  This research introduces a mathematical framework to comprehending human
mobility patterns, integrating mathematical modeling and economic analysis. The
study focuses on latent-variable networks, investigating the dynamics of human
mobility using stochastic models. By examining actual origin-destination data,
the research reveals scaling relations and uncovers the economic implications
of mobility patterns, such as the income elasticity of travel demand. The
mathematical analysis commences with the development of a stochastic model
based on inhomogeneous random graphs to construct a visitation model with
multipurpose drivers for travel demand. A directed multigraph with weighted
edges is considered, incorporating trip costs and labels to represent factors
like distance traveled and travel time. The study gains insights into the
structural properties and dynamic correlations of human mobility networks, to
derive analytical and computational solutions for key network metrics,
including scale-free behavior of the strength and degree distribution, together
with the estimation of assortativity and clustering coefficient. Additionally,
the model's validity is assessed through a real-world case study of the New
York metropolitan area. The analysis of this data exposes clear scaling
relations in commuting patterns, confirming theoretical predictions and
validating the efficacy of the mathematical model. The model further explains a
series of scaling behaviors in origin-destination flows among areas of a
region, successfully reproducing statistical regularities observed in
real-world cases using extensive human mobility datasets. In particular, the
model's application to estimating income elasticity of travel demand bears
significant implications for urban and transport economics.
