Journal of Advances in Mathematics and Computer Science

Aquaculture plays an increasingly important role in food security, nutrition, and income generation in Kenya. However, sustainable fish production remains constrained by poor harvesting strategies and fluctuating environmental conditions. This study develops a modified logistic growth model for tilapia harvesting at Aquasamaki Farm, Mogotio, Kenya, by incorporating a dynamic environmental quality factor into the classical logistic framework. The environmental quality factor is modelled as a function of pH, alkalinity, and ammonia oxygen balance, thereby allowing the intrinsic growth rate of the fish population to vary with water quality conditions. The resulting model is further extended to include harvesting, and equilibrium analysis is undertaken to determine sustainable population levels under different environmental regimes. Numerical results show that under optimal water quality conditions, the fish population stabilizes near its carrying capacity, supporting sustainable harvesting. Under moderate environmental stress, the equilibrium population declines substantially, indicating reduced resilience and increased vulnerability to overharvesting. Under severe stress, no biologically feasible equilibrium exists, implying that population collapses will occur if harvesting is maintained. Graphical simulations further demonstrate that worsening water quality shifts the equilibrium population downward and may eliminate it. The study concludes that sustainable tilapia harvesting depends jointly on harvesting pressure and environmental quality. It therefore recommends adaptive harvesting policies, supported by real-time water quality monitoring, to improve sustainability and productivity in aquaculture systems.