A MATHEMATICAL MODELLING STUDY FOR DESALINATION OF SEA-WATER USING MARSH PLANTS
By
Deepika Marwar1, Alok Malviya2, Maninder Singh Arora3
1,2Department of Mathematics, VSSD(PG) College, CSJM University, Kanpur, Uttar Pradesh, India-208002
3Department of Mathematics, PPN (PG) College, CSJM University, Kanpur, Uttar Pradesh, India-208001
Email: deepika91marwar@gmail.com, alok92nov@gmail.com, manindersingharora kn04@csjmu.ac.in
(Received: August 02, 2025, In format: September 01, 2025; Revised: October 02, 2025; Accepted: October 04, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55209
Abstract
Water scarcity poses a significant challenge, particularly in regions affected by drought or inherently dry conditions, leading to a stark imbalance between the availability and demand for fresh water. This situation underscores the necessity for water conservation, purification for reuse, and desalination. Among the various strategies employed for desalination, utilizing marsh plants is one of the most cost-effective approaches. This paper focuses on enhancing the availability of potable water through economical methods, specifically the use of marsh plants within water reservoirs. We introduce a nonlinear mathematical model to examine the process of desalinating saline water in a reservoir environment, considering the interplay between soil properties and marsh plants growth, which is influenced by the salinity levels in both water and soil. Our study involves four nonlinearly interacting variables: salt concentration in the water, biomass density of marsh plants, soil concentration, and salt concentration in the soil. We have established the existence of an equilibrium point through isocline analysis. The analytical exploration of the model includes determining the local and global stability of the equilibria. The validity of our findings is further corroborated through numerical simulations for graphical representations and sensitivity analysis of the system with respect to key parameters.
2020 Mathematical Sciences Classification: 34D20, 34D23, 34A34.
Keywords and Phrases: Desalination, Marsh plants, Soil salinization, Sensitivity