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

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 Ordin...

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Bibliographic Details
Published in:Ecological modelling Vol. 508; p. 111229
Main Author: Hu, Changying
Format: Journal Article
Language:English
Published: Elsevier B.V 01.09.2025
Subjects:
Antidegradation scalars
Government environmental strategies
Ordinary differential equations
Pollutant concentration
River pollution treatment time
River water quality antidegradation
Ordinary differential equations
River pollution treatment time
Antidegradation scalars
Pollutant concentration
River water quality antidegradation
Government environmental strategies
ISSN:0304-3800
Online Access:Get full text
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Summary: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. [Display omitted] •Two ODE models enhance sustainable river quality management globally.•The Recovery Time Model calculates the time required to restore river quality.•The Antidegradation Model determines pollution thresholds after recovery.•A Python program assists in calculating recovery times and pollution thresholds.
ISSN:0304-3800
DOI:10.1016/j.ecolmodel.2025.111229