Persistence and optimal harvesting of prey-predator model with Holling Type III functional response

The purpose of this work is to study the effect of harvesting on dynamics of prey- predator model with Holling Type III functional response. Mathematical analysis of the model equations with regard to the boundedness of solutions, existence of equilibria and their stabilities in both local and global manner are carried out. A combined harvesting policy for prey and predator species is discussed by using Pontrayagin’s Maximum principle and the effect of tax on prey-predator system is also shown. Butler-Mc Gehee lemma is used to identify the conditions which influence the persistence of the system. Finally, some numerical simulations are given to verify the mathematical conclusions.