Biological Conservation of a Prey-Predator System Incorporating Constant Prey Refuge Through Provision of Alternative Food to Predators: A Theoretical Study

We describe a prey-predator system incorporating constant prey refuge through provision of alternative food to predators. The proposed model deals with a problem of non-selective harvesting of a prey-predator system in which both the prey and the predator species obey logistic law of growth. The long-run sustainability of an exploited system is discussed through provision of alternative food to predators. We have analyzed the variability of the system in presence of constant prey refuge and examined the stabilizing effect on predator-prey system. The steady states of the system are derived and dynamical behavior of the system is extensively analyzed around steady states. The optimal harvesting policy is formulated and solved with the help of Pontryagin's maximal principle. Our objective is to maximize the monetary social benefit through protecting the predator species from extinction, keeping the ecological balance. Results finally illustrated with the help of numerical examples.