Optimal control strategy for a discrete-time mathematical modeling of water pollution

Abstract

Water pollution is a major issue with serious consequences for human health and the environment, particularly in developing countries. It highlights that contaminated water is a source of waterborne diseases, such as cholera, and underscores the importance of integrating temperature variations into pollution management strategies. A discrete mathematical model is proposed, segmenting the problem into three compartments: at-risk water, polluted water, and the total sum of pollutants, accompanied by difference equations that represent their interactions. The challenge of optimal control aims to reduce pollutant concentrations through three approaches: awareness, purification, and source reduction. Numerical simulations conducted with MATLAB show that these interventions can significantly reduce water pollution. In conclusion, the article emphasizes that the application of mathematical modeling and optimal control strategies is crucial for mitigating the effects of pollution and proposing sustainable solutions for water management.