Mathematical Modelling of Environmental Pollution Dynamics: From Contaminant Transport to Ecological Risk Prediction

Environmental pollution is complex because contaminant transport, chemical transformation, environmental compartments, biological processes, and human activity interact. Mathematical modelling describes these processes and can predict pollutant fate, forming the basis for quantitative ecological risk assessment. This review considers mathematical methods for characterising the spatial and temporal dynamics of environmental contaminants in soil, water, sediment, and atmosphere. It focuses on differential equation modelling, advection–dispersion equations, reaction–transport modelling, compartmental modelling, stochastic modelling, and numerical simulation techniques. It critically assesses the mathematical representation of contaminant sources, movement, adsorption/desorption, degradation, bioaccumulation, and transformation. The discussion focuses on using models to generate pollutant concentration gradients and exposure pathways for ecological risk estimation and environmental management. The review also considers uncertainty and sensitivity analyses as key tools for assessing model reliability and identifying the parameters that most influence environmental outcomes. It also examines optimisation approaches for remediation planning, including source control, contaminant removal, biodegradation, and treatment allocation. The review discusses emerging AI and machine learning applications as complementary tools for parameter estimation, surrogate modelling, nonlinear prediction, and real-time environmental monitoring. The review also considers incorporating mechanistic mathematical models alongside data-driven models to improve predictions in complex, uncertain environments. The review emphasises the need for multiscale, interdisciplinary mathematical models that connect contaminant dynamics and ecological responses and inform risk based decision-making. Future research directions include coupled multi-compartment models, uncertainty-aware prediction, hybrid mechanistic–machine-learning models, and optimisation based environmental remediation strategies.