance movement and interaction, deriving new statistical distributions and applying these concepts to human migration dynamics and population interactions.

Contribution

It presents a novel class of statistical distributions for substance distribution in network channels and models interactions between different substances, with applications to migration and population studies.

Findings

Derived new statistical distributions for stationary substance distribution.

Analyzed interaction scenarios between two substance types in network nodes.

Applied models to human migration and population interaction dynamics.

Abstract

We discuss a discrete-time model for motion of substance in a channel of a network. For the case of stationary motion of the substance and for the case of time-independent values of the parameters of the model we obtain a new class of statistical distributions that describe the distribution of the substance along the nodes of the channel. The case of interaction between a kind of substance specific for a node of the network and another kind of substance that is leaked from the channel is studied in presence of possibility for conversion between the two substances. Several scenarios connected to the dynamics of the two kinds of substances are described. The studied models: (i) model of motion of substance through a channel of a network, and (ii) model of interaction between two kinds of substances in a network node connected to the channel, are discussed from the point of view of human migration dynamics and interaction between the population of migrants and the native population of a country.