A System of Stochastic Differential Equations for Handling Uncertainties in Water Demand

Abstract

Managing uncertainties in water demand is a challenging task in modern water resource management, especially when factors like unpredictable rainfall patterns and sudden shifts in population growth influence consumption trends. Stochastic Differential Equations (SDEs) provide a powerful mathematical framework for modeling and analyzing the inherent uncertainties in water demand. In this study, SDEs are applied to examine water demand in Johor over the period 2005 to 2020, enabling the modeling and forecasting of demand within the context of these uncertainties. The water balance model, which tracks the inflow, outflow, and storage of water, is introduced to provide a more dynamic and realistic representation of water resource fluctuations. The study employs the Euler-Maruyama method for numerical solutions, offering a flexible and accurate approach for simulating the dynamic behavior of water demand. The findings highlight the importance of incorporating random variations and uncertainties into water demand forecasting, offering valuable insights for decision-makers in the water industry. This research combines stochastic models with water balance models to improve how we predict and manage water resources, helping to ensure a steady water supply and reduce long-term risks from water shortages.