Mathematical Modeling of Air Pollution Dispersion: A Comprehensive Review

Abstract

Air pollution is a pressing global concern affecting human health, ecosystems, and climate dynamics. Mathematical modeling serves as a critical tool for predicting pollutant behavior and designing mitigation strategies. This paper reviews major air pollution modeling techniques, including Gaussian and advection-diffusion models, Lagrangian particle tracking, Eulerian grid systems, and hybrid approaches, alongside emerging machine learning-based prediction models. Mathematical formulations such as the advection-diffusion equation, stochastic processes, and probabilistic frameworks are discussed in detail. Applications in complex terrains, street canyon environments, and health risk modeling are explored. The review concludes with future directions focusing on real-time hybrid modeling and integration with machine learning for sustainable environmental management.

Keywords: Air pollution modeling, advection-diffusion equation, Lagrangian particle model, Gaussian plume model, stochastic modeling, machine learning, environmental health risk.