A mathematical guidance on river water pollution management strategies using ordinary differential equations

Abstract

Governments worldwide face increasing pressure to develop effective river pollution control strategies that meet environmental regulations, support sustainable socio-economic development, and protect public health. This study advances governmental strategy-making by developing two models using Ordinary Differential Equations. The Recovery Time Model estimates how long it takes for a polluted river to reach safe conditions under given inflow limits, helping governments set realistic treatment goals. The Antidegradation Model computes maximum allowable inflow concentrations (Antidegradation Scalars, $ADS$) aligned with different regulatory objectives—improvement, maintenance, or controlled degradation—thereby guiding decisions that balance environmental and socio-economic priorities. To support practical implementation, we develop a user-friendly Python program that enables government officials to obtain the recovery time and the antidegradation scalars easily, thus promoting effective river water quality management strategies. While the models have not yet been deployed in real-world regulatory systems, the Hun River case study illustrates their potential to guide timely and balanced policy decisions. Future work involving collaboration with local governments could validate their long-term impacts on both environmental quality and economic planning.