Prey-Predator model with treatment in Tilapia and Mudfish as predator and disease carrier

Abstract

The relationship between tilapia and mudfish forms a highly dynamic ecosystem where both predation and disease transmission occur simultaneously. In this system, mudfish not only prey on tilapia but also act as vectors of streptococcosis disease, which spreads to tilapia in shared water conditions. This study develops and analyses a coupled predator-prey disease model tailored to the tilapia-mudfish aquatic environment. The model identifies five key equilibrium points: trivial, axial, predator-free, disease-free, and endemic, which explain how the ecological system behaves under various ecological scenarios. The basic reproduction number was computed to characterize conditions that trigger disease persistence or elimination. To improve the health and population of tilapia, optimal control theory was used to introduce treatment as a time-dependent control intervention. By applying Pontryagin's Maximum Principle, the study determined and simulated an optimal treatment strategy, showing how the control effort varies over time, starting with a strong intervention and gradually reducing as the infection level declines. Comparative simulations with and without control further illustrated the effectiveness of treatment. The findings show that treatment can reduce disease prevalence, strengthen the tilapia population, and prevent ecological collapse between the predator and prey. This study focuses on developing a viable treatment framework to enhance the sustainability of aquaculture production, specifically by prioritizing treatment within an integrated aquaculture environment.