Effect of harvesting and infection on predator in a prey-predator system

In this article, we propose and analyze a mathematical model of a prey-predator system where infection spreads among the predators and predator is subject to harvesting. Dynamical behavior of the system is studied, and the consequences of harvesting on the long-run equilibrium fish biomass are evaluated. Optimal control theory has been used to determine the optimal harvesting policy for fish stocks to maximize the discounted utility of harvesting over time, employing a constant time discount rate. Some simulation works are given to verify our analytic results.