<![CDATA[Water pollution dynamics are shaped by interactions among contaminant states, yet many mathematical models do not explicitly distinguish how phase conversion influences long-term persistence. This study analyzes a five-compartment nonlinear model comprising available water, soluble pollutants, completely insoluble pollutants, semi-insoluble pollutants, and treated water. The objectives were to establish mathematical feasibility, characterize equilibrium states and pollutant-specific persistence thresholds, determine global asymptotic stability using Lyapunov functions, and examine temporal behavior numerically. Positivity and boundedness were analyzed to define an admissible region, thresholds were derived through the Next-Generation Matrix, and fourth-order Runge-Kutta simulations were performed over 0≤t≤100 using the baseline parameter configuration. The model admits a pollutant-free equilibrium and pollutant-persistent equilibria, while the threshold values were R1=40.0947, R2=2.6437, R3=1.9790, giving R0=40.0947. These values indicate that the soluble-pollutant pathway exerts the strongest persistence pressure under the baseline configuration. Lyapunov analysis identifies the stability conditions governing the relevant equilibria, and the numerical trajectories are consistent with persistence of the soluble compartment and decline of the completely insoluble and semi-insoluble compartments. One-at-a-time parameter perturbations further show that pollutant-transfer and recovery parameters alter peak magnitude, persistence duration, and convergence behavior. The study demonstrates that combining phase-resolved compartmental structure, pollutant-specific thresholds, global stability analysis, and numerical simulation provides an interpretable framework for explaining how pollutant heterogeneity and inter-phase conversion shape long-term water-pollution dynamics. This integration clarifies why different pollutant phases can follow distinct asymptotic pathways even when they coexist within the same modeled aquatic system over time.]]>
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