Modeling urbanization dynamics by labor force migration

Individual participants in human society collectively exhibit aggregation behavior. In this study, we present a simple microscopic model of labor force migration based on the active Brownian particles framework. In particular, agent-based simulations show that the model produces clusters of agents from a random initial distribution. Furthermore, two empirical regularities called Zipf's and Okun's laws were observed. To reveal the mechanism underlying the reproduced aggregation phenomena, we use our microscopic model to derive an extended Keller--Segel system, which is a classic model describing the aggregation behavior of biological organisms called taxis. The obtained macroscopic system indicates that the concentration of the workforce in the real world can be explained through a new type of taxis central to human behavior, highlighting the relevance of urbanization to blow-up phenomena in the derived PDE system. We then characterize the transition between the aggregation and diffusion regimes both analytically and computationally. The predicted long-term dynamics of urbanization -- originating in the asymmetric natures of employed and unemployed agents -- are compared with global empirical data, particularly in the realms of labor statistics and urban indicators.