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ON MODELLING WATER QUALITY WITH STOCHASTIC DIFFERENTIAL EQUATIONS

Part of: Equations and systems with randomness Stochastic analysis

Published online by Cambridge University Press:  09 January 2024

MAHMOUD B. A. MANSOUR Open the ORCID record for MAHMOUD B. A. MANSOUR [Opens in a new window]
MAHMOUD B. A. MANSOUR*
Affiliation:
Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt
*
e-mail: m.mansour4@hotmail.com
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Abstract

Based on biochemical kinetics, a stochastic model to characterize wastewater treatment plants and dynamics of river water quality under the influence of random fluctuations is proposed in this paper. This model describes the interaction between dissolved oxygen (DO) and biochemical oxygen demand (BOD), and is in the form of stochastic differential equations driven by multiplicative Gaussian noises. The stochastic persistence problem for the model of the system is analysed. Further, a numerical simulation of the stationary probability distributions of BOD and OD by approximations of the stochastic process solution is presented. These results have implications for the prediction and control of pollutants.

Keywords

stochastic differential equationswater quality dynamicspersistence

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 34F05: Equations and systems with randomness 92D25: Population dynamics (general)
Type
Research Article
Information
The ANZIAM Journal , Volume 65 , Issue 3 , July 2023 , pp. 273 - 284
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Australian Mathematical Society

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